Sediment Transport in Alluvial Channels, 1966—1972 GEOLOGICAL SURVEY PROFESSIONAL PAPER 562 This volume was published as separate chapters A—K UNITED STATES DEPARTMENT OF THE INTERIOR ROGERS C. B. MORTON, Secretary GEOLOGICAL SURVEY V. E. McKelvey, Director (A) (B) (C) (D) (E) (F) (G) (H) (I) (J) (K) CONTENTS [Letters designate the separately published chapters] Sediment transport in Cache Creek drainage basin in the Coast Ranges west of Sacramento, California, by Lawrence K. Lustig and Robert D. Busch. Flume experiments on the transport of a coarse sand, by Garnett P. Williams. The behavior of large particles falling in quiescent liquids, by G. E. Stringham, D. B. Simons, and H. P. Guy. Response of a laboratory alluvial channel to changes of hydraulic and sediment- transport variables, by R. E. Rathbun, H. P. Guy, and E. V. Richardson. Fluorescent sand as a tracer of fluvial sediment, by Vance C. Kennedy and Dorothy L. Kouba. Statistical properties of dune profiles, by Carl F. Nordin, Jr. Field measurement of the initiation of large bed particle motion in Blue Creek near Klamath, California, by E. J. Helley. Flume width and water depth effects in sediment-transport experiments, by Garnett P. Williams. Transport and dispersion of fluorescent tracer particles for the flat-bed condition, Rio Grande conveyance channel near Bernardo, N. Mex., by R. E. Rathbun, V. C. Kennedy, and J. K. Culbertson. Summary of alluvial-channel data from Rio Grande conveyance channel, New Mexico, 1965—69, by J. K. Culbertson, C. H. Scott, and and J. P. Bennett. An experimental study of heavy mineral segregation under alluvial-flow condi- ditions, by Lawrence L. Brady and Harvey E. Jobson. * U~S- GOVERNMENT PRINTING OFFICE: 1973—5l5—658/l4 95-7: we y, 5 (o a '14 Sediment Transport in V Cache Creek Drainage Basin in the Coast Ranges West of Sacramento, California GEOLOGICAL SURVEY PROFESSIONAL PAPER 562—A Preparea’ in cooperation wz'ta tfie State of Ca/zform'a Department of Wter Resources Sediment Transport in Cache Creek Drainage Basin in the Coast Ranges West of Sacramento, California By LAWRENCE K. LUSTIG and ROBERT D. BUSCH SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS GEOLOGICAL SURVEY PROFESSIONAL PAPER 562—A Preparea’ in cooperation wit/z tne State of California Department of Miter Resources UNITED STATES GOVERNMENT PRINTING OFFICE WASHINGTON : 1967 UNITED STATES DEPARTMENT OF THE INTERIOR STEWART L. UDALL Secretary GEOLOGICAL SURVEY A V ‘ William T. Pecora, Director For sale by the Superintendent of Documents, US. Government Printing Oflice Washington, DC. 20402 CONTENTS Page Page Abstract_______-_____---__-_________--______,_ ______ A1 Sediment dischargeofstreams ________________________ A14 Introduction _______________________________________ 1 Problems of sampling and computation ____________ 14 Location and extent of the area _______________________ 2 Suspended-sediment discharge ____________________ 19 Environmental conditions affecting sediment transport- _ 2 Total sediment discharge ________________________ 28 Upper part of the basin _________________________ 2 Bed material ___________________________________ 32 Middle part of the basin _________________________ 5 Deposition of sediment in the settling basin ____________ 32 Lower part of the basin __________________________ 7 Conclusions ________________________________________ 35 Geology ___________________________________________ 8 References _________________________________________ 36 Precipitation and runoff _____________________________ 10 Efl’ect of the runofi deficiency upon sediment dis- charge _______________________________________ 11 ILLUSTRATIONS Page ) PLATE 1. Map of the Cache Creek drainage basin showing the general geology and the locations of sediment stations- _ In pocket FIGURE 1—12. Photographs showing— 1. Tributary stream of North Fork Cache Creek ________________________________________________ A3 2. Badland-typc topography in the drainage area of North Fork Cache Creek _______________________ 4 3. Cache Creek channel from the dam below the Clear Lake outlet _________________________________ 5 4. Channel and valley of Bear Creek, viewed downstream _________________________________________ 6 5. Junction of Cache Creek and Bear Creek _____________________________________________________ 7 6. Cache Creek channel above Rumsey, viewed upstream _________________________________________ 8 7. Cache Creek valley between Rumsey and Capay ______________________________________________ 9 8. Cache Creek valley near the sediment station at Capay ________________________________________ 10 9. Surficial slump and creep on'hillslopes near Capay ____________________________________________ 11 10. Head of a gully in Upper Cretaceous sedimentary rocks near Capay _____________________________ 12 11. Cache Creek channel below Capay, showing the extensive area of deposition in the reach below the point of stream diversion _______________________________________________________________ 13 12. Cache Creek channel near the Yolo sediment station ___________________________________________ 14 13—17. Graphs showing flow-duration curves: 13. North Fork Cache Creek ___________________________________________________________________ 15 14. Cache Creek near Capay ___________________________________________________________________ 16 15. Cache Creek at Yolo ______________________________________________________________________ 17 16. Cache Creek above Rumsey, 1960—63 _______________________________________________________ 18 17. Bear Creek, 1960—63 _______________________________________________________________________ 19 18. Graph showing size-distribution curves of suspended sediment in streams of the Cache Creek drainage basin and from the settling basin at the weir __________________________________________________________ 20 19. Graph showing sediment—transport curves of streams in the Cache Creek drainage basin, 1960-63 ........... 22 20—24. Graphs showing sediment-duration curves: 20. North Fork Cache Creek, 1960—63 __________________________________________________________ 23 21. Bear Creek, 1960-63 _______________________________________________________________________ 24 22. Cache Creek above Rumsey, 1960—63 ________________________________________________________ 25 23. Cache Creek near Capay, 1960—63 ___________________________________________________________ 26 24. Cache Creek at Yolo, 1960—63 ______________________________________________________________ 27 25—28. Graphs showing relation of— 25. Total sediment discharge and instantaneous water discharge ____________________________________ 29 26. Bedload discharge, as a percentage of total sediment discharge, and instantaneous water discharge- _ _ 29 27. Bedload discharge and mean velocity of flow at the time of the water-discharge measurement ______ 30 28- Bedload discharge and instantaneous water discharge __________________________________________________ 30 29. Scatter diagram showing the differing values of bedload discharge that are obtained by the method of sub- division _____________________________________________________________________________________ 31 III ( 3‘33 IV CONTENTS Page FIGURE 30. Graph showing the relation of various fractions of sediment discharge and water discharge for Cache Creek at the Yolo sediment station _______________________________________________________________________ A33 31. Graph showing size-distribution curves of bed-material samples from Cache Creek at the Yolo sediment station__ - 34 TABLES TABLE 1. Mean annual water discharge at three stations in the Cache Creek drainage basin for the period of record and for Page the 1960—63 period _______________________________________________________________________________ A11 2. Annual suspended-sediment yield at sediment stations in the Cache Creek drainage basin ______________________ 28 3. Total sediment-discharge data from Cache Creek at the Yolo sediment station _______________________________ 29 4,5. Annual sediment-discharge data from Cache Creek at the Yolo sediment station _____________________________ 30 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS SEDIMENT TRANSPORT IN CACHE CREEK DRAINAGE BASIN IN THE COAST RANGES WEST OF SACRAMENTO, CALIFORNIA By LAWRENCE K. LUSTIG and ROBERT D. BUSCH ABSTRACT This report treats the sediment-transport characteristics of streams in the Cache Creek drainage basin during the 1960—63 period and the relations of these characteristics to environ- mental factors. The general geology of the area is shown on a map compiled from several sources. The rocks that crop out in the basin range in age from Late Jurassic to Recent. Pliocene and Pleistocene continental deposits are apparently a major source of sediment in the basin ; erosion of these deposits has resulted in badland topography, indicative of their silt-clay content. The upper part of the basin, to the north, receives as much as 50 inches of precipitation each year, but this annual rainfall decreases to the south, and the middle part of the basin receives less than half this amount. The occurrence of badland topog- raphy and gullying, combined with the decrease in annual precipitation, is probably the cause of a marked increase in sediment yield in the middle part of the basin. 7 Because precipitation and runoff were deficient during the 1960—63 period, relative to the long-term period of record, a qualitative analysis of flow-duration data is presented. Al- though estimates Of sediment discharge based upon 1960-63 observations must be low relative to the long-term sediment dis- charge, the deviation is probably not great. Sediment-transport curves for each of five sediment stations are shown as least-squares regression lines of best fit. The ex- ponents of water discharge, which are a measure of the rate of increase of suspended-sediment discharge with an increase in water discharge, Show that the streams in the upper, middle, and lower parts of the basin have distinctive sediment-transport characteristics. Sediment discharge increases downstream, but the rate of increase is much greater in the middle part of the basin than in the upper part. The rate decreases between Capay and Y010 because artificial controls at Capay induce sediment deposition through surface—water diversion. The total suspended-sediment discharge for the 1960—63 period was 476,700 tons from North Fork Cache Creek, 174,800 tons from Bear Creek, 2,261,000 tons from Cache Creek above Rumsey, 3,320,000 tons from Cache Creek near Capay, and 2,132,000 tons from Cache Creek at Yolo. Total sediment discharge is computed ( 1) by substitution of daily mean water-discharge values in a regression equation that relates instantaneous water discharge and bedload discharge, and addition of the bedload discharge thus obtained to the suspended-sediment discharge, and (2) by adjustment of in- stantaneous sediment-discharge values to daily mean values through the method of subdivision of days. Bedload discharge comprises approximately 7 percent of the total sediment dis- charge by these methods. Total sediment discharge at the Yolo sediment station for the 1960—63 period was approximately 2,300,000 tons. The trap efliciency of the settling basin is estimated from data on suspended-sediment concentration at the weir of the basin and water-discharge values at Yolo-. The results indicate that the trap efficiency is at least 50 percent and may be as great as 60 percent. Various difficulties inherent in procedures for sampling of suspended sediment and the computation of both suspended and total sediment discharge lead to possibility of error but do not invalidate the results of the investigation. INTRODUCTION The development of a comprehensive water plan for a given basin is often a complex problem; the solution must often satisfy the varied water needs of difi'erent parts of the basin. This Observation clearly applies to the Cache Creek drainage basin. The upper part of the basin contains Clear Lake, the largest natural lake located wholly within the boundaries Of the State of California, and an ideal lake in many respects for recreational purposes. The primary water need in this area is stabilization of the lake level, which is dependent on both the rainfall-runoff input and the water dis- charge at the outlet of the lake. Other water needs must be served, however. The out- let of Clear Lake is Cache Creek, which flows from the lake through the lower, part Of the basin. Because this area is primarily agricultural, a major water need in the lower part of the basin is to minimize both the frequency and magnitude of flood stages on Cache Creek and thus prevent the inundation of cultivated fields and orchards. The California State Department Of Water Resources is considering several alternate plans of control and improvement within the drainage basin in an attempt to meet these and other water needs. A1 A2 The efficient evaluation of these plans, which may in— clude the construction of dams, reservoirs, and settling basins, requires information on sediment transport in the Cache Creek drainage basin. Accordingly, the investigation reported here was un- dertaken to determine the quantity and distribution of the sediment transported by streams of the Cache Creek drainage net. Although a few observations were made in previous years, the data in this report pertain to the 1960-63 period. During this period, suspended-sedi— ment samples were collected at five sediment stations within the drainage basin. Additional samples were obtained at the outlet of an existing settling basin in the lowermost part of the drainage basin, and seven total sediment-discharge measurements were made on Cache Creek at the Yolo sediment station. These data are used to estimate the suspended-sedi- ment discharge at each of the five sediment stations, and the total sediment discharge at the Yolo station. A geologic map of the basin has been compiled from sev- eral sources to indicate the probable sources of sediment. The effect of the net sediment transport on the settling basin below the Yolo station is also considered. The operation of sediment stations in the drainage basin and the analysis and computation of data were performed by personnel in the Sacramento District Office of the Quality of Water Branch, in cooperation with the California State Department of Water Re- sources, and under the direct supervision of George Porterfield. The authors gratefully acknowledge the valuable counsel provided by Mr. Porterfield on many aspects of data interpretation and report preparation. Constructive criticism on these matters was also pro- vided by Charles H. Hembree, Thomas Maddock, J r., Paul C. Benedict, and James M. Knott. LOCATION AND EXTENT OF THE AREA The Cache Creek drainage basin (pl. 1) extends from the highlands north and northeast of Clear Lake to the Yolo Bypass, adjacent to Sacramento, Calif. It lies within Lake, Y010, and Colusa Counties in the Coast Ranges of northern California. The northwest trend of the basin conforms to the regional trend of the Coast Ranges and 'to the coastline of California in these latitudes. The marked elongation of this basin is unusual for so large a drainage basin. The overall length is approxi- mately 100 miles, whereas the width ranges from 6 miles near Rumsey to more than 30 miles in the upper (north- ern) .part of the basin. This configuration is deter- mined by both structure and topography. The total drainage area of the basin is difficult to ascertain. An extensive network of sloughs, canals, SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS and levees, some of which are shown on plate 1, occur below Capay, in the lower part of the basin. Because these channels both enter and leave the general area, the drainage divide cannot be located with certainty. That part of the basin boundary that lies between a point to the north of Capay and Knights Landing is particularly uncertain, and any computation of total drainage area is therefore dependent on the judgment of the researcher. The area shown on plate 1 reflects the considered opinion of the authors and is approxi- mately 1,300 square miles. ENVIRONMENTAL CONDITIONS AFFECTING SEDIMENT TRANSPORT The sediment-transport characteristics of streams in the Cache Creek drainage basin are strongly affected by environmental conditions. In fact, a later section of this report will show that the sediment—transport char— acteristics of the streams are, in part, directly depend- ent on their location within the basin. For the present, only the broader features of the upper, middle, and lower parts of the basin will be discussed. Cli— matic conditions will be indicated only in general terms, because precipitation and runoff will be discussed sep- arately in a later section. UPPER PART OF THE BASIN The upper part of the basin, as here defined, is the area above the junction of Cache Creek and Bear Creek (pl. 1). Clear Lake and its tributaries are omitted from this discussion because the sediment transported to the lake is virtually trapped, and the area therefore contributes little to the sediment discharge from the basin. North Fork Cache Creek drains a large region in which rocks of the Franciscan Formation crop out (pl. 1). This region includes the highlands, where the Coast Ranges attain elevations of about 4,000 feet. Be- cause of heavy orographic precipitation, the rugged hillslopes are covered by dense vegetation. Stream channels contain much coarse debris, and channel gradi- ents are commonly greater than 100 feet per mile. The valleys are generally narrow and deep, but they widen in some places, particularly at pronounced stream me- anders. Within such stream reaches the valley floors are covered with coarse alluvium; the View shown in figure 1 is typical of the terrain. Near the sediment station on North Fork Cache Creek (pl. 1) the stream flows through an alluvial valley bounded by hills that are much lower than those in the headwaters. The Pliocene and Pleistocene continental deposits are drained in this area and probably yield much sediment. The deposits range from alternating CACHE CREEK DRAINAGE BASIN, CALIFORNIA A3 FIGURE 1.—~View of a tributary stream of North Fork Cache Creek, showing stands of pine on the steep slopes and the general density of vegetation, which includes much manzanita. The wide flat area on the valley floor is a point bar of coarse gravel; it is on the concave side of a stream meander in this upstream View. layers of silt-clay, sand, and gravel to heterogeneous mixtures of sediment of these size classes. The topog- raphy in this lower reach of North Fork Cache Creek includes many steep blufl's dissected by badland-type gullies. Areas of intense erosion, such as the area shown in figure 2, occur Where the silt-clay content of the deposits is fairly high; the bluff shown in the view contains about 30 percent silt-clay. Cache Creek proper flows from the outlet of Clear Lake (pl. 1) to the junction with North Fork through terrain similar to that in the upper reaches ‘of North Fork. Both the relief and the channel gradient of Cache Creek are somewhat less, however, than they are in North Fork. A View downstream from the dam located a short distance below the Clear Lake outlet is shown in figure 3. Coarse debris abounds in the stream channel and, as a consequence, flow tends to be turbulent. Because vegetation occurs along the banks of the stream channels in the upper reaches of both Cache Creek and North Fork, save near pronounced meander bends, high stages of flow will not necessarily transport proportion— ally great quantities of sediment. Above the junction of the two streams, however, Cache Creek flows through the Plio-Pleistocene deposits and their associated bad- land-type topography. The availability of sediment by erosion and entrainment during large runoff events in- creases markedly in this region. In its upper reach, Bear Creek (pl. 1) flows through an alluvial valley bounded by low hills on the east and by the rugged highlands on the west. The valley is approximately 10 miles long and 1 mile wide, and the gradient is gentle. Apparently, the sediment trans- port characteristics of Bear Creek are strongly influ— enced by this valley. The Bear Creek channel contains coarse bed material, but its width-depth ratio is large (fig. 4); because the gradient is gentle, much of the A4 coarse bed material must be reduced in size before it can be transported under the present flow regime. It is sig- nificant that the Bear Creek drainage system transports about 1,800 tons of suspended sediment per square mile, whereas North Fork Cache Creek transports more than 2,400 tons per square mile. The difference may be due to the highly erodible terrain in the drainage area of North Fork Cache Creek. Certainly, however, the ul- tramafic rocks and associated serpentine-zones in the Bear Creek drainage area (pl. 1) would yield equally large quantities of sediment if the environmental con- ditions were more favorable to transportation of material. Below the alluvial valley, Bear Creek flows through steep canyons for approximately 12 miles. The stream and its tributaries primarily drain Lower Cretaceous marine rocks in this lower reach, and environmental conditions are similar to those of Cache Creek and Bear Creek above the confluence of the two streams. A View SEDIMIENT TRANSPORT IN ALLUVIAL CHANNELS of the junction of these streams (fig. 5) shows that steep- ly dipping sedimentary units crop out along the Ivalley walls and channel banks, forming bluffs that are rela- tively barren of vegetation. These easily erodible sedi- mentary formations provide large amounts of sediment for transport at high as well as low stages of flow. Summary—The environmental conditions in the up- per part of the basin change progressively downstream. Decrease in precipitation, owing to orographic con- trol, is accompanied by a general decrease in the abun- dance of vegetation, particularly bordering the stream channels. These conditions, together with the high erodibility of the Pliocene and Pleistocene continental deposits and the Lower Cretaceous marine formations, tend to increase both sediment availability and sediment discharge downstream. They supplement the normal increase in sediment discharge downstream due to the increase in drainage area and water discharge. FIGURE 2,—View of badland-type topography in the drainage area of North Fork Cache Creek. This topography is associated with outcrops of Pliocene and Pleistocene continental deposits, particularly in areas where the silt-clay content of the sediments is high. The badlands shown in this view contain approximately 30 percent silt—clay. CACHE CREEK DRAINAGE BASIN, CALIFORNIA A5 FIGURE 3.—View of the Cache Creek channel from the dam below the Clear Lake outlet, showing coarse debris in the channel and the growth of vegetation along the channel banks. MIDDLE PART OI" THE BASIN Below the junction of Cache Creek and Bear Creek (fig. 5) a sequence of Upper Cretaceous marine forma- tions crops out, capped in some places by younger gravels. The sedimentary rocks are predominantly sandstone,- and they dip moderately to steeply. In sev— eral places Cache Creek flows across ledges of these clas- tic units; the channel appears to rest virtually upon bedrock. This condition prevails between the junction of Cache Creek and Bear Creek and the head of the alluvial valley near Rumsey (pl. 1). The View in figure 6 shows Cache Creek along one such reach above Rum- sey. The massive sandstone unit shown at the right in 232-457 0—67H—2 the photograph contributes large blocks of debris di- rectly to the channel, thus promoting turbulent flow in the stream. This condition is similar to that prevailing in much of the upper part of the basin, as previously described, but the valley here is much wider than, for example, the valley of Cache Creek below the Clear Lake outlet (fig. 3). Precipitation is lower here than in the northern high- lands, and there is a corresponding decrease in the num- ber and size of conifers. Thus, the hillslope area eX- posed to erosion is greater, and there is higher sediment yield from these slopes and from bank cutting by the stream (fig. 6). A6 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS FIGURE f1.—View downstream of the channel and valley of Bear Creek. Cattle in the channel, in the left middle distance, indicate the scale. In a later part of this report it will be shown that the sediment yield from the region between Rumsey and the Capay sediment station (pl. 1) , here defined as the mid- dle part of the basin, is much greater than would be predicted on the basis of drainage area alone. Here approximately 100 square miles of land contributes more sediment than does an area twice as large in the upper part of the basin. Because the number of tributary streams, total stream length, and water discharge are all determined by the extent of the drainage area, a dis- proportionate sediment yield indicates that the middle part of the basin must differ environmentally from the other parts. The view across the Cache Creek valley shown in fig- ure 7 illustrates certain significant environmental condi- tions. First, wide areas of Pliocene and Pleistocene de- posits again crop out along the valley walls; vegetation is scanty and numerous badland zones occur where the silt-clay content of the rocks is high. Second, the orchards visible in the distance are representative of more extensive cultivation in this part, tending to in— crease erosion of the valley floor. Additional factors not shown in the figure are the several tributary chan- nels that drain Upper Cretaceous and Tertiary sedimen- tary rocks on the west side of the valley (pl. 1), and the precipitation distribution in the region. The sediment contribution from the tributary streams and waterways is difficult to assess. The channels are indistinct where they cross cultivated fields, but several of the larger channels undoubtedly carry runoff during widespread storms in the narrow belt of hills in which the tributary streams head. The primary cause of the disproportionate sediment yield, however, is thought to be the decrease in quantity and frequency of precipi- ‘ tation. Although mean annual precipitation is ap— proximately twice as great in the upper part of the basin, empirical rules (Langbein and Schumm, 1958) 1 indicate that sediment yield increases as the precipita- tion decreases to about 12 inches per year. CACHE CREEK DRAINAGE A7 BASIN, CALIFORNIA FIGURE 5.—View of the junction of Cache Creek and Bear Creek. The View is across Bear Creek and up Cache Creek; the junction of the two streams is at lower left. Steeply dipping sedimentary units in the left foreground and right middle distance are relatively bare of vegetation, providing a ready source of sediment in this area. Summary—The middle part of the basin has lower relief, less precipitation and vegetation, more gentle gradients (about 10—15 ft per mile), and greater sedi- ment yield than the upper part of the basm. The in— crease in sediment yield is due to a combination of environmental conditions rather than solely to an in- crease in drainage area and stream discharge. These conditions include badland topography, land cultiva- tion, and a decrease in mean annual precipitation. LOWER PART OF THE BASIN The lower part of the basin is here defined as the area below the sediment station near Capay (pl. 1). The station is on a reach of Cache Creek that flows through Upper Cretaceous marine rocks; the land is largely grass covered and is similar in appearance to much of the Coast Ranges at lower elevations (fig. 8). Trees are relatively few, but they tend to grow in groves; the local hydrologic environment favors such growth conditions. Sediment load from this terrain reaches the streams in two Ways. First, sheetflow over the grasslands trans— ports moderate quantities of sediment to the streams. Second, and more important, surficial slump and soil creep gradually create gullies; runoff concentrates in the gullies, erosion is accelerated, and sediment yield increases. Two conspicuous areas of surficial slump in the lower part of the basin are shown in figure 9. The steplike topography results from soil saturation and subsequent downslope movement along planes that are concave upward. The gradual growth of such features produces a gully. Certain gullies, such as the one in figure 10, have grown headward to the crests of the hills. In this instance, tree roots have been exposed to a depth of nearly 5 feet. A8 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS FIGURE 6.——View upstream of the Cache Creek channel above Rumsey. Valley width tends to increase in this upper reach of the middle part of the basin. The streanr flows across bedrock here. The coarse material in the channel is derived from the massive sandstone formation shown at the right. at higher stages of flow than that shown in this view. At Capay, below the sediment station (pl. 1), a series of small dams and other artificial controls diverts the surface flow from Cache Creek, and sediment deposi4 tion occurs over a wide area on the flat alluvial plain (fig. 11) . The natural channel regains good definition a few miles downstream, however, and continues beyond the Yolo sediment station (fig. 12) to the settling basin and the Yolo Bypass (pl. 1). The area 'below Capay is a large alluvial fan with a high gravel content, over which Cache Creek meandered before the settling basin and other controls were established. The channel shown leading to Knights Landing (pl. 1) was a former path of flow. Summary—The lower part of the basin consists’of an upper reach in which Upper Cretaceous sedimentary rocks crop out and the processes of surficial slump and There is some suggestion of bank cutting by the stream creep occur, and a lower reach that is a flat plain with scattered low gravel hills. Both elevations and pre- cipitation values are lower than elsewhere in the basin, and deposition rather than erosion of sediment is the dominant process. Much gravel and sand is trans- ported to the lowermost boundary of the basin, however. GEOLOGY The Cache Creek drainage basin (pl. 1) lies within the Coast Ranges of northern California. The ranges are structurally controlled, and the regional trend, in- cluding both topographic expression and the strikes of all major faults and folds, is approximately N. 30° W. The general geology of the area was well summarized by Lachenbruch (1962), and much of the discussion here is derived from his work. CACHE CREEK DRAINAGE BASIN, CALIFORNIA A9 FIGURE 7.—-View across the Cache Creek valley between Rumsey and Capay. Pliocene and Pleistocene continental deposits crop out on. the far side of the valley in this area. Badland topography, akin to that shown in figure 2, is ubiquitous, and the sediment derived from it is transported directly into Cache Creek. The stream parallels the range of hills but is obscured in this view by the orchards in the middle distance. Cultivation of land is extensive in this part of the basin, as suggested by the tilled soil in the foreground. The Franciscan Formation forms the core of much of the Coast Ranges, but in the Cache Creek basin these rocks crop out only in the upper part of the basin. The group consists of a heterogeneous assemblage of clastic marine sedimentary rocks, mafic volcanic rocks, and mafic and ultramafic intrusive rocks that exhibit vary- ing degrees of metamorphism. Chert and limestone occur in lesser abundance. The lithologic and structural complexities of the Franciscan Formation and the scar- city of fossils have prevented precise correlation of units of the group with one another and with other Mesozoic rocks in the area; however, the rocks are thought to range in age from Late Jurassic to Late Cretaceous. Aside from the partly serpentinized ultramafic rocks (pl. 1), which are both regionally and locally fractured and sheared, the Mesozoic rocks in the Cache Creek basin are shales, sandstones, and conglomerates. Many of the sandstones contain a micaceous matrix and are therefore graywacke. These rocks have noticeable current and slump features, particularly in the Upper Cretaceous marine sequence that crops out between Bear Creek and the general area of Guinda (pl. 1). The eugeosynclinal deposits described above are over- lain by early Tertiary and Quaternary deposits to the east of Clear Lake and in the middle part of the basin (pl. 1). Outcrops of Paleocene and Eocene rocks con- sist predominantly of massive sandstones which show better sorting than the older rocks, and interbedded conglomerates and silty shales. The Pliocene and Pleistocene continental deposits, as previously de- scribed, consist of silt-clay, sand, and gravel and occur both as discrete units and as heterogeneous mixtures. The younger overlying alluvium is similar to these con- tinental deposits but is generally not as coarse. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS FIGURE 8.~—View of the Cache Creek valley near the sediment station at Capay. The general aspect of the landscape in this area is typical of the appearance of the Coast Ranges at lower elevations. outcrops, as shown in the foreground. PRECIPITATION AND RUNOFF The movement of storms from the Pacific Ocean to the east and south produces precipitation, primarily rain, in the Cache Creek drainage basin. Approxi- mately 85 percent of the precipitation occurs from No. vember to March. Precipitation records in the area, several of which date from 1900 or earlier, reveal that although con- siderable fluctuation in precipitation may occur at a given station, the mean annual precipitation reflects orographic control. Near Knights Landing (pl. 1), in the lowest part of the basin, the mean annual rainfall ranges from 16 to, 18 inches. Near Capay and Rumsey, where elevations range from about 250 to more than 400 feet, the mean annual rainfall is between 21 and 24 inches. In the vicinity of Clear Lake, where elevations are about 1,500 feet, the mean annual precipitation is 37 inches; in the northern highlands, where elevations Grasslands are broken by scattered bedrock are about 3,000—4,000 feet, precipitation totals 50 inches or more per year. The fluctuations in mean annual precipitation, that can occur in the basin are illustrated by the maximum rainfalls of record, which range from 32 inches per year in the lower part of the basin to more than 100 inches in the northern highlands. These maximum values are approximately double the long-term mean precipitation at a given station. It is therefore not surprising that fluctuations in mean annual runofl.’ have also occurred in the basin. Table 1 lists the mean annual water .discharge at three stations within the basin for the period of record and for the 1960—63 period covered by this report. These data show that the mean annual runoff during the 1960— 63 period was less than the long-term mean runoff at each of these stations and was probably deficient else- where in the basin as well. The lesser surface runoff CACHE CREEK DRAINAGE BASIN, CALIFORNIA corresponds partly to a diminution in precipitation and partly to an increase in surface water diversion and ground water use for agricultural purposes; such use must necessarily increase when precipitation decreases, because consumptive requirements do not 'ary greatly. Fluctuations in water discharge, in themselves, are not the primary concern of this report. Sediment dis— charge is related to water discharge, however, and the probable effect of treating a period that is not repre~ sentative of long—term conditions must be considered. TABLE 1.—Mean annual water discharge at three stations in the Cache Creek drainage basin for the period of record and for the 1960-63 period \ i Mean Mean Net change Length annual annual in mean Station of record discharge discharge annual (years) for period for 1960-63 discharge of record (acre-feet) (acre-feet) i (acre-feet) North Fork Cache Creek ............ i 32 133, 900 94,200 —39, 700 Cache Creek at Capayn A. 20 420, 600 326,300 —94, 300 367, 100 206, 630 —160, 470 Cache Creek at Yolo. ,,,,,,,,,,,,, 60 A11 EFFECT OF THE RUNOF’F DEFICIENCY UPON SEDIMENT DISCHARGE The usefulness of an investigation of sediment dis- charge within a given drainage basin is limited, to some extent, by the degree to which extrapolation of the re- sults is justifiable. If, for example, sediment—discharge data are intended to provide criteria for the design of reservoirs, the designer will wish to extrapolate the re- sults of a short—term investigation over a period of per- haps 50—100 years into the future. For such purposes, the period of observation must adequately represent long—term phenomena. If it can be shown, for exam— ple, that a relation exists between water discharge and sediment discharge, and if the water discharge for the period of observation is not significantly disproportion- ate to previous long—term water discharge values, then it can reasonably be argued that the sediment discharge during the period of observation approximates the long- term sediment discharge. Extrapolation of results FIGURE 9.—View of surficial slump and creep on hillslopes near Capay. Two zones of slumping are visible in the left foreground, on the far bank of Cache Creek, and similar features are visible on the higher parts of the slopes to the right. A12 would, therefore, be justifiable. Unfortunately, one can never predict at the outset of an investigation whether a given period of observation will indeed be representative of long-term periods. The period of ob- servation of the Cache Creek drainage basin is known to have included several years during which the annual runoff was significantly less than the mean for the long- term period of record (table 1). To evaluate this vari- ation in runoff, so as to qualify the results of this report if necessary, flow duration curves for both the period of obser ration and the long-term period were plotted for each sampling station. Flow duration curves for streamflow stations on North Fork Cache Creek, Cache Creek near Capay, Cache Creek at Yolo, Cache Creek above Rumsey, and Bear Creek are shown in figures 13 through 17, re— spectively. The location of each station is shown on plate 1. These frequency curves show the percentage of time that any given water discharge is equaled or ex- SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS ceeded. Because data on the water discharge of Bear Creek (fig. 17) include only a single year prior to the period of observation covered by this report, and be— cause no previous data are available for Cache Creek above Rumsey (fig. 16), duration data cannot be com- pared with a long—term record at these two stations. The three remaining stations adequately depict the flow characteristics in the drainage basin, however, because they are located in the upper, middle, and lower parts of the basin, respectively. The flow-duration curves for stations on both North Fork Cache Creek and Cache Creek near Capay (figs. 13, 14) show that the data for the 1960—63 period plot to the left of the long-term mean at high water—discharge values and, following intersection with the long—term duration curves, plot to the right at low water-discharge values. The discharge value at the initial point of in- tersection is approximately 40 cfs (cubic feet per sec— ond) for North Fork Cache Creek (fig. 13) and 80 cfs FIGURE 10.——View of the head of a gully in Upper Cretaceous sedimentary rocks near Capay. The extent of gullying in the lower part of the basin near Capay is illustrated in this View. far downslope, such as that shown in figure 9. This gully may have originated through slumping CACHE CREEK DRAINAGE BASIN, CALIFORNIA for Cache Creek near Capay (fig. 14). That is, these discharge values were equaled or exceeded less often during the period of observation than during the long- term period of record, whereas lower discharge values occurred more often during the period of observation. The curves for Cache Creek near Capay (fig. 16) inter- sect again at a discharge value below 80 cfs, but this re— sults, in part, from complications introduced by sur- face-water diversions and is, in any event, unimportant in principle. The flow-duration data Jfor Cache Creek at Yolo (fig. 15) show no intersection between the curves that repre- sent the 1960—63 and long-term periods. That is, at the outlet of the drainage basin, the deficiency in runoff during the period of observation is represented by a A13 decrease in the frequency of occurrence of any given water discharge. Because sediment discharge is a function of water discharge, and because water discharge was deficient relative to the long-term period of record at each of these stations, it is clear that the estimates of sediment discharge provided by this report must be regarded as minimum values. Although the flow-duration data for stations on Cache Creek near Capay and North Fork Cache Creek show an increase in the frequency of occurrence of low-water flows during the 1960—63 period, this increase cannot compensate for the deficit of high-water flows, which account for a much larger proportion of sediment transport than the low-water flows. FIGURE 11.——View of the Cache Creek channel below Capay showing the extensive area of deposition in the reach below the point of stream diversion. The channel proper extends across this View in the middle distance. It is subject to surface flows during times of controlled release of water from upstream, and during the winter rainy season. The tree trunks show that at high stream stages much of this entire area is subject to inundation. 232—457 0-67——3 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS FIGURE 12.—View of the Cache Greek channel near the Yolo sediment station. of the channel in this reach, which is in the lower part of the drainage basin. 3 pool and riffle sequence of broad amplitude. wide and about 40 feet deep. SEDIMENT DISCHARGE OF STREAMS Evaluation of the sediment discharge of streams in the Cache Creek drainage basin is a major aim of this investigation. Before treating the basic sediment data and their interpretation, however, it is pertinent to consider some of the problems that arise in the sampling of sediment in streams and the computation of records. In the section which follows below, problems associated with the estimation of total sediment discharge are omitted; these will be discussed in the section of this report entitled “Total Sediment Discharge.” PROBLEMS OF SAMPLING AND COMPUTATION The sampling of streams and computation of data were accomplished in conformance with standard pro- cedures of the US. Geological Survey. Suspended sediment was sampled with the US. D—49 sampler, or “fish” as it is commonly designated, at all but low flows. A 3/16—inch—diameter nozzle was used with this sampler. Low flows were sampled using the US. DH— Note the abundance of gravel on the bed The undulations of the bed suggest The trapezoidal cross section at the station is approximately 135 feet 48 hand sampler equipped with a 1A-inch-diameter nozzle. In both types of sampling, the first question that arises is whether any particles of greater diameter than the nozzles were in suspension at the time of sampling. If this occurred then such particles were unmeasured, thus producing an erroneous determina- tion of the size distribution and the concentration of suspended sediment. Although it is thought to be un- likely, the occurrence of such particles in suspension is possible and this source of error should be recognized. The D—49 sampler is so designed that the entrance velocity of the water-sediment mixture is equal to the instantaneous velocity of flow. Because velocity of flow varies with time and is a function of depth, determina- tion of the true sediment concentration in a given volume of water within a vertical section of the stream is not possible. Also, because the velocity-depth relation may vary somewhat among different streams, the re— ported concentrations, which are weighted according to discharge, are not strictly comparable. CACHE CREEK DRAINAGE BASIN, CALIFORNIA A15 10,000 i I I , IIIIII I 1000 I|||||I IIIIIII I I 10 IIIIIII WATER DISCHARGE, IN CUBIC FEET PER SECOND I IIIIIII I I I | I I I I I I I | I | I I I |||III I |III||| I IIIIIII I I IIIIIIII IIIIIII I I I | I I I | I I I 0.1 0.01 0.050.102 0.5 l 2 5 10 20 3O 4O 50 60 70 80 90 95 97 98 99 99.5 99899.9 99.99 PERCENTAGE OF TIME INDICATED DISCHARGE WAS EQUALED OR EXCEEDED FIGURE 13.——Flow—duration curves of North Fork Cache Creek. The dashed curve represents the 1960—63 period; the unbroken curve represents the long-term period of record (1931—63). The fact that the curves intersect at a water discharge of 40 cfs indicates that greater water-discharge values occurred more frequently during the long-term period of record than during the 1960—63 period, and lesser values occurred more frequently during the 1960—63 period than during the long-term period of record. The problem is compounded because the reported suspended-sediment concentration at a given cross section is derived from the concentrations measured at several vertical sections. In the Cache Creek drainage basin, the number of verticals where sediment-discharge measurements were made of streams ranged from three to nine, and depended on the stage at the time of sampling. Changes in bed form, bed roughness, and turbulence with stage, however, render any choice of the number of vertical sections that are required some- what arbitrary. The basic problem is that the absolute concentration, whether weighted for discharge or not, is never known; and the degree of accuracy of the usual sampling procedures cannot, therefore, be stated with certainty. If, however, the sediment-concentration measure- ments at a given cross section are assumed to be highly reliable, then a problem of extrapolation of these re- sults arises. In most investigations of sediment trans— port, including the present study, the goal is to deter- mine the sediment-transport characteristics of streams that are many miles in length. Information gained at a cross section must therefore be extrapolated to a reach, and the reach, in turn, must be representative of many miles of that stream. Such extrapolation assumes that the principle of continuity prevails during the period of sampling or record. A16 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 100000 . 1 1 1 1 1 1 1 1 1 10,000 1 / 1000 11111 ,.. O 0 111111 1 WATER DISCHARGE, IN CUBIC FEET PER SECOND 1 10 111111 1 1 1 1 1 1 1 1 1 1 1 0.07 0105 0.1 0.2 0.5 1 2 5 10 20 30 40 1 1 1 1 1 1 1 1 1 I 1 1 1111111 1111111 1 111111 1 1 1 1 1 1 1 1 1 1 1 1 1 50 6O 7O 80 9O 95 97 98 99 99,5 998 99.9 99.99 PERCENTAGE OF TIME INDICATED DISCHARGE WAS EQUALED OR EXCEEDED FIGURE 14.—Flow-duration curves of Cache Creek near Capay. The dashed curve represents the 1960—63 period; the unbroken curve represents the long-term period of record (1943-63). Note that water-discharge values greater than approximately 80 cfs occurred more frequently during the long-term period of record than during the 1960—63 period and that lesser water-discharge values generally occurred with greater frequency during the 1960—63 period. Continuity, as applied here, means that for each unit of sediment that enters a stream above a given station, an equal unit, not necessarily the same one, must pass the station and be discharged in a downstream direc— tion. A given unit of sediment, however, may at dif- ferent times be derived from hill-slope erosion in head— water reaches of the basin, from stream terraces, from bank caving, or from erosion of the bed and banks of the channel. Because of the diversity of the possible sources of sediment, changes in channel morphology above and below a given station may occur. The prin— ciple of continuity clearly must prevail over the long term. During a 4- or 5-year sampling program, how— ever, it is quite possible that the vagaries of local erosion and aggradation within the channel may cast doubt on the extrapolation of data from a given cross section. A major problem in sampling sediment in streams is depth limitation. The suspended—sediment sampler is so constructed that samples cannot be obtained within approximately 0.4 foot of the rater-sediment interface. CACHE CREEK DRAINAGE BASIN, CALIFORNIA The quantity of suspended sediment in this region can be computed, in part, from the general relation of the suspended sediment distribution with depth, namely dc cw: — lad—ya where c=local concentration, w=fall velocity, A17 Ic=a factor that involves the eddy—viscosity coef- ficient, and y=depth. Upon integration, an expression can be obtained that relates the concentration of sediment of a given Size range at any depth to the concentration at known depths. Some fraction‘of the sediment that is in salta- tion or suspension within 0.4 foot of the bottom must 100,000 ‘ | i ‘ 7 i I _ l I l l | l | | :1 e _ 10.000 : : 3 : i— : E o 1000 : : O I— _ L|J — _. (I) ,— _ m # _ UJ _ _. D. ,_ _ E L|J LLJ LL _ _ 9 CD 8 100 : : E E I ui : : (D D: — .E < I — E. O ‘9 D _ _ D: e g 10 1: : 1 _ _ O 1 l l l I i | l l l i l l l l l l l i i i i l l 0.01 0050.1 0.2 0.5 1 2 5 10 20 30 4o 50 60 70 80 9o 95 97 98 99 99.5 99.8 99.9 99.99 PERCENTAGE OF TIME INDICATED DISCHARGE WAS EQUALED OR EXCEEDED FIGURE 15.——Flow-durati0n curves of Cache Creek at Yolo. The dashed curve represents the 1960—63 period; the unbroken curve represents the long-term period of record (1904—63). Flows of any given water discharge occurred more frequently during the long-term period of record than during the 1960—63 period. Zzzr» A18 still be assigned, however, to that portion of the total sediment discharge that is transported as bedload. This fraction may be small or large, but whether or not it is negligible depends upon the particular characteristics of a given stream and its sediment load. This element of uncertainty in the sampling of the suspended-sediment load in its entirety affects the determination of both the suspended-sediment and the bedload discharge. The fact that the fall velocities of particles are signif- icant in sediment transport leads to still another possi- bility of error. “’hen suspended-sediment samples are analyzed, a dispersing agent is commonly added before pipet determinations of particle-size distribution are made. The arbitrary size classes established for sedi- ment analysis are not entirely applicable to stream transport evaluation, however, because the sediment in the stream moves according to hydraulic principles. The percentage of clay in a sample analyzed after addi- tion of a dispersing agent may not be a true indication of the actual percentage of particles of clay size that are transported by the stream. Clay that is in transport in the flocculated state is hydraulically equivalent to silt and, perhaps, even to sand. This possible source of SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS error in the determination of particle-size distribution is difficult to avoid. It can seriously affect the results of any sediment investigation. In the computation of sediment discharge, problems of interpretation frequently arise. Some of the possible circumstances are the following: 1. Malfunction of a stream recorder will produce gaps in the hydrograph. 2. Certain runoff events may, in part, be produced by the controlled release of water upstream. This Will complicate the interpretation of water-sediment relations. 3. Gage-height readings may be unavailable for all run- off events, and missing water-discharge values must then be estimated. 4. Multiple—peak events complicate the water-sediment relationship; increases in water discharge after the initial rise may not carry increased quantities of sediment because much of the available sediment has already been transported. 5. Sediment samples may be available for rising or fall- ing stages but not for the peak of a given runoff event. Interpretation and estimation are then re- 10,000 I I [ \ l | | | l : _ \\ “ * \\ _ _ \\ H _ \ _ \ _ \ __— \ 0 \ Z 1000 — \ : O : \ _ 0 \ _ ""' _ \ w — \ _ E _ \\\ : a T \\\ .— .5 \\ _ fl \ g I“ _ \ \ 2;? \ 3 \ _ Q 100 : \ : E : \\ _ Lu. ~ \ : _ \ (5 a - \ a I _ \ _ 0 \ 2 \ _ Q _ \ n: E \ < 10 ~ \\ : g : \\ _ : \\ I \\ ._ — \ \\\ _ — \ \ \ _ _ \\ \ 1 | | I I | I I I | I I I | I I I I I I I | | I 0.01 0.05 0.1 0.2 0.5 1 2 5 10 20 30 40 50 60 70 80 90 95 97 98 99 99.5 99.8 99.9 99.99 PERCENTAGE OF TIME INDICATED DISCHARGE WAS EQUALED OR EXCEEDED FIGURE 16.—Flow-duration curve for Cache Creek above Rumsey, 1960—63. CACHE CREEK DRAINAGE BASIN, CALIFORNIA quired for determination of water-sediment rela- tions. 6. The available instantaneous values for water and sediment discharge may not adequately approxi— mate daily mean values. This Will greatly compli- cate the computation of total sediment discharge, and in certain circumstances Will effectively prevent computation. The problems that are inherent in both sampling and analytical procedures do not invalidate the results of this report. As previously stated, the sampling and computation in this investigation conform to the stand- ards of the US. Geological Survey, and the results are, accordingly, the best that can be obtained at present. The problems mentioned are common to nearly all sedi— ‘ ment investigations, and the sound consideration of any A19 set of data requires awareness of the possible sources of error. SUSPENDED-SEDIMENT DISCHARGE The sediment stations on streams Within the Cache Creek drainage basin (pl. 1) are well distributed for the detection of differences in sediment-transport charac- teristics. As previously stated, the streams of the drain- age net flow through a basin that varies in geologic, top- ographic, and climatic conditions. Conceivably, these variations might be reflected by corresponding variation of the suspended-sediment discharge of the streams. The correspondence is in fact demonstrated by the size distribution of suspended sediment, the sediment-trans- port and sediment—duration curve, and the suspended- sediment discharge at each station. These data, for the 1960—63 period, are discussed below. 10,000 : I I I I I I I I I I I I I I I I : _ \ _ \ \ lOOO — \\ — : \ : : \ — _ \ I D _ \\ _ s — \ ~ 3 \ a) “ \ _ n: \\ LLJ “L 100 — \ _ I- — \ — fl 2 \ H LL _ \ : o — \ _ _ _ \ _ “:3 \ o — \ _ E. — \ - 5 \\ I! E 10 : \\ _ o _ \ Z 9 — \ _ 2 _ \\ Z 3 \\ _ \ fl \ \ \\ 1 : \\\ : E \ : _ \ _ \ _ ,_ \ _ _ \ \ _ \ _ \ _ \ \ \\ 0,1 I I I I I I I I I I I I I I I I I I I I I \I I 0.01 0.05 0.1 0.2 0.5 1 2 5 10 20 30 40 50 6O 70 80 90 95 97 98 99 99.5 99.8 99.9 99.99 PERCENTAGE OF TIME INDICATED DISCHARGE WAS EQUALED 0R EXCEEDED FIGURE 17.—Flow-duration curve for Bear Creek, 1960—63. A20 The mean particle-size distribution of suspended sedi- ment at stations on North Fork Cache Creek, on Bear Creek, and on Cache Creek above Rumsey, near Capay, and at Yolo (pl. 1) is shown in figure 18. The size dis- tribution of sediment that passes through the settling basin below Yolo is also shown. Although the size distribution curves are similar, they are reasonably distinct. The data Show that, in gen- eral, a larger percentage of fine sediment is in suspen- sion in Cache Creek near Capay and at Yolo than above Rumsey or on North Fork Cache Creek. At the first two stations, for example, Cache Creek transports only 13—16 percent sand—size particles in suspension, whereas above Rumsey and on North Fork Cache Creek, 22—33 percent of the sediment in suspension is in this size range. This distinction reflects the fact that coarser sediment makes up a greater percentage of the avail— able supply in the upper part of the basin. The data from Bear Creek belie this as a general rule, however. Bear Creek transports only 17 percent sand-size parti— SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS cles as suspended sediment, despite the fact that it tra— verses the upper part of the basin. The difference is partly explained by the fact that water discharge is lower and that much of the available sediment in the Bear Creek valley, as previously noted (fig. 4), may be too coarse for transportation under present conditions. The size distribution of suspended sediment at the weir of the settling basin below Yolo will be described in a later discussion of deposition of sediment in the settling basin. It can be seen, however, from the size- distribution curve shown in figure 18, that Virtually all sediment transported in suspension through the area 'is in the silt-clay size range. Sediment-transport curves for the five sediment sta— tions discussed above are shown in figure 19. These curves demonstrate the relation between daily mean sediment discharge and water discharge, and the regres- sion equation for each curve is a least-squares fit of the data. The data used to compute the regression equa- tions include only the actual measurements of water and 99.9 l I l T 99.8 — _ 99.5 — __ 99 _ A/EJ 98 — _ fl ,7) 95 — _ 0 Lu 1— 90 r- V < 2 D E 80 — _q Z <( I 70 — m I. 35 60_ , Z EXPLANATION E _ m w 50 D a 40 — North Fork Cache Creek E O E 30 - A g “- Bear Creek LL _ 7 O 20 Lu A 3 Cache Creek above Rumsey i- 10 H e Z 8 o E 5 — Cache Creek near Capay _ a. CI 2 * Cache Creek at Yolo w 1 — O _ (15 — Settling basin at the weir v 0.2 — 7 0.1 i iiiiiii i iiiiiiii iiiiiii 0,001 0.01 0.1 I MEAN PARTICLE DIAMETER, IN MILLIMETERS FIGURE 18.—Size—distribution curves of suspended sediment in streams of the Cache Creek drainage basin and from settling basin at the weir. CACHE CREEK DRAINAGE BASIN, CALIFORNIA sediment discharge during the 1960—63 period. Esti- mated values were omitted because such values must be derived from the actual sample data and hence should not be allowed to affect the relationship determined. The curves are based upon 82 samples from North Fork Cache Creek, 60 samples from Bear Creek, 646 samples from Cache Creek above Rumsey, 38 samples from Cache Creek near Capay, and 470 samples from Cache Creek at Yolo, and the respective water—discharge values. Sediment—transport data commonly do not plot as a single straight line on logarithmic paper. Mathemati- cally, this would suggest that water and sediment dis- charge are related by some function other than a power function, or perhaps are not related at all. Experience has shown, however, that sediment-transport data do plot as straight lines on such paper within a given range of discharge values; that is, the relation at both high and low discharge values is that of a power func- tion, but the rate of increase of sediment discharge with water discharge, or the slope of the curve, is different for these high and low values. Accordingly, there are three approved ways of presenting sediment-transport data: (1) as a scatter diagram, (2) as a graph of two straight lines of different slope, or (3) as shown in figure 19, a simple least-squares fit of the discharge data. The last method was chosen for this report because neither the scatter of the plotted data nor an apparent break in slope at low discharge values is excessive, and because the essential purpose of inclusion of the data is to demonstrate the gross distinctions in sediment- transport characteristics among the streams. It is clear from the data that the five sediment sta— tions, each of which is assumed to be representative of many miles of streambed, can be placed in three sepa- rate categories. This classification is based on the re— gression equations, particularly the exponent of water discharge. As shown on the curves (fig. 19), this ex— ponent is approximately 1.8 and 1.9 for Bear Creek and North Fork Cache Creek, respectively, whereas it ranges from about 2.0 to 2.5 for Cache Creek at the Rumsey and Capay stations. That is, although sediment dis- charge increases with an increase in water discharge at each of the four stations, the rate of increase of sedi- ment discharge is considerably greater near the Rumsey and Capay stations. This difference reflects the fact that the Bear Creek and North Fork stations are nearer to the headwaters of the Cache Creek drainage basin. Both the smaller drainage area above these stations and the greater percentage of stream reaches in rocky ter- rain mitigate against a great increase in suspended- sediment discharge with increased water discharge. Moreover, the mean annual water discharge of perennial A21 streams is always greater in the lower or downstream part of a given drainage basin because of an increase in drainage area and a concomitant increase in the number of stream tributaries. On the basis of the data just given and the assump— tion that the effects of other factors are equal, the rate of increase of suspended-sediment discharge with an in- crease in water discharge should be greater at the Yolo station than near the Rumsey and Capay stations, which are farther upstream (pl. 1). The sediment-transport curve for Cache Creek at the Yolo station, however, shows that the effects of other factors are apparently unequal (fig. 19). The exponent of water discharge in the regression equation is approximately 1.5; that is, at this lowermost station in the drainage basin, the rate of increase of suspended-sediment discharge with water discharge, is lowest rather than highest. The reason for this seeming anomaly is the diversion of the surface water of Cache Creek above Yolo, at Capay, as pre- viously mentioned. A series of small dams there have a twofold effect on the sediment—transport character— istics of Cache Creek at Yolo. First, these barriers promote sediment deposition above Capay; and second, the periodic, controlled release of water from Capay to a large network of canals and sloughs, some of which are shown on plate 1, causes'additional sediment to be diverted from its natural path to Yolo. The effect of these various works of man is to reduce not only the rate of increase of suspended—sediment discharge with water discharge at Yolo from the normal value, but also the absolute value of the suspended-sediment discharge; it will be shown later in this report that the total annual tonnage of suspended sediment passing the Yolo sta- tion is actually less than that passing the station near Capay. Summary—The sediment-transport data show that the rate of increase of suspended-sediment discharge with an increase in water discharge rises downstream. This rise would normally be greatest at Yolo, near the drainage outlet for the basin, but the artificial barriers at Capay have reduced this value to the lowest in the drainage basin. This difference in sediment-transport characteristics among streams in the Cache Creek drainage basin is also borne out ‘by sediment-duration data. The sedi- ment-duration curves for stations on North Fork Cache Creek, Bear Creek, and Cache Creek above Rumsey, near Capay, and at Yolo are shown in figures 20—24, respectively. These curves are similar to flow-duration curves in that they show the frequency with which a given suspended-sediment discharge is either equaled or exceeded. A22 1,000,000 100,000 10 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS IIIII IIIII l 10 000 — -------------------- >- , _ a: : Bear Creek 01 _ Lu 0. _ W _ z O ,_ _ E m. _ U n: < 5 1, 1000 C D .— ’_ _ z _. Lu _ E o I- u: U.) _ 0 LL] 0 __ 2 Lu 4:. m D U’ 100 IIIII I lIIllII I IIIIIIIII I IIIIIIII I IIIIIIII II EXPLANATION Cache Creek at Yale Cache Creek near Capay I LIJIIII T FIIIIT IIIIIII I IIIII II IIIII | I IIIIIII 10 100 1000 DAILY MEAN WATER DISCHARGE, IN CUBIC FEET PER SECOND 10.000 100.000 FIGURE 19.—Sediment—transport curves of streams in the Cache Creek drainage basin, 1960—63 period. least—squares regrwsion lines of the sample data. The curves are Note that the rate of increase of suspended-sediment discharge with an increase in water discharge is greater for Cache Creek above Rumsey and near Capay than for North Fork Cache Creek and Bear Creek; the rate of increase is least for Cache Creek at Yale. CACHE CREEK DRAINAGE BASIN, CALIFORNIA 10°90" : I I I I I I I I I I I I I I I ‘ I I I I I : : ' : - I _ I | _ _ \ ._ \ _ \ n \ \ 10,000 —— L : : \\ 9 ¥ \\ _ : \ : I \ __ \ ¥ \ i _ \ \ \\ 1000 — E é Z \ : D : \ : E I \\ : a — \ _ I9 _ \ _ E \ a \ g 100 : \ : < : \ : é I \ _ a Z \ I — I — 2 _ \ k E \ bi \ 10 : \\ : E I 3 _ \ _ _ \ _ _ \ n \ \ v \ \ 1 : \ j _ \ n : \ : I \ \ _ _ \ _ \ \ fl \\ O, I I I I I I I I \I I I I I I I I 0.01 0.05 0.1 0.2 0.5 1 2 5 10 20 30 40 50 6O 7O 80 90 95 97 98 99 99.5 99.8 99.9 99.99 PERCENTAGE OF TIME INDICATED DISCHARGE WAS EQUALED OR EXCEEDED FIGURE 20.—Sediment-duration curve of North Fork Caxche Creek, 1960—63. These data clearly indicate that the same classifica- tion of stations pertains. North Fork Cache Creek and Bear Creek show similar sediment-transport char— acteristics, which are distinctly different, however, from those of a second pair of stations, namely Cache Creek above Rumsey and near Capay. A suspended-sediment discharge of 1,000 tons per day, for example, is equaled or exceeded about 2 percent of the time at the upper- most pair of stations and 7 percent of the time at the stations on Cache Creek above Rumsey and near Capay, Which are farther downstream. At a suspended-sedi— ment discharge rate of 10,000 tons per day, the respec- tive frequency values are approximately 0.4- and 3.0 percent. The effects of artificial conditions again are evident from a comparison of the sediment-duration data for Cache Creek near Capay (fig. 23) and at Yolo (fig. 24). For any given value of suspended-sediment discharge, the frequency of occurrence is greater at Capay than at Yolo, whereas under natural conditions the reverse A24 would be true. A second example of departure from sediment-transport characteristics that would be ex- pected under pristine conditions is afforded by the marked breaks in the slope of the duration curves for Cache Creek above Rumsey (fig. 22) and near Capay (fig. 23). These breaks result from the controlled re- lease of water from Clear Lake (pl. 1). This water flow periodically removes much of the available sedi- ment that would normally be transported in suspension from the upstream rocky channel, thus reducing the SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS concentration of suspended sediment in subsequent natural runoff events Finally, the absolute magnitude of the suspended- sediment discharge during the 1960-63 period suggests differences in sediment-transport characteristics at these stations, in the effects of man, and in certain geologic controls. The estimated magnitude of the suspended- sediment yield for each of the 4 years of observation is shown in table 2. Also listed is the drainage area above each station. The total suspended-sediment-yield data 100,000 _ I ‘ ‘ l 1 1 1 i l l : : | : _ I 7 l __ \ A I |\ 10,000 : \\ E _ \ _ : \ v _ \ n _ \ n \ _ l n. E I _ I \ \ 1000 : \ : > __ n < A I _ o _ \ v n: — \ 7 E y \ — m — \\ E Z 9 \ v a \ :3“ 100 : \ : Q: — _ < — \ _ é : \ : a — \\ _, '2 T \ n g _ \ _ a \ “J \ (f) 10 : \\ : : \ : A \ n 7 \ fl \ _ \ \ .— \ 1 : \ : : \ E Z \ _ _ \ n \ \ \ \ , \ \ I 041 1 I 1 l l l 1 I I I 1 z 1 a I l I l 1 1 1 1 0.01 0.05 0.1 0.2 0.5 1 2 5 10 20 3o 40 50 6O 70 80 90 95 97 98 99 99.5 99,8 99.9 99.99 PERCENTAGE OF TIME INDICATED DISCHARGE WAS EQUALED OR EXCEEDED FIGURE 21.—Sediment-duration curve of Bear Creek, 1960—63. SEDIMENT DISCHARGE, IN TONS PER DAY CACHE CREEK DRAINAGE BASIN, CALIFORNIA 1 ,000,000 A25 _I|IIIII III IIII III IIIIIIW /_ 100,000 IIIIIII / I / 10,000 IIIIIII / I 1000 ||I||II / | / 100 |I||I|| / | I / / I IIIIII / I / IIIIIII | / | I / / IIIIIIII IIIIIII \IIIIIII IIIIII I I IIIIIII IIIIIII IIIIIII I IIIIIII l I|I|l|| I I .1 0.01 0050.1 0.2 0.5 1 2 5 10 20 30 4O 50 6O 70 80 90 95 97 98 99 99.5 99899.9 PERCENTAGE OF TIME INDICATED DISCHARGE WAS EQUALED OR EXCEEDED FIGURE 22.—Sedjment-duration curve of Cache Creek above Rumsey, 1960—63. 99.99 A26 show, once again, that although the yield of North Fork Cache Creek is greater than that of Bear Creek, these upstream stations exhibit similar transport characterics if differences in drainage area are considered. The sediment yield increases markedly downstream and the 2- to 3-million-ton sediment yield at the Rumsey and Capay stations clearly distinguishes this pair from the upstream stations. As previously noted, the sediment yield between Capay and Yolo decreases by more than 1 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS million tons for the 4-year period. This decrease may be attributed to artificial controls; most of it must be the result of deposition above the controls at Capay, but some fraction of the total amount of sediment is probably transported into the distributary network of canals and sloughs in the lower part of the basin. Part of this decrease may also result from deposition below Capay and subsequent removal of some of the sediment through gravel quarrying for commercial purposes. 1'°°°'°°° : I I I I I I I I I I I I I I I I I I : 100.000 : : 10,000 V _. >. ~ _ < — __ D : : m — _ LIJ Q. — m (I) — m Z O ,_ h _ E (”3 1000 — : n: : _ < _ _ I a U _ 9 ~ _ Q ~ ~ ,_ H a Z LIJ g — _ D LLI (/3 100 : : 10 : : 1 I I I I I I I I I I I I I I I I I I I I I I I 0.01 0.05 0.1 0.2 0.5 1 2 5 10 20 30 40 50 60 7O 80 90 95 97 98 99 99.5 99.8 999 PERCENTAGE OF TIME INDICATED DISCHARGE WAS EQUALED OR EXCEEDED FIGURE 23.—Sediment-duration curve of Cache Creek near Capay, 1960—63. 99.99 SEDIMENT DISCHARGE, IN TONS PER DAY 1,000,000 100,000 10,000 1 000 100 10 CACHE CREEK DRAINAGE BASIN, CALIFORNIA A27 IIII|| IIIIII I |I|||I I ||IIIIII |||||II I IIIIIII I |II|||| I I I | I I I I I | I | I I I | | I I I I I | I I | I I | I I I | I I I I | I I|I||| I IIIIII I |||I|| I I IIIIIII I I||I||I ||||II I I 0.05 0.1 0.2 0.5 1 2 5 10 20 30 40 50 60 70 80 90 95 97 98 PERCENTAGE OF TIME INDICATED DISCHARGE WAS EQUALED OR EXCEEDED FIGURE 24.—Sediment—duration curve of Cache Creek at; Yolo, 1960—63. 99 99.5 99.8 99.9 99.99 A28 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS TABLE 2.—Annual suspended-sediment yield, in tons, at sediment stations in the Cache Creek drainage basin [Contributory drainage area above each station is given in parentheses] North Fork Cache Cache Cache Water Cache Bear Creek Creek Creek near Creek at year Creek (96.8 sq mi) above apay Yolo (198 sq mi) Rumsey (1,052 sq mi) (1,137 sqmi) (954 sq mi) 1 140, 885 17, 550 284, 090 363, 911 260, 446 16, 868 6, 388 148, 517 85, 692 84, 263 110, 960 54, 236 653, 999 791, 575 652, 052 207, 958 97, 957 1, 174, 218 2, 078, 905 1, 134, 971 476, 700 174,800 2, 261, 000 3, 320, 000 2, 132, 000 1 Includes the Clear Lake drainage area (528 sq mi) . which contributes sediment to the lake proper. The effective drainage area above this station is 426 square miles, The data in table 2 clearly indicate the effects of geologic conditions. The sediment yield of Cache Creek near Capay exceeded that of Cache Creek above Rumsey by 1,059,000 tons during the period of observa- tion. The approximate difference in drainage area above each station, however, is only 98 square miles. If the area that is tributary to Clear Lake (pl. 1), which contributes sediment that accumulates in the lake, is subtracted from the area above the Rumsey station, the data indicate that an effective drainage area of 426 square miles above the Rumsey station produced 2,261,- 000 tons of sediment during 1960—63 whereas the 98 square miles between the Capay and Rumsey stations contributed 1,059,000 tons. That is, the area between the stations contributed 2.04 times as much suspended sediment as might be predicted from drainage area alone. This difference in sediment yield per square mile may be attributable to the more highly erodible units that crop out in the valley above Capay, particu- larly the Pliocene and Pleistocene deposits in which many areas of badlands (fig. 2, 7) occur. This area of high sediment yield is a significant element in the choice of suitable locations for reservoirs in the basin; a struc— ture above Rumsey, for example, would not reduce the annual sediment yield at Yolo by an amount that would be predicted on the basis of the drainage-area reduction. TOTAL SEDIMENT DISCHARGE The total sediment discharge of a stream may be de- fined as the sum of the sediment transported in suspen- sion and the sediment transported as bedload during a given time interval. In accordance with this defini- tion, the bedload discharge discussed in this report rep- resents the difl'erence between total sediment discharge and the observed suspended-sediment discharge. In this broad usage, bedload discharge includes that fraction of sediment near the streambed which is in suspension but is not sampled, as well as that fraction of sediment which is transported solely by traction. Although the determination of total sediment dis- charge seems only to require that suspended—sediment and bedload discharges be observed at a given station and added, it is a complex problem. Because the bed- load discharge of a given stream cannot be sampled and measured using present instruments, total sediment discharge must be determined by indirect methods. One such method was provided by Colby and Hem- bree in 1955. They modified the bedload function devised by Einstein (1950) for computation of total sediment discharge from observations at a cross section of a stream. These observations include the hydraulic geometry of the cross section, the concentration of sus- pended sediment, and the particle-size distribution of the suspended sediment and of the material in the streambed. The estimate of total sediment discharge obtained by use of the modified Einstein method is improved if there is an overlapping of the sizes of sedi- mentary particles in suspension and in bedload trans: port. Because the total sediment-discharge data given in this report are based upon the modified Einstein method, it should be noted that such overlapping of size classes did‘ occur during each total load measurement. The modified Einstein method is one of the best pro— cedures available for the computation of total sediment discharge, and it has been proved valid for sand-bed streams. Its applicability to streams that flow in sand and gravel channels, such as Cache Creek, remains somewhat uncertain, however. Another method might have been used, but one of the fundamental problems in sediment-transport studies is that the predictive ef- ficiency of any total-sediment-discharge method can- not be ascertained unless the true bedload discharge of a given stream is known. And it is precisely this value which cannot be determined routinely with pres- ent instrumentation. Hence, one cannot determine which of several procedures provides the “best” answer. Seven measurements of the total sediment discharge were obtained at the Yolo sampling station (pl. 1) be- tween January 1959 and January 1964 (table 3). A wide range of instantaneous water-discharge values is represented, and this range should be sufficient to de- fine the instantaneous water-sediment relations of Cache Creek at Yolo. Instantaneous water discharge and total sediment dis— charge are related by the power function Q8=0.00189 (2.01381, as demonstrated by the graph in figure 25. To— tal sediment discharge, therefore, increases rapidly with an increase in water discharge, but figure 26 shows that this is accompanied by a decrease in the percentage of thetotal discharge that represents bedload discharge. As previously noted, bedload discharge is here con- sidered as the difference between the total sediment dis- charge and the suspended—sediment discharge. Al— though the absolute quantity of sediment in the bed— CACHE CREEK DRAINAGE BASIN, load fraction does not decrease (table 3), it represents a smaller percentage of the total sediment discharge, because suspended sediment makes up the bulk of the total load at high water-discharge values. TABLE 3.—Total sediment-discharge data from Cache Creek at the Yolo sediment station, for selected dates [Bedload discharge is determined by subtracting suspended‘sediment discharge from total sediment discharge] Instan- Suspended Total taneous Mean sediment Bedload sediment Date water velocity load (tons per load discharge (it per sec) (tons per day) (tons per (cis) day) day) 276 1. 96 118 58 176 12, 800 6. 18 272, 700 6, 900 279, 600 6, 000 5. 07 65, 100 2, 130 67, 230 109 1. 65 3. 5 18 22 748 2. 64 1, 290 257 l, 550 _______________ 7, 540 5. 31 62, 700 5,310 68, 010 1964 Jan. 28 ______________ 396 2. 54 96 24 120 1'°°°'°°°: I I IIIIIII I IIIIIIII I I IIIIIL— 100,000 : : : : ~ —I I I | 10,000 -I IIIIIII IIIIIII 1 000 I|||||| IIIIIII TOTAL SEDIMENT DISCHARGE, IN TONS PER DAY I | 100 llllIII IIIIIII I I I I I III 100,000 ,0 | IIIIIIII I I 100 1000 IIIIIII I I 10.000 INSTANTANEOUS WATER DISCHARGE, IN CUBIC FEET PER SECOND FIGURE 25.—Relation of total sediment discharge and instan— taneous water discharge. CALIFORNIA A29 5 10°F I IIIIIIII I IIIIIIII I IIIIIIJ: E " : 28 _ “1n: o< 7 Ir: _. “o “-0; <5 —— 2; LIJ fl 8? : 0‘” A 9.! .. off 7 0 as _ as D E 1 I IIIIIIII I IIIIIIII I IIIIIII 100 1000 10,000 100,000 INSTANTANEOUS WATER DISCHARGE, IN CUBIC FEET PER SECOND FIGURE 26.——Relation of bedload discharge, as a percentage of total sediment discharge, and instantaneous water discharge. The data in table 3 also indicate that a relation exists between bedload discharge and the mean velocity of flow. The graph in figure 27 shows that these variables are also related by a power function. Bedload dis- charge may be expected to increase with an increase in velocity of flow, because as the mean velocity increases, the velocity at the streambed surface also increases, and consequently there is additional bedload transport. Moreover, the fact that water discharge is related to sediment discharge implies that a relation must exist between velocity and bedload. Because the width and elevation of the streambed are fairly stable at the sediment station, velocity tends to increase with water discharge. The data discussed thus far are pertinent only to the dates and times of measurement of the total sediment discharge at Yolo. The water-discharge values given in table 3 and plotted in figures 25 and 26, and also thn mean velocity values, are instantaneous. That is, they are values for a specific time of measurement and mav or may not approximate daily mean values. If one assumes that instantaneous values do approxi— mate daily mean values, then a simple method of computing the total sediment discharge for each year of record may be used. A graph of instantaneous water discharge and bedload discharge is given in figure 28. The least-squares regression equation for this relation is sz=0.0246 Q1013“. If daily mean water-discharge values are substituted in this expression for each day of flow, and then cumulated, a value of total bedload dis— charge for a given year can be obtained. Addition to the annual suspended-sediment discharge for that year will provide the required total sediment discharge. This procedure was followed in computing the data given in table 4. The mean value of the bedload of A30 Cache Creek at Yolo, as a percentage of the total load, is 6.7 by this method. TABLE 4.——Annual sediment-discharge data from Cache Creek at the Yolo sediment station [Bedload values computed with the assumption that instantaneous water-discharge values approximate daily mean values] Suspended— Bedload Total Bedload Water year sediment (tons) sediment (percent) load (tons) load (tons) 260, 400 14, 130 274, 500 5. l 84, 260 7, 470 91, 730 8. 1 652, 100 37, 620 689, 700 5. 5 1,135, 000 94, 850 1, 230, 000 7. 7 2, 132, 000 154, 100 2, 286, 000 .............. __________________________________________ 6. 7 As previously noted, instantaneous water-discharge values may not approximate daily mean values. Analysis of the data for Cache Creek for 1959, for ex- ample, reveals that the instantaneous values are approximately 30 percent greater than the correspond- ing daily mean values of water discharge at high stages of flow, and are about 10 percent greater at low stages of flow. This suggests that the relation shown in figure 28 provides too low an estimate of the annual bed- load discharge and, therefore, of the total sediment discharge. .Accordingly, an alternate method of com— putation would seem desirable. 100,000 IIIIIII I .IIIIII IIIHT. IIIIII I | 10,000 I I‘RIIIII IIIIII I I 1000 IIIIIII IIIIIII I I p, BEDLOAD DISCHARGE, IN TONS PER DAY 100 IIIII IIIIIII | I 10 I IIIIIIII I IIIIIIII I IIIIIII, 0.1 l . 10 100 MEAN VELOCITY AT THE TIME OF DISCHARGE MEASUREMENT, IN FEET PER [SECOND FIGURE 27.——Relati0n of bedload discharge and mean velocity of flow at the time of the water-discharge measurement. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 100,000 TIIIIIIII I IIIIIIII I IIIIII llIIl—I IIIIH‘ 10,000 I IIIIIII IIIIIII | I 1000 IIIIIII IIIIIII I I I BEDLOAD DISCHARGE, IN TONS PER DAY é IIIIIII IIIIIII | I OI I I [III I I 10,000 I I I I II 100,000 ,0 IIIIIIIII III 100 1000 INSTANTANEOUS WATER DISCHARGE, IN CUBIC FEET PER SECOND FIGURE 28.-—Relation of bedload discharge and instantaneous water discharge. The method used for this purpose is that of subdi- vision. This consists, principally, of (1) defining a bedload curve, for each day which has a wide range of water discharge, based on the water-sediment relations of the stream (fig. 28), (2) subdividing each day into a number of intervals, thus obtaining the bedload dis- charge during each interval, and (3) computing the total-sediment discharge by cumulation of the bedload during the intervals and adding this bedload to the suspended-sediment discharge for the day. The results of computing bedload by the subdivision method are given in table 5. TABLE 5.—Annual sediment-discharge data from Cache Creek at the Yolo sediment station [Bedload values computed by the method of subdivision] Suspended Bedload Total Bedload Water year sediment (tons) sediment (percent) load (tons) load (tons) 14, 720 275, 100 5. 4 7, 770 92, 030 8. 4 38, 400 690, 500 5. 6 95, 750 1,231, 000 7. 8 156, 600 2, 289, 000 ____________________________ 6. 8 'The additional correction because of subdivision is indicated on the plot shown in figure 29. These data show the differing values of bedload discharge that will CACHE CREEK DRAINAGE BASIN, CALIFORNIA be obtained, the difference depending upon the method of computation used. Specifically, it can be seen that the values obtained by the method of subdivision differ from the values obtained When subdivision is not em- ployed. This is true because the slope of a line of best fit will depart slightly from 45°, which would indicate equality of bedload discharge values regardless of sub- division. The correction required by these data is ap- proximately 2,500 tons for the 1960—63 period. In the present instance, the adjustments described above produce a relatively minor change in the total sediment-discharge estimate. The total sediment load A31 for the 1960—63 periods (table 4) increased by 2,500 tons (table 5), which represents a percentage increase of about 0.1 percent. The increase, of course, is due en- tirely to adjustment of bedload discharge values. Be- cause the rate of increase of bedload discharge with an increase in water discharge is low, the initial approxi- mation (table 4) appears sufficient for most purposes. If a given stream has a greater rate of increase of bed- load discharge with an increase in water discharge than that indicated for Cache Creek, then adjustment by the method of subdivision will be required. 10000 I I | I I I 8000— 6000 —- 4000 '- 2000 — 800 _ 600 — 400 — 200 ~— 100 — ' so — 60— 40— BEDLOAD DISCHARGE, IN TONS PER DAY (WITHOUT SUBDIVISIONS) 20_ . 10 I III III A ll 10 100 ’ 1000 10,000 BEDLOAD DISCHARGE, IN TONS PER DAY (BY SUBDIVISIONS) FIGURE 29.—Scatter diagram showing the differing values of bedload discharge that; are obtained‘by the method of subdivision. These data pertain to Cache Creek at the Yolo sediment station for the 1960—63 period. A32 The several curves in figure 30 show the relation of various fractions of sediment discharge for Cache Creek at the Yolo station and also provide another simple, though less precise, method of determining the total sediment and bedload discharges listed in table 4. Curve 1 shows the relation of bedload discharge and water discharge, where bedload discharge is defined as the difference between total sediment discharge and suspended-sediment discharge. Curve 2 shows the re- lation of the mean suspended-sediment discharge for the 1960—63 period and water discharge. In this in- stance, the relation is plotted as two straight-line seg- ments that differ in slope, because a precise rather than a gross relation is desired. The sum of curves 1 and 2 is curve 3, which represents the relation between the ad- justed total sediment discharge and water discharge. If curve 3 is used to compute total sediment discharge for the 1960-63 period by the flow duration method, the figure for total discharge of Cache Creek at Yolo as approximately 2,330,000 tons. If curve 2 is used to compute the bedload for the 1960—63 period, figure for the bedload discharge is 154,000 tons. BED MATERIAL The size limits of the bed material of a given stream can be variously defined, but any definition is dependent upon the flow regime at a given time. The lower size limit of material transported as bedload discharge is a function of the velocity of flow, the suspended—sediment discharge, and other factors. Hence, this lower size limit is variable through time. For this report, some arbitrary lower limit must be chosen and therefore sedimentary particles coarser than 1.0 mm are here termed bed material. This size bound- ary is selected because material coarser than 1.0 mm was not found in the suspended—sediment samples obtained during the period of record. It is recognized, however, that at high velocities some particles of this size or larger may be in suspension, whereas at low velocities particles smaller than 1.0 mm may settle to the stream- bed or undergo transport by traction. Size—distribution curves for the bed-material samples obtained from the streambed of Cache Creek at Yolo are given in figure 31. These samples were obtained at the time of each total-load measurement, and inspec- tion of the curves shows that some material was finer than 1.0 mm in each case. The bed material coarser than 1.0 mm, however, ranges from 36 to 86 percent. This range corresponds to a considerable range of instantaneous water-discharge values, namely from 748 to 12,800 cfs. The size distribution of bed-material samples affects the estimate of the total sediment discharge when the SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS estimate is computed by the modified Einstein method. The samples are reliable, however, only if the streambed material at the times of sampling was representative of the average condition during the 1960—63 period. The question of whether instantaneous values of water dis- charge approximate mean values, which was raised previously, is also relevant. A test of the reliability of bed-material sampling, however crude it might be, was desirable, and therefore composite samples of the bed material of the Cache Creek channel were collected at random cross sections over a 7-mile reach below the Yolo sediment station. This was done while the channel was dry, as shown in figure 12. The weight percentage of sediment coarser than 1.0 mm ranged from 57 to 86 over the 7 -mile reach, and the mean value for a given cross section was 69 percent. Because the sediment in the streambed below the Yolo sediment station can be assumed to represent the aver- age size of the material that is transported past the station over a long-term period, the mean value of 69 percent is useful. Curve 4 in figure 30 shows the rela- tion between water discharge and the material coarser than 1.0 mm transported by Cache Creek. Because curve 1 of this figure shows the relation of bedload dis- charge and water discharge, the percentage of the bed‘ load discharge that is coarser than 1.0 mm can be com- puted. According to this method, approximately 48 percent of the bedload of Cache Creek is coarser than 1.0 mm. The mean value of 69 percent, obtained as previously described, is probably greater than the actual value because it includes the effects of selective transport of finer sediment in this lowermost reach of the channel. These percentages appear to agree fairly well and the range of instantaneous values of the percentage of bed material coarser than 1.0 mm is probably representative of long-term conditions at the Yolo sediment station. DEPOSITION 0F SEDIMENT IN THE SETTLING BASIN The Cache Creek settling basin below Yolo is shown on plate 1. Because of extensive artificial controls al- most all the water in the stream passes the station at Yolo and continues directly to the settling basin, a distance of approximately 8 miles. The channel lead- ing to Knights Landing, shown on plate 1, is natural but abandoned. Because flow is directed through the settling basin and over a weir that leads to the Yolo Bypass, an estimate of sediment deposition, or the trap efficiency of the settling basin, can be made from data on the sediment discharge at the Yolo station and at the weir of the basin. One of the goals of this investi— gation was to obtain ‘an estimate of the trap efficiency CACHE CREEK DRAINAGE BASIN, CALIFORNIA A33 1000900 11111111111111111111 11 800,000— _ 600.000 — -— 400.000 _ 200.000 — 100,000 -' 80,000 — 60,000 — 40,000 — 20,000 '- 10,000 — 8000 — 6000 *— 4000 — 2000 — 1000 t— 800 " 600 — 400 — SEDIMENT DISCHARGE, IN TONS PER DAY 200 — 100 — 80 — 60 — 40— 20— 10— ] 1 1 l/ 1 1 1 1 1 1 1 1 1 1 1 1 1 lo 100 1000 10,000 100,000 WATER DISCHARGE, IN CUBIC FEET PER SECOND FIGURE 30.—Relation of various fractions of sediment discharge and water discharge for Cache Creek at the Yolo sediment station. Curve 1 shows the relation of bedload discharge and water discharge. Curve 2 shows the relation of the mean suspended-sediment discharge for the 1960453 period and water discharge. Curve 3 shows the relation of the adjusted total sediment discharge and water discharge; it is the sum of curves 1 and 2. Curve 4 shows the relation of the discharge of particles coarser than 1.0 mm and water discharge. A34 in the settling basin; and for this reason, suspended- sediment samples were obtained at the weir whenever possible. During the 1960—63 period 27 samples were taken; much of the following discussion is based on these samples. The size distribution of samples obtained at the weir was not discharge weighted because water-dis- charge data were unavailable. In order to estimate the suspended—sediment discharge at the weir, it is there- fore necessary to combine the suspended—sediment con- centration at the weir With the water discharge on the date of sampling at the Yolo station. Implicit in this approach is the assumption that the water discharge at Yolo and at the weir are the same. Because most of the runoff events occur during the win- ter months, it seems improbable that any appreciable portion of the total runoff over the 8—mile reach of channel between Yolo and the weir is lost through evaporation. Possibly, however, the lowering of the water table in this area through ground-water pumping may be sufficient to cause some loss of surface flow by way of seepage into the surficial sediments. If so, the actual water discharge at the weir may be somewhat SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS less than the water discharge at Yolo. The estimate of suspended—sediment discharge at the weir may thus be too high, and because trap efliciency is determined by the difference between the suspended-sediment discharge at Yolo and at the weir, the estimate of the trap efficiency of the settling basin may be too low. The trap efficiencies discussed here, however, are pred- icated upon suspended-sediment discharge alone. Be- cause no particles in the sand-size range pass over the weir, the settling basin must necessarily trap all the coarse sediment in transport that passes the Yolo sta- tion. As previously indicated, the true percentage of bedload discharge that passes Yolo is uncertain, but it is thought to be at least 7 percent of the total sediment discharge. Hence, the estimate of the trap efficiency of the settling basin should be increased by this amount, which probably exceeds greatly any reduction of the ‘ estimate because of water-discharge differences. The difference between the suspended-sediment dis- charges at Yolo and at the weir, indicates that trap efficiency of the settling basin during the 1960—63 period ranged from 53 to 64: percent. The maximum water discharge that occurred at Yolo on the dates of sam- 99'9 I ' I I I I I I I I EXPLANATION Qw {61’s} , 99'5 _ Sept.18,1958 ————— 0 ————— No flow ///I’l T 99'0 E Jan.15, 1959 ——o——— 276 /// . — 980 w Feb. 16 —a—.— 12,800 [1+ # Feb. 17 —{j—._ 6,000 / 95 _ Mar. 18 — - +- —_ 109 /;/ fl Feb. 3. 1960 ______ 748 / / 90 T Feb. 9 —————————————— 7,540 " ///d/ - Oct. 8, 1963 ~——— No flow / 80 — Jan. 28, 1964 70 ~ 60 — 50 A 40 — 30— 20*“ PERCENTAGE OF PARTICLES FINER THAN INDICATED SIZE I‘I'JI I ILII 4 6 8 10 ‘ 20 4O 60 100 PARTICLE DIAMETER. IN MILLIMETERS FIGURE 31.—Sizedistributi0n curves of bed-material samples from Cache Creek at the Yolo sediment station. The samples were obtained at the time of each total-load measurement. CACHE CREEK DRAINAGE BASIN, CALIFORNIA pling at the weir was 11,800 cfs. Because suspended- sediment discharge increases with water discharge, the trap efficiency computed for this date indicates the sedi- ment deposition that results from large runoff events or, conversely, of the amount of sediment that passes through the settling basin and over the weir. The data show that 49 percent of the suspended sediment was trapped in the settling basin during this runoff event. It should be noted, however, that the moisture content of the settling basin immediately before large runoff events is of great importance; if the basin is almost dry, some net erosion of surface sediment may actually oc- cur, thus markedly lowering the estimated trap efficiency. More specific evaluation of the data is not possible because in addition to the qualification just noted, the absolute bedload discharge at Y010 and at the weir must be considered. The available data suggest, however, that approximately half of the suspended-sediment discharge, and perhaps 60 percent of the total sediment discharge, is trapped by the settling basin. CONCLUSIONS The mean annual runoff in the Cache Creek drainage basin during the 1960—63 period was 173,000 acre-feet less than the long-term, 60—year average. F low-dura-' tion data Show that there was an increase in 'the fre- quency of low-water flows in the upper and middle parts of the basin and a decrease in the frequency of high-water flows in all parts of the basin during the 1960—63 period. This runon deficiency is a logical con- sequence of a precipitation decrease during the period of study. Therefore, if the estimates of sediment dis- charge provided .in this report are extrapolated for planning purposes, they should be regarded as mini- mum values. This qualification assumes, of course, that the long—term climatic records are indeed indica- tive of future trends. Both the rate and absolute magnitude of suspended- sediment discharge increase with an increase in water discharge downbasin. These normal sediment-trans— port characteristics are altered by artificial controls at Capay. Diversion of surface water at this point pro- duces a reduction of sediment discharge below Capay. During the 1960—63 period, the total quantities of suspended sediment transported by North Fork Cache Creek and by Bear Creek were 476,700 and 174,800 tons, respectively. The suspended—sediment load was more A35 than 2 million tons above Rumsey and more than 3 mil- lion tons near Capay. The controls at Capay reduced the suspended-sediment load to slightly more than 2 million tons at Yolo. , Suspended-sediment discharge, and probably total sediment discharge as well, is affected by variations in environmental conditions within the basin. Apparently, because of geologic and topographic conditions, a 98-square-mile area between Rumsey and Capay con- tributes twice the quantity of sediment. that would be expected from proportional computations based on drainage area alone. This suggests that any future controls within the basin above Rumsey will not reduce the sediment discharge of Cache Creek below the instal- lation in strict accordance with such proportional computations. The bedload discharge of Cache Creek at the Yolo sediment station is approximately 7 percent of the total sediment discharge. Similar results are obtained from computations based on the assumption that instantane- ous values of water discharge approximate daily mean values, and computations that employ the method of subdivision and adjustment. Presumably this similar- ity exists because Cache Creek transports only a small percentage of its total load as bedload and, further, be- cause the average water discharge is fairly high. At the average water discharge value of 881 cfs, the vast bulk of the load is transported as suspended sediment; hence adjustments that involve correction of the esti— mated bedload fraction have little influence on the es- timated total sediment load. The total sediment load of Cache Creek during the 1960—63 period was 2,289,000 tons. This total load es- timate is limited primarily by the runoff deficit during the period of record; for extrapolation purposes it should be considered a slightly conservative estimate. The accuracy, however, is probably equal to that of the methods employed for sampling and computation. The trap efficiency of the settling basin below Yolo was estimated by combining the concentration of sus- pended sediment that passed through the basin with the water discharge measured at the Yolo station. The results indicate that the settling basin traps approxi- mately half of the suspended sediment that enters the basin, and, depending upon the true percentage of sedi— ment that is transported as bedload, the trap efficiency may equal or slightly exceed 60 percent under normal conditions. A36 REFERENCES Brice, J. C., 1953, Geologic map of the Lower Lake quadrangle, California: California Div. Mines and Geology Bull. 166, pl. 1. Colby, B. R., and Hembree, C. H., 1955, Computation of total sed- iment discharge, Niobrara River near Cody, Nebraska: U.S. Geol. Sudvey Water-Supply Paper 1357, 187 p. Einstein, H. A., 1950, The bed-load function for sediment trans- portation in open channel flows: US. Dept. Agriculture Tee. Bull. 1026, 71 p. (1951). SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS Jennings, C. W., and Strand, R. G., 1960, Geologic map of Cali- fornia, UkiahSheet: California Div. Mines and Geology. Lachenbruch, M. C., 1962, Geology of the west side of the Sacra- mento Valley: California Div. Mines and Geology Bull. 181, p. 53—66. / Lachenbruch, M. 0., Rogers, Donald, and Silcox, John,’ 1961, Geologic map of the Sacramento Valley: CalifOrnia Div. Mines and Geology Bull. 181, pl. 2. Langbein, W. B., and Schumm, S. A., 1958, Yield of sediment in relation to mean anual precipitation: Am. Geophys. Union Trans, v. 39, p. 1076—1084. 38°30' UNITED STATES DEPARTMENT OF THE INTERIOR PREPARED IN COOPERATION WITH THE STATE OF CALIFORNIA PROFESSIONAL PAPER 562— A GEOLOGICAL SURVEY DEPARTMENT OF WATER RESOURCES PLATE 1 123°OO' 122°3OI 122°00' 121°30' P I I i EXPLANATIO N SEDIMENTARY AND IGNEOUS AND METASEDIMENTARY ROCKS METAIGNEOUS ROCKS | E > ............ ‘— 0: Contact <1: <1: I) Z O >- Fault m >_ II §§ at; 9 739015, 3% S S D 0: O Drainage d1v1de 8%; I—ZUJ N E S . . [I < |_ O 5: Contlnental deposrcs m < E IIIIIIIIIIIIIIIIIIIIIIIIIII IIIIIHIIHII uumuu m m i— 3 Volcanic O Levee w I O rocks § w _ g e g l— > A 3 § 3 . . D: D: Sediment station N3 :7; Marine and nonmarine '|"_J < ll, deposits g .......... Re R 1-19.53}: 3 8 ..... U‘) R @ . D b E Marlne O C) deposits LIJ m , U R) S 1323;523:3737? Marine E S 33 :f:§:f:§:§:f:fzf:§:§ depOSItS L” 3,: ;;;:-:-:~:-:-:-:-:- undivided 5 O Marine 9 k deposits 8 O 8 Ultramafic E rocks, partly Knoxville Q serpentinized Formation U) U) SE \ :) _) Franciscan Formation Rocks, undivided — 39°OO’ Knights x,“ Landing NIH, a 124u 123" I 22222222222 .......... 7 38°45’ 5:3, I ~/ 1 9" , . , o 1 39. '1‘ i “ ’ WM/ 5, g“ SACRAMENTO W 118 e 38‘» i ’T’ 7 ~ 3 ;:~:-:-:-: SAN FRANCISCO ¢ ‘ ak a do: , ...... “a \ o .._._,:.:.:.:.'_.:.:, :::: a .......... a V 4» .............................. 20 o 20 100MILES CANAL TO PUTAH CREEK INDEX MAP SHOWING AREA OF THIS REPORT 38 °30’ I 123°00' Base from Army Map Servuce 1:250 000 series: Ukiah, 1960; Sacramento, 1961; and Santa Rosa, 1964 122°30’ 122000, MAP OF THE CACHE CREEK DRAINAGE BASIN IN THE COAST RANGES WEST OF SACRAMENTO, CALIFORNIA SHOWING THE GENERAL GEOLOGY AND THE LOCATION OF SEDIMENT SAMPLING STATIONS SCALE 1:250 000 5 O 5 10 15 20 25 MILES I—I I—I I—l I-—-—-————l n 5 O 5 10 15 20 25 KILOMETERS I l—-———I l——-—-l IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII “‘79667W66152 121°30' Compiled from geologic maps by J. C. Brice. 1953; C. W. Jennings and R. G. Strand, 1960; M. C. Lachenbruch, Donald Rogers, and John Silcox, 1961 2E 75/ ,1 MY my ”"5 Flume Experiments on ¥ , the Transport of a , Coarse Sand MS- L/ GEOLOGICAL SURVEY PROFESSIONAL PAPER 562—B - N. ‘o Flume Experiments on the Transport of a Coarse Sand By GARNETT P. WILLIAMS SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS GEOLOGICAL SURVEY PROFESSIONAL PAPER 562—B UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON :1967 UNITED STATES DEPARTMENT OF THE INTERIOR STEWART L. UDALL, Secretary GEOLOGICAL SURVEY William T. Pecora, Director For sale by the Superintendent of Documents, US. Government Printing Office Washington, DC. 20402 - Price 30 cents (paper cover) CONTENTS Page Symbols ___________________________________________ IV Results ____________________________________________ Abstract ___________________________________________ B1 General ________________________________________ Introduction _______________________________________ 1 Sediment-transport rates _________________________ Equipment and application __________________________ 2 Relations of variables ........................... Flume _________________________________________ 2 Surface velocity __________ . ______________________ Water circuit and discharge measurement __________ 2 Comparison With data 0f Gilbert and Murphy """ . . Bed forms _____________________________________ Sediment mfeed """""""""""""""""""" 2 Interrelations between characteristics __________ Sediment-transport measurement """"""""" 3 Characteristics related to fluid flow strength____ Sediment ----------------------------------------- ,3 Characteristics related to sediment-transport Procedure _________________________________________ 3 rates ____________________________________ Initiation of runs and attainment of equilibrium con- Conclusions ________________________________________ ditions ______________________________________ 3 Description of bed configuration, by run _______________ Measurements __________________________________ 5 References _________________________________________ ILLUSTRATIONS FIGURES 1—16. Graphs: 1. Size analysis of sand ______________________________________________________________________ 2. Power versus transport relation ____________________________________________________________ 3. Shear (-yDS) versus transport relation _______________________________________________________ 4- Shear (—yRS) versus transport relation _______________________________________________________ 5. Mean velocity versus transport relation _____________________________________________________ 6. Regime bed factor versus transport relation _________________________________________________ 7- Transport relations adjusted for flume wall drag (Einstein method) _____________________________ 8. Discharge versus transport relation _________________________________________________________ 9. Slope versus transport relation _____________________________________________________________ 10. Relations of slope to discharge and mean velocity- __ __ ________________________________________ 11- Surface velocity versus transport relation _____________________________________________________ 12- V/V. relation for various depths ___________________________________________________________ l3. Relations of surface velocity to slope and discharge ___________________________________________ 14. Comparison of stream power versus transport relations with data of Gilbert and Murphy _________ 15. Comparison of shear versus transport relation with data of Gilbert and Murphy ................. 16- Mean velocity versus shear (DS) relations compared with data of Gilbert and Murphy ............ 17- Sketch Showing pattern of typical meandering scars __________________________________________________ 18-25. Graphs: 18- Variation in bed-form height with travel velocity _____________________________________________ 19. Variation in bed-form wavelength with travel velocity ________________________________________ 20. Bed-form height versus measures of flow strength ____________________________________________ 21. Bed-form wavelengths versus measures of flow strength _______________________________________ 22- Bed-form velocity versus measures of flow strength ___________________________________________ 23- Relation of bed-form height to sediment-transport rate ________________________________________ 24. Variation in bed-form velocity with sediment-transport rate ___________________________________ 25- Comparison of computed versus measured transport rates _____________________________________ III Page B6 6 6 13 16 18 20 22 23 25 28 28 30 Pase B3 9 TABLE CONTENTS TABLES 1. Experimental results _______________________________________________________________________________ 2. Computed quantities _______________________________________________________________________________ 3. Hydraulic radius, shear stress, and stream power corrected for wall drag by methods of Einstein and of Johnson and Brooks ___________________________________________________________________________________ 4. Bed-form measurements ____________________________________________________________________________ SYMBOLS Symbol Dimensions a Coefficient in velocity-shear equation ____________________________________________ L1/2T'l b Exponent in velocity-shear equation. 0 Bed-form velocity or rate of travel ______________________________________________ LT“ C Chezy C’ _____________________________________________________________________ L1/2T'l D Depth of water _______________________________________________________________ L f Darcy-Weisbach f. F Froude number. 9 Acceleration due to gravity ____________________________________________________ LT—2 h Bed—form height ______________________________________________________________ L i Sediment-transport rate _______________________________________________________ IV'T‘lL‘l l Bed-form length (crest to crest) ________________________________________________ L n Manning n __________________________________________________________________ L”6 Q Water discharge ______________________________________________________________ L3 7“1 Q5 Discharge adjusted to eliminate that part of flow aflected by sidewalls ______________ L’T‘l R Hydraulic radius ______ ' _______________________________________________________ L Rb Hydraulic radius of bed (a theoretical hydraulic radius excluding that part of flow cross section which is influenced by sidewalls) ________________________________________ L S Slope (ft per ft). t Temperature (degrees centigrade). V Mean water velocity __________________________________________________________ LT—l Vs Surface velocity of water ______________________________________________________ LT—l W Width of channel _____________________________________________________________ L 7 Specific weight of water (=62.4 lbs per cu ft) ____________________________________ FL—a Page B7 8 13 22 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS FLUME EXPERIMENTS ON THE TRANSPORT OF A COARSE SAND By GARNETT P. WILLIAMS ABSTRACT A newly constructed 52-foot laboratory flume was used to study sediment transport in a series of 37 runs with a coarse (1.35 mm) sand at water depths of 0.1, 0.3 and 0.5 foot. The data obtained during these runs show that relations between variables can be clarified by maintaining a constant flow depth. For the range of conditions examined, unique relationships were found between any two variables as long as depth was constant. The bed forms ranged from an initial plane bed to antidunes, but ripples and a plane-bed transition from dunes to antidunes did not occur. The data obtained by Gilbert in 1914, using a. comparable grain size, agree with the results of the present study. One method of determining the critical flow strength needed to initiate sediment movement indicates that, with the flume and sediment used in this study, the critical flow strength is determined not only by such factors as sediment characteristics and bed slope but also by water depth. (An exception to this last statement was found when shear stress expressed as 7R8 was used as the measure of flow strength.) Surface velocity is related to all other variables, particularly to rate of sediment transport. INTRODUCTION A laboratory flume was constructed in 1964 by the US Geological Survey in Washington, D.C., to ex- plore various problems in sedimentology, geomorphol- ogy, and hydrology; its initial use is in the field of sediment transport. Studies of the movement of debris by water aid in the interpretation of numerous geologic processes, pollution, filling of dams and reser- voirs, and other phenomena. Use of the laboratory permits the control of many variables which usually cannot be controlled in the natural environment. Although rivers frequently carry coarse sand and gravel, most previous laboratory studies have dealt with medium and fine sands, with particle diameters less than 1.0 mm. Therefore, coarser grain sand was used in the present sediment-transport experiments. Many of the available data on transport of coarse- grained sand are from the work of G. K. Gilbert (1914) and of E. C. Murphy, who performed most of the experiments in the Gilbert study. All laboratory investigations require a decision as to which of the pertinent variables should be controlled by the operator. In flume studies, which attempt only to simulate natural alluvial conditions, the large number of possibly relevant variables can usually be limited to sediment characteristics (such as size, size distribution, shape, density), sediment-transport rate, water dis— charge, mean velocity, depth, and bed slope and rough- ness. Other factors, such as water temperature, may have some influence under certain conditions. The sediment characteristics are usually predetermined by the operator and, thus, must be classified as independent variables. In the present study, the sediment-trans- port rates and the water depths (0.1, 0.3, and 0.5 ft) were also controlled by the operator. The dependent variables, therefore, were water discharge (or mean velocity, at constant depth and width), slope, and bed roughness. (True independence or dependence of vari- ables in sediment transportation is questionable, for the role of each variable in governing other variables or merely reacting to changes in other variables is still poorly understood. Thus, describing a variable as completely dependent or completely independent is both difficult and risky.) The purposes of this report are to describe the equip- ment and procedures used in a series of sediment- transport experiments, to present the data of the initial group of a continuing series of experiments, and to examine some of the observed relationships between variables. Certain features of these experiments differ from most previous fiume studies on sediment trans- port, and the data collected during this study will therefore supplement the published information. For example, the use of coarser grained sediment and con— stant depth in a nonrecirculating flume in this study will provide new data. Although a constant depth is commonly maintained in flume studies in which the water and sediment are continuously recirculated, the writer knows of no studies involving nonrecirculating flumes in which the water depth was held constant. This investigation was begun under the supervision of Luna B. Leopold, to Whom thanks are given for valuable assistance and suggestions throughout the Bl B2 study—from design and construction of equipment to completion. William W. Emmett assisted in planning the laboratory and performed a major role in the design and construction of the laboratory equipment. Ralph A. Bagnold provided valuable suggestions on various aspects of the investigation. Additional assistance in construction and in some preliminary runs was given by O. Lehn Franke. EQUIPMENT AND APPLICATION FLUME The test section of the flume was 52 feet long. The maximum usable width was 4 feet, but for the present experiments an inner trough 1.0 foot wide was used. This trough had transparent plexiglas walls 15 inches high and a wood floor. At a point 2.0 feet from the downstream end of the flume the plexiglas walls were hinged vertically. Known collectively as the tailgate, these hinged sec- tions could be converged at the end of the flume to dam the water to any desired level. This method was used to make the water depths as uniform as possible. On top of each of the outer (permanent) flume walls was a rail traversing the entire flume length. On these rails rode a carriage to which was fixed a point gage for depth measurements. The height of the gage tip rela- tive to the rails was read directly from an adjacent scale, to within 0.001 foot. The slope of the flume was adjustable from horizontal to about 0.02 foot per foot. The test section was hinged at the upstream end. Two large chain hoists, suspended from an independent permanent steel brac- ing, bore the weight of the flume at the downstream end. The desired slope was obtained by raising or lowering the downstream end of the flume, using these chain hoists. WATER CIRCUIT AND DISCHARGE MEASUREMENT A large sump located below the floor level contained the water supply for the flume. From this sump the water was pumped to a constant-head tank located high on the wall of the building. The water then flowed to the flume by gravity through either or both of two pipes (one 6 in. in diameter, the other 4 in.). The amount of water was regulated by a valve in each pipeline. Excess water was allowed to flow from the constant-head tank directly back to the sump. Also placed within each line, between the constant- head tank and the flume, was a bend meter for measur- ing the discharge. This was a common pipe elbow with holes drilled through the wall at the inner and outer vertices of pipe curvature. These holes were connected by tubing to a manometer, and the difference in pressure between the inside and outside parts of the SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS bend was a direct indication of the discharge flowing through the elbow.1 From the constant-head tank, water passed through pipes to a stilling tank (4 ft X 4 ft x 3.4 ft deep) at the head of the flume. From this tank it flowed through a horizontal preliminary channel 1 foot wide and 4 feet long, on the same level as the upstream end of the flume. In passing through this preliminary channel the water was screened by wire mesh to eliminate large- scale disturbances in the flow. The water next went through a 4—foot-long zone where the sediment was fed into the system, and then entered the 52-foot-long flume test section. As the water-sediment mixture left the flume at the downstream end, it was directed into a collection box. This box had compartments in which the sediment was trapped. The excess water flowed over a lower wall of the box and was channeled back to the sump, thereby completing its circuit. SEDIMENT INFEED Sediment was fed into the stream by gradually raising a supply of sand above the channel level and permitting the flowing water to scour the material off the rising floor and into the test section. The technique used proved to be satisfactory, except for a minor amount of sediment leakage. The sediment infeed area was a bin 4 feet square and 3.5 feet deep located immediately upstream from the flume test section. Within the bin was a false bottom which could be cOntinuously raised or lowered by means of two screw jacks run by a motor above the bin. Reduction gears between the motor and the screw jacks and a speed control on the motor provided a wide range of rates at which the false bottom could be lifted. The dial setting on the motor-speed control was a direct indication of the rate at which the false bottom was being raised. Two wooden walls, 4 feet long and 1 foot apart, were fixed onto the false bottom. These were placed in such a position that a straight channel 60 feet long was obtained; the last 52 feet was the flume test section, and the first 8 feet was the preliminary channel and the wooden walls of the infeed section. Sand was loaded into the 4-square-foot section be- tween the walls of the infeed bin. After the loading, the top of the sand was placed at the same level as the top of the adjacent sand surface in the flume test sec— tion. As the area within the wooden walls and the rate at which this area (that is, the false bottom) was being raised were known, it was easy to compute the 1 Calibration was done at the Hydraulics Laboratory of the Georgia Institute of Technology, and the author gratefully acknowledges that department’s kindness in permitting the use of their facilities. FLUME EXPERIMENTS ON THE TRANSPORT OF A COARSE SAND rate at which sediment (immersed weight per unit time) was being exposed to the flow. The dial setting on the motor-speed control was therefore directly related to rate of sediment infeed. As the false bottom slowly rose, some sand leaked out between the upstream and downstream ends of the false bottom and the walls of the bin. During the course of the investigation this condition proved im- possible to correct and served to detract somewhat from an otherwise satisfactory infeed technique. It is believed, nevertheless, that the sand was being intro- duced into the fiume at an approximately constant rate so that the disadvantage was an inability to state exactly what the rate of infeed was at a given dial setting. SEDIMENT-TRANSPORT MEASUREMENT The water-sediment mixture left the flume and was directed into a partitioned collection box just below the downstream end of the flume. The sediment settled to the bottom of this box, and the excess water flowed over the top of one wall and back into the main cir- cuit. For some of the runs, the water-overflow region of the collecting box was covered with a fine wire screen to insure that no sand escaped from the box. (Little difficulty was encountered, however, because the sand used in the tests was fairly coarse.) The measured sediment—transport rate represented the total quantity of sand transported, and no dis- tinction could be made between bedload and suspended load. The collection box rested on a large floor scale, and the amount of sand and water in the box was weighed directly at the beginning and end of each run. The gain in sediment (immersed weight) and the time interval between weighings provided the rate of trans- port. This rate, accordingly, is expressed in pounds (immersed weight) per second per unit channel Width. During the actual weighing process, the water—sediment mixture leaving the flume was diverted into a by—pass trough so that the weighing could be done undisturbed. SEDIMENT The sediment used in the experiments was nearly 100 percent quartz sand of a rather narrow size range (fig. 1). This range was about 0.60—2.50 m, in terms of sieve aperture, and the median size was 1.35 mm. A Visual-accumulation-tube size analysis was also per- formed, in which the sizes are expressed in terms of fall diameter (that diameter of a quartz sphere having the same fall velocity as a sand grain). The range meas- ured by this method was 0.46—1.25 mm, and the median fall diameter was 0.76 mm. The specific gravity and porosity of the material were 2.66 and 0.445, respectively. B3 100 I I f‘l’lll Visual —accumulation- l tube analysis 1 \ 80- 0» o I PERCENT FINER THAN INDICATED SIZE 4:. o | 20— \Sieve analysis | | 0.5 1.0 2.0 3.0 PARTICLE DIAMETER, IN MILLIMETERS FIGURE 13~Size analysis of sand. The tall velocity was determined in a water—filled plastic tube that was 1.35 meters long and had an inner diameter of 29.6 cm. Particles were timed individually over a distance of 100 cm, after allowing 20 cm for the period of acceleration. The average rate of fall for 75 randomly selected grains was 14.5 cm per sec (centi— meters per second) at a water temperature of 315° C. A correction for temperature (U.S. Inter-Agency Comm. Water Resources, 1957) would adjust this rate to 14.2 cm per sec at 24° C. PROCEDURE INITIATION OF RUNS AND ATTAINMENT OF EQUILIBRIUM CONDITIONS To begin a run, the operator first decided upon a sediment transport rate and depth (the independent variables). An estimate of the probable discharge and equilibrium slope was then made, and the flume was set at this estimated slope to shorten the time needed to reach equilibrium conditions. Sediment was spread evenly over the floor of the flume to a depth of about 1%2 inches. B4 The sediment infeed and discharge were then turned on. By means of several vertical scales at the flume wall a rough estimate of the depth and downstream change (if any) in depth was obtained. If the flow depth was obviously not within an appropriate range (described below), the discharge was altered to change the depth. If, on the other hand, the depth appeared to be within the proper range, no change in discharge was made. The tailgate was adjusted when necessary to raise or lower the water level at the downstream end, until the depth appeared to be uniform throughout the flume. The next step in the procedure was a rather detailed measurement of depth, slope, and degree of uniformity of depth throughout the flume. This was done by making longitudinal profiles of both the water surface and the bed surface along the center line of the channel. Depth readings were taken with the point gage on each of these surfaces. The horizontal interval at which readings were taken was generally 4 feet, though some- times 2-foot intervals were used. The readings of depth and distance downstream were plotted on arith- metic scales, and straight lines of best fit were estimated visually for the bed and water surfaces. If these straight-line profiles diverged or converged in a down- stream direction, the tailgate opening was changed to make depth uniform. After any change in tailgate setting, additional profile measurements were made, until the lines on the graph indicated a uniform flow. The perpendicular distance between the two parallel profile lines was taken as the depth of flow. The rangb of depth tolerance was about :I:7 percent of the desired depth because experience has shown that errors involved in depth measurements at the higher manageable dis- charges did not justify attempts at greater accuracy. If necessary, the discharge was adjusted to bring the depth into the range of tolerance; however, it was frequently unnecessary to change the original setting. Once the desired depth and a uniform flow were established, the slope was allowed to adjust until it became stabilized. Changes in slope were determined by making profile measurements at intervals ranging from 20 minutes to several hours. In many runs no change in slope occurred, indicating that the equilibrium slope was the same as that of the flume itself. In most of the other runs a slight increase in slope, com- pared to that of the flume, took place. If the slope changes brought about a decrease or, increase in water depth so that depth exceeded the tolerance range, the discharge was adjusted accordingly. Any such alteration in discharge necessitated additiona profile measurements, possible tailgate changes, and periods of waiting for any further slope changes, unti equilibrium was established. ‘ SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS On a few occasions the slope ceased changing and equilibrium appeared to have been reached; the sub- sequent profiles, however, indicated that the bed was aggrading or degrading uniformly throughout the flume. Repeat profiles were therefore made in nearly all runs to insure not only that the slope had ceased changing but that the bed and water surfaces were occupying the same spatial elevation with time. The bed elevation (relative to the fiume rails) at a given downstream location had to be within i3 percent of the elevation obtained from the previous profile. The criteria for equilibrium, in other words, were (a) con- stant ‘slope with time and (b) no net gain or loss of sediment in flume, with time. Both of these factors were deduced from the profiles. If the profiles indicated that the flume was gaining sediment even though the bed slope was not changing, this was interpreted as a need for greater flow strength to accommodate a given sediment infeed. The usual procedure was to open the tailgate. This lowered the water depth downstream and caused scour, so that the overall bed slope was increased. Conversely, if the flume was losing sediment in spite of a constant slope, the tailgate was closed. Usually when this problem occurred, the sediment infeed became depleted before equilibrium conditions could be established, and a new run had to be made. The usefulness of the attempted procedure for arresting bed-elevation changes at con- stant slope was therefore not conclusively determined. Most instances of bed-elevation change at constant bed slope occurred in runs at the 0.1—foot depth; in fact, it was difficult to obtain equilibrium conditions at this depth, especially at lesser sediment transport rates. (Rate of sediment supply of course has a direct influence on time required for slope readjustments.) At the 0.1—foot depth, the water—surface profile was particularly sensitive to minor changes of the tailgate and discharge. In a few runs, many days were needed to attain equilibrium at a depth of 0.1 foot. Dis- charge could generally be adjusted rather early in the experiment, whereas the correct tailgate setting often required considerable time and trial-and-error methods. After some points on the sediment-transport graph had been obtained, the process was somewhat easier, because approximate tailgate settings could be ex- trapolated before the water was turned on. It was necessary, therefore, to establish a consistent experi- mental procedure. The writer suspects that the cor— rect tailgate setting can be influenced by the depth to which the sediment is laid down on the flume bottom prior to a run. Generally, the time needed to reach equilibrium in the experiments varied from about one half hour to many days. (This excludes nights, at which time FLUME EXPERIMENTS ON THE the pump was always stopped.) Often a run could be completed in a single day or less. The following factors greatly facilitated the attainment of equilib- rium: 1. A high rate of sediment transport (a high value of the fluid flow strength). 2. Depths of 0.3 and 0.5 rather than 0.1 foot. 3. An accurate estimate of the flume slope setting. Secondary factors which could expedite attainment of equilibrium were an appropriate initial choice of water discharge to provide the desired depth, and good judg- ment in determining the tailgate opening. By far the greatest hindrance to a prompt attainment of equilib- rium was a shallow depth (0.1 ft) or some feature associated with this depth. MEASUREMENTS As soon as equilibrium conditions had been realized, the run was started. This involved a measurement of the following: 1._Discharge, as read from the manometer. This was recorded at the start and finish of each run. 2. Water temperature, also measured at the start and finish of each run. 3. Slope: (a) The slope of the flume (or more precisely, that of the flume rails upon which the point gage rode) was determined by setting up a surveyor’s level independent of the flume structure and measuring the vertical drop in a known dis- tance downstream. The average of two mea- surements was taken as the final value. (b) The slope of the bed (and water surface) relative to the flume rails was taken from the plotted profiles. Horizontal profiles on the graph in- dicated that the bed and water surfaces were parallel to the fiume rails. The extent to which the lines departed from the horizontal on the graph reflected the extent to which their inclination departed from that of the flume rails. Slope relative to flume rails and slope of flume rails themselves were combined to give the actual bed (and water surface) slope. 4. Depth, from profiles described in 3b. 5. Sediment-transport rate. An effort was made to collect sediment in the collection box for as long a period as possible. To ensure a representative sediment sample, this period was always long enough to allow at least several (and usually many) bed forms to move out of the flume and into the collection box. This procedure helped obviate possible error due to variations in the transport rate between the trough and the crest of bed forms, 248—117 0—67—2 TRANSPORT OF A COARSE SAND B5 error which was suspected to be the cause of point scatter in sediment-transport diagrams. 6. Bed-form characteristics: (a) General type of bed form and other note- worthy features. (b) Wavelengths. A rapid traverse was made of the fiume length, and in this traverse the location of every well-defined bed-form crest was recorded. From these data an average wavelength could be obtained, as well as an estimate of the degree of uni— formity of wavelengths along the flume. (c) Trough-crest height, perpendicular to bed slope (usually estimated from a scale on the flume wall). (d) Rate of movement downstream. A single representative bed feature was selected and timed while it passed over a known distance. Occasionally, several bed forms were timed individually and an average rate of move- ment recorded. 7. Surface velocity. Two or three small pieces of wood were individually timed for rate of move- ment as they floated along the water surface. (Most pieces were shaved from a stick with a pocket knife and were 1—2 in. long but relatively narrow and flat. In some of the runs at the greater depths, small blocks of woods measuring at most 3 in. X 1 in. X 1 in. were used.) The average velocity of the group was taken as the final value. This surface velocity was multiplied by 0.80 to provide a rough estimate of the mean flow velocity, as is explained in the results section. (The actual value of mean velocity was obtained by dividing discharge by cross—sectional area, based on depth as given in profiles.) 8. Sediment samples. Material in the collection box and material left on the bed were sampled after the completion of the run. The samples were dried and then sieved on a Ro-Tap. (The aver- age of 36 such analyses provided the sediment-size characteristics described.) Photographs were taken, usually during and after the run. Those taken during the run were made from a side view, whereas those taken after the water had drained out of the flume depicted an upstream view. A pitot static tube was used for velocity measure- ments in some early runs, but this practice was soon discontinued. Because the bed and water surfaces were often irregular, the vertical height at which the readings were being taken was uncertain. Secondly, any reading was greatly affected by the proximity of a bed form. Finally, the presence of the tube near the bed caused scour in the sediment below the tube, and B6 the effect of this scoured region on the velocity value could not be determined. The measured values for several of the variables were checked by various methods. The mean velocity as obtained from the discharge, and depth was com- pared with the mean velocity as estimated from float measurements. This same estimate of mean velocity could be used with the discharge to provide a check on the depth as obtained from the profiles. Finally, the attainment of equilibrium and the slope value were verified by repeated profile measurements. Repeat readings were taken on many of the variables as a standard procedure. .Runs in which mean flow velocities were greater than about 3.5 ft per sec could not be made with the present equipment. Faster velocities could not be investigated because the supply of sediment in the submerged infeed bin was depleted before all of the necessary experimental measurements could be completed. Also, at the 0.5- foot depth the maximum water capacity of the flume system was nearly reached. No convenient method was available for maintaining a constant water temperature. In most runs the water temperature ranged from 11° to 27°C. Temperature during any run varied only a degree or two, if at all. A significant temperature effect on rate of sediment transport is doubtful for the grain sizes used in this study. According to Colby and Scott (1965), the percentage change in bed—material discharge that, accompanies a particular temperature change is gen- erally small for particles 1 mm in diameter or larger. Reproducibility at depths of 0.3 and 0.5 foot was excellent. Attempts were not made to reproduce any of the runs at the 0.1-foot depth. Run 23 was conducted with the flume horizontal rather than at a slope. This procedural deviation was made because colleagues suggested that the setting of the flume at some particular slope (prior to the run) was prejudicing the final slope value. That is, they felt that a range of equilibrium slopes was possible; the measured slope value might be a minimum possible slope, a maximum possible slope, or someintermediate slope, depending on how the operator performed the experiments. For a given depth and velocity, the various possible values of slope could presumably be accommodated by changes in the bed roughness. Run 23 satisfied the stated prerequisites for equilibrium and is therefore included in the results, but no insight was obtained into a possible range of slope values. The physical conditions within the flume during run 23 unavoidably difl'ered in one respect from the conditions of all other runs. The entrance region in the flume was positioned vertically in such a way that after the sand wedge had formed in the flume, the water passing SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS through the infeed section had to flow very slightly uphill before coursing over the sand in the flume. This difference in conditions was sufficient to cause diagrams for run 23 to be distinguishable from diagrams for other runs made at a similar depth in many of the illustrations presented later in this report. The horizontal flume showed the following disadvantages: 1. The total time needed to conduct a run increased about tenfold. Some of the extra time was re- quired for slope adjustments by the water-sedi— ment mixture, and some was required for tempo- rarily stopping the run to refill the sediment-infeed bin. 2. The maximum discharge capacity of the flume was drastically reduced by the large amount of sand that accumulated in the flume. 3. About 1%—2 times as much sediment was needed to perform a run, because so much sediment was stored in the wedge within the flume. RESULTS GENERAL The measured and computed values for all runs, excluding bed-form data, are listed in tables 1 and 2. In these tables the runs made at each of the three depths have been arranged in order of increasing sedi- ment-transport rate. The bed configurations ranged from plane bed to antidunes. A plane-bed stage be- tween dunes and antidunes did not occur. (Bed forms are discussed later.) Sediment movement was always in the form of bedload, according to visual observation, and little if any material was transported as suspended load. The size distribution of material caught in the collection box did not difl’er significantly from that of material remaining on the flume bed. SEDIMENT-TRANSPORT RATES Various measures of the strength of flowing water can be related to the rate at which sediment is trans- ported. Examples of such measures are the following: 1. Stream power. The power for a whole channel can be defined as the product of the weight of fluid (in pounds) flowing per second and the energy per unit weight of fluid (in foot pounds per pound). This product can be written as 'yQXenergy, where 'y=specific (unit) weight of water and Q=dis- charge of water. The dimensions are FLT—1. When the flow is uniform the energy loss per foot of channel length is given by the slope S, so that the power per unit length of channel becomes VQS (dimensions FT'I). The stream power per unit bed area is then 708/ W, where W: channel width. The dimensions are FL‘lT‘ 1, pounds per second FLUME- EXPERIMENTS ON THE TRANSPORT OF A COARSE SAND B7 TABLE 1,—Experimental results Sediment transport Run Q S D V R t V. (cfs) (ft per ft) (ft) (fps) Measurement 2' (ft) (°C) (fps) period (lbs per sec (sec) per It) 1 ______________ 0. 127 0. 00411 0. 100 1. 27 17, 940 0. 00145 0. 083 18. 5 1. 68 2 ______________ . 142 . 00495 . 100 1. 41 10, 140 . 00291 . 083 19. 2 l. 89 3 ______________ 158 . 00590 . 102 1. 55 5, 400 . 00593 . 085 21. 0 2. 08 4 ______________ 154 . 00751 . 101 1. 53 2, 460 . 00935 . 084 12. 5 2. 22 5 ______________ . 166 . 01082 . 095 1. 75 1, 440 . 01980 . 080 11. 9 2. 41 6 ______________ 191 . 01280 . 101 1. 89 1, 684 . 03444 . 084 17. 6 2. 67 7 ______________ 220 . 01505 . 099 2. 22 2, 183 . 05772 . 083 15. 5 2. 86 8 ______________ 233 . 01992 . 094 2. 48 960 . 11200 . 079 23. 5 3. 39 9 ______________ 292 . 02218 . 097 3. 01 473 . 16810 . 081 24. 7 3. 85 10 _____________ . 405 . 00110 . 297 1. 36 24, 180 . 00025 . 186 21. 3 1. 56 11 _____________ . 440 . 00121 . 314 1. 40 26, 040 . 00031 . 193 22. 7 1. 67 12 _____________ . 440 . 00136 . 313 1. 41 23, 820 . 00054 . 193 19. 8 1. 76 13 _____________ . 438 . 00162 . 294 1. 49 23, 400 . 00107 . 185 18. 6 1. 85 14 _____________ . 452 . 00182 . 294 1. 54 12, 240 . 00171 . 185 16. 5 1. 87 15 _____________ . 470 . 00200 . 300 1. 57 14, 040 . 00256 . 188 18. 4 2. 06 16 _____________ . 498 . 00210 . 303 1. 64 6, 360 . 00361 . 189 17. 2 2. 16 17 _____________ . 503 . 00211 . 304 1. 65 2, 400 . 00375 . 189 17. 8 2. 10 18 _____________ 512 . 00236 . 295 1. 74 5, 040 . 00585 . 186 17. 1 2. 14 19 _____________ 530 . 00272 . 294 1. 80 3, 620 . 00925 . 185 17. 8 2. 30 20 _____________ . 551 . 00318 . 290 1. 90 2, 340 . 01090 . 183 16. 1 2. 31 21 _____________ . 570 . 00397 . 288 1. 98 2, 160 . 01597 . 183 16. 2 2. 50 22 _____________ . 650 . 00509 . 287 2. 26 1, 980 . 03156 . 182 15. 9 2. 92 23 _____________ . 790 . 00471 . 298 2. 65 2, 940 . 03262 . 187 30. 8 2. 86 24 _____________ . 741 . 00557 . 297 2. 49 2, 130 . 03826 . 186 12. 3 2. 92 25 _____________ . 794 . 00643 . 306 2. 59 1, 353 . 04805 . 190 15. 5 3. O5 26 _____________ . 860 . 00721 . 307 2. 80 960 . 06875 . 190 21. 8 3. 33 27 _____________ 1. 050 . 00824 . 324 3. 24 720 . 09722 . 197 23. 5 3. 67 28 _____________ l. 120 '. 01088 . 321 3. 49 510 . 16280 . 194 25. 0 3. 74 29 _____________ . 845 . 00137 . 509 1. 66 14, 040 , . 00203 . 252 21. 0 1. 91 30 ............. . 795 . 00133 . 485 1. 64 9, 180 . 00207 . 246 26. 0 1. 92 31 _____________ . 866 . 00144 . 505 1. 72 10, 020 . 00288 . 251 22. 9 1. 97 32 _____________ . 905 . 00172 . 517 1. 75 8, 460 . 00479 . 254 23. 6 2. 02 33 _____________ . 960 . 00184 . 512 1. 87 18, 420 . 00610 . 253 23. 2 2. 25 34 _____________ . 958 . 00216 . 502 1. 91 3, 840 . 00716 . 250 17. 9 2. 20 35 _____________ l. 050 . 00251 . 517 2. 03 6, 300 . 01128 . 254 18. 7 2. 38 36 _____________ l. 100 . 00314 . 504 2. 18 2, 640 . 01970 . 250 20. 8 2. 54 37 _____________ l. 320 . 00416 . 510 2. 59 1, 800 . 03333 . 252 20. 8 3. 14 per foot; these same units are used to measure the sediment-transport rate. 2. Shear stress based on depth. The shear, or tractive force, exerted on a unit bed area is commonly defined as the weight of the water above the unit bed area times the slope of the channel. The volume of water (areaXdepth) above a unit bed area will be numerically equal to the depth of the water D, and the weight will therefore be given by 7D (dimensions FL‘”). The shear per unit bed area is therefore yDS, in pounds per square foot. 3. Shear stress based on hydraulic radius. For very wide channels the depth is equal to the hydraulic radius B, so that the shear stress over a unit bed area would be 7R8. The shear stress com- puted in this manner is assumed to represent an average shear per unit area of channel boundary. However, for narrow sediment-bearing channels with smooth sidewalls the shear probably is not equally distributed over the walls and floor of the channel; the computed shear stress is then of questionable value. 4. Mean water velocity V, defined as Q/WD. 5. Regime theory bed factor, Vz/D. (Except for a gravitational constant 9, this is the square of the Froude number F, where F: V/W) No single measure of flow strength has yet gained widespread acceptance. A meaningful comparison might be obtained by relating the sediment-transport rate (1‘) to each of the measures listed above. The relations are shown in figures 2—6. Several features are immediately noticeable in these diagrams. First, if depth is held constant, in any plot the data for any chosen depth fall on a single curve and show very little point scatter. This fact should be emphasized because it suggests that permitting the depth to vary may well cause much of the scatter found in sediment-transport diagrams. (Although it B8 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS TAB LE 2.—C’omputed quantities Run 08 (X 103) RS (X 103) DS (X 103) V1/D W/D V/V. Chezy C Darcy- Manning n Froude No. Weisbachf F l __________ 0. 522 0. 342 0. 411 16. 1 10. 00 0. 76 68. 7 0. 0546 0. 0142 0. 71 2 __________ . 703 . 412 . 495 19. 9 10. 00 . 75 69. 5 . 0533 . 0141 . 79 3 __________ . 932 . 500 . 602 23. 6 9. 80 . 75 69. 2 . 0537 . 0142 . 86 4 __________ 1. 16 . 631 . 758 23. 2 9. 90 . 69 61. 0 . 0692 . 0161 . 85 5 __________ 1. 80 . 863 1. 03 32. 2 10. 52 . 73 59. 5 . 0727 . 0163 1. 00 6 __________ 2. 44 1. 075 1. 29 35. 4 9. 90 . 71 57. 6 . 0775 . 0170 1. 05 7 __________ 3. 31 1. 243 1. 49 49. 8 10. 10 . 78 63. 1 . 0647 . 0155 1. 25 8 __________ 4. 64 1. 576 1. 87 65. 4 10. 63 . 73 62. 5 . 0660 . 0155 '1. 43 9 __________ 6. 48 1. 800 2. 15 93. 4 10. 30 . 78 71. 0 . 0511 . 0137 1. 70 . 445 . 205 . 327 6. 2 3. 36 . 87 95. 1 . 0284 . 0117 . 44 . 532 . 233 . 380 6. 2 3. 18 . 84 91. 5 . 0307 . 0123 . 44 . 598 . 262 . 426 6. 4 3. 19 . 80 87. 0 . 0339 . 0129 . 44 . 710 . 300 . 476 7. 6 3. 40 . 81 86. 1 . 0347 . 0130 . 48 . 823 . 337 . 535 8. 1 3. 40 . 82 83. 7 . 0367 . 0133 . 50 . 940 . 375 . 600 8. 2 3. 33 . 76 80. 9 . 0393 . 0138 . 51 1. 05 . 396 . 636 8. 9 3. 30 . 76 84. 5 . 0360 . 0133 . 53 1. 06 . 398 . 641 9. 0 3. 28 . 79 82. 9 . 0374 . 0135 . 53 1. 21 . 438 . 696 10. 3 3. 38 . 81 83. 3 . 0371 . 0134 . 56 1. 44 . 504 . 800 11. 0 3. 40 . 78 80. 4 . 0398 . 0139 . 59 1. 75 . 584 . 922 12. 4 3. 44 . 82 78. 5 . 0417 . 0142 . 62 2. 26 . 725 1. 14 13. 6 3. 47 . 79 73. 6 . 0475 . 0152 . 65 3. 31 .928 1. 46 17. 8 3. 48 . 77 74. l . 0469 . 0151 . 74 3. 72 . 880 1. 40 23. 6 3. 36 . 93 89. 2 . 0323 . 0125 . 86 4. 13 1. 038 1. 65 20. 9 3. 36 . 85 77. 3 . 0430 . 0145 . 81 5. 10 l. 220 l. 97 21. 9 3. 26 . 85 74. 2 . 0467 . 0151 . 83 6. 20 l. 371 2. 21 25. 5 3. 25 . 84 75. 7 . 0449 . 0148 . 89 8. 65 1. 620 2. 67 32. 4 3. 08 . 88 80. 6 . 0396 . 0140 1. 00 12. 19 2. 100 3. 49 37. 9 3. 11 . 93 76. 2 . 0443 . 0148 1. 09 1. 16 . 346 . 697 5. 4 1. 96 . 87 89. 3 . 0323 . 0132 . 41 1. 06 . 327 . 645 5. 5 2. 06 . 85 90. 6 . 0313 . 0129 . 42 1. 25 . 362 . 727 5. 9 1. 98 . 87 90. 5 . 0314 . 0130 .43 1. 56 . 437 . 889 5. 9 1. 94 . 87 83. 7 . 0367 . 0141 . 43 1. 77 . 465 . 942 6. 8 1. 95 . 83 86. 6 . 0343 . 0136 . 46 2. 07 . 541 1. 084 7. 3 1. 99 . 87 82. 3 . 0379 . 0143 . 47 2. 64 . 638 1. 30 8. 0 1. 94 . 85 80. 2 . 0400 . 0147 . 50 3. 45 . 788 l. 58 9. 4 1. 98 . 86 77. 9 . 0424 . 0151 . 54 5. 49 1. 050 2. 12 13. 2 1. 96 . 82 79. 9 . 0403 . 0147 . 64 may be possible by interpolation to sketch lines of constant depth for data from runs in which depth was allowed to vary, such a procedure would certainly be much less precise.) Thus, although the general depth effect could be perceived regardless of how the experi- ments were run (depth constant from run to run or depth varying), the maintenance of a constant depth permitted more accurate determination of the relations. A second characteristic of the graphs is that, with the exception of the 7R8 plot, a unique relationship does not exist between the measures of flow strength and sediment—transport rate. A given rate of sediment movement, as the independent or imposed variable, can be accommodated by various values of 'yQS’, V, yDS, and Vz/D. Conversely, according to figures 2, 3, 5, and 6, a given flow strength can transport sediment at various rates. The determining factor on these diagrams is the water depth. Surprisingly, if shear expressed as 738 is used as the measure of flow strength, the effect of depth is practically eliminated, and all the data can be described by a single curve (fig. 4). On the other four diagrams, however, the depth effect is evident, though to differing extents. The velocity- transport relation suggests that the effect of depth might be eliminated at slightly greater depths on this particular plot. There may be a tendency on the V2/D graph for the lines of greater depths to converge, but this plot has magnified the depth efl'eet more than any of the others. Such an influence may or may not be desirable. The diagrams of stream power and shear (yDS) do not seem to show any tendency to eliminate the influence of depth for the range of conditions examined. Power and shear (yDS) both involve a depth-slope product, so that in a laboratory flume the main distinction between the two is the inclusion of mean velocity in the computation of stream power. Significantly, the same depth-slope product (or velocity— depth—slope product) can give different sediment- transport rates. As depth increases, with a corre— sponding reduction of slope so that DS remains constant, the sediment-transport rate decreases. The general depth effect on sediment—transport rates was discussed by Colby (1964b, p. A25—A29). POWER (7.13%). IN POUNDS PER SECOND PER FOOT 0.1 SHEAR (TDS), IN POUNDS PER SQUARE FOOT 0.01 0.1 FLUME EXPERIMENTS ON THE TRANSPORT OF A COARSE SAND B9 IIIII I |I|III|I| I IIIIlIIl IIIIIIIII I III EXPLANATION Symbol Depth, _ in feet _ A 0.1 ° : O 0.3 _‘ u 0.5 ° — I||I I IIIIIIII I III||||I I |II||I|I ||I| 0.001 0.01 0.1 SEDIMENT-TRANSPORT RATE. IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH FIGURE 2.—Power versus transport relation. I I EXPLANATION Symbol Depth, _ In feet A 0.1 o 0.3 :1 0.5 III IIIIIIII I |I|III|| IIIIIIII I | 0.001 0.01 0.1 SEDIMENT-TRANSPORT RATE. IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH FIGURE 3.—Shear («,DS) versus transport relation. B10 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS I IIIIIIII III IIIIIII | I IIIIIII I I ’5 EXPLANATION 8 Symbol Depth, uJ — in feet —‘ g A 0.1 :> 8 o 0.3 o E D 0.5 A n. 0.1 — ' : (n : _ D _ z _ D _ o _ n- _ E _ :2 m fl 2~ I.— n: < _ LIJ ._ I m 0.01 I IIIIIIII | IIILIIII I IIIIJIII I l 0.001 0.01 0.1 SEDIMENT—TRANSPORT RATE, IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH FIGURE 4.—Shear (7R8) versus transport relation. I |II||III I IAI EXPLANATION U! | 4 _ Symbol Depth, in feet 3 T A 0.1 o 0.3 N I III 0.5 MEAN VELOCITY. IN FEET PER SECOND l I I I IILLI I I I IIIIII I III IIIIII I IIIIIIIl | | 0.001 SEDIMENT-TRANSPORT RATE, IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH 0.01 0.1 FIGURE 5.—Mean velocity versus transport relation. The fact that a given flow strength, as defined by 708’, V, VDS, and V2/D, can be related to various sediment-transport rates may be a reason for some of the difficulties encountered in seeking reliable sediment- transport formulas. What determines the particular 08’ or QS combina- tion that will be derived for a given sediment load? When sediment suddenly enters a reach of stream at a faster rate, does the slope remain constant and the depth increase to provide the necessary flow strength? A current hypothesis (Langbein, 1964) asserts that each dependent variable will change in value by equal and least possible increments, insofar as permitted by limitations within the system. A single straight line cannot be fitted to the plot of data for'the present runs at a given depth, regardless of which measure of flow strength is involved. All the relations exhibit a change in the trend of the data plot near 0.004m ' g“ D 0.5 < I- 2 — _ LLUJ “I“: D mz l | |||II||I I IIIIIIII |I|||||II | I 0.001 0.01 0.1 SEDIMENT-TRANSPORT RATE, IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH FIGURE 11.—Surface velocity versus transport relation. 1-°° I I I I I I I I I Depth = 0.3foot X X 0.90— _ Depth = 0.5 foot M: 0.80 — Depth: 0.1 foot _ X X X X XX X X 0,70 — ._ 0.60 | I I I I I I I 1 2 3 4 5 7 8 9 10 11 mg @— FIGURE 12.—V/V. relation for various depths. although Width was constant throughout. Average V/Vs values as indicated by the line of best fit are 0.85, 0.83, and 0.74 for depths of 0.5, 0.3, and 0.1 foot, respectively. The V/V, ratio is thus seen to decrease with depth by a very small increment, so that V8 de- parts farthest from V at a very shallow depth. For the present runs, use of the approximations would intro- duce possible V/Vs errors of about 3.0, 12.0, and 7.0 percent for the 0.5-, 0.3-, and 0.1-foot depths, re- spectively. Figure 12, then, shows the proportionality that exists between V, and V for a given depth (or WVD ratio). A fixed proportionality also exists between V, and Q for a given depth, as might be expected (fig. 13A). Since Q varies directly with V for a constant (flapth and width, Q also varies directly with V,. The relation between surface velocity and slope is shown in figure 133. If the plot of slope as a function of mean velocity were transferred for comparison purposes to figure 13B, it would be clear that the sur- face-velocity versus slope proportionality is exactly the same as that between mean velocity and slope, as would be expected. This relation is Vsocso'“. In summary, the surface velocity in this study was consistently related to all the other variables. Con- sequently, use of surface velocity may be an aid in determining the values of other variables, at least within the range of conditions examined here. Sur— face velocity is obviously easier to measure, and, for the present data, its relation to other variables is dependable. Vs alone can provide a reasonably good appraisal of both sediment-transport rate and mean flow velocity. When water depth is also known, Vs could be used to uniquely determine the slope and the discharge. Thus, such factors as power and shear also are uniquely related to surface velocity, for a given depth. B18 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS SURFACE VELOCITY IN FEET PER SECOND l> 1 l | l I | I III B EXPLANATION. Symbol De pm.— in feet 0 A 0.1 0 0.3 D 0.5 l ll||l||| l 0.5 1 DISCHARGE. IN CUBIC FEET PER SECOND 0.001 0.005 0.01 SLOPE, IN FEET PER FOOT FIGURE 13.—Relations of surface velocity to slope and discharge. The surface-velocity relations may never be well defined for many natural-stream situations, owing to the complexities of these situations, nor for other laboratory investigations. However, sufficient infor- mation is not yet available to negate the possibility that reliable relations exist. In future laboratory and field studies, it may be worthwhile to measure surface velocity and see What relations exist between it and the other variables. COMPARISON WITH DATA OF GILBERT AND MURPHY In this section the data from the present investi- gation are compared with the Gilbert-Murphy data (Gilbert, 1914) for their grade E, a comparable grain size (0.84—2.00 mm, nominal diameter 1.71 mm). With this grain size Gilbert and Murphy used flume widths of 0.66, 1.00 and 1.32 feet, and depths ranging from 0.077 to 0.562 foot. In the present comparison, all their grade E data have been included regardless of widths and depths. Their results have been computed for unit flume width, and their transport rates (dry weight) have been converted to immersed weight by the . . . 2.65—1.00 relatlon immersed weight=——2T 0.624>0.40ft v — E — v a O. V, _ _ D Z I) — __ E + E _ Present study “ r75 0: t K 5 I 0.01 — -— U) I I | I I I II I I I I I | I | I I I I I | | I I I I I 0.001 0.01 0.1 SEDIMENT—TRANSPORT RATE, IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH FIGURE 15.—Comparison of shear versus transport relation with data of Gilbert and Murphy. The general agreement between part of the Gilbert— Gilbert-Murphy work on stream traction using grade E Murphy work and the present study is perhaps signifi- sand: cant, for it indicates that some of the Gilbert-Murphy 1. Two different flumes were used. One of these had data are reproducible. Several details of experimental a length of 24.5 feet from sediment infeed to sedi- equipment and procedure difiered in the two investi- ment catchment (31.5 ft, overall), and the other gations, but, these differences apparently did not greatly had an overall length of 150 feet. (The present afl’ect the experimental results. For example, in the study employed a 52-foot-long flume.) B20 mm c» SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS MEAN VELOCITY, IN FEET PER SECOND III I ll|| EXPLANATION Symbol Depth, in feet A 0.1 o 03 } Present study El 0.5 4 — x Gilbert-Murphy grade E (all depths) MEAN VELOCITY IN FEET PER SECOND 1 0.0001 0.001 US. IN FEET FIGURE 16.——Mean velocity versus shear (DS) relations compared with data of Gilbert and Murphy. . Various flume widths were used. . Depth was not controlled—transport rate and dis- charge were the independent variables. . The flume was horizontal and was devoid of sand at the beginning of each run; that is, slope was not estimated and not preset. . The method of sediment infeed was different from the present study. Sand was dropped into the stream from above—usually by hand (by dumping in a boxfull at timed intervals), but occasionally by a hopper (at low transport rates). . Transport rate was measured during a relatively short period. 7. Sediment—infeed rate did not always equal the col- lection rate. Some of the above features might account for some point scatter in the Gilbert-Murphy data. BED FORMS For sediment finer than 0.6 mm in median fall diam- eter, the usual sequence of bed forms produced in flume studies by increasing stream power was defined by Simons, Richardson, and Nordin (1965a) as ripples, ripples on dunes, dunes, transition, plane bed, anti— dunes, and chutes and pools. For material coarser than 0.6 mm they reported that the ripple and ripple— FLUME EXPERIMENTS ON THE on-dune stages are absent, and that the transition and plane-bed stages may or may not occur. The types of bed configuration produced in the pres- ent study by increasing stream power were plane bed (at extremely low sediment-transport rates), dunes (at depths of 0.3 and 0.5 ft), and antidunes. A descrip- tion of the bed configuration for each run is given in the section starting on p. B28. The initial flat—bed stage appeared to be relatively unstable, as extremely low crests (probably incipient dunes) occasionally formed at a few locations during the first run (D=0.3 ft). At very low sediment-transport rates, definitive bed forms appeared. These first bed forms were different in runs at the 0.1-foot depth than in runs at greater depths. At a depth of 0.1 foot, the run at lowest stream power produced an almost flat bed. With increase in flow strength (and hence in transport rate) a peculiar bed feature appeared that was a few grain diameters high. Such a bed form, herein called a meandering scar, began at the flume wall and curved toward the center of the channel downstream (fig. 17). It usually faded out completely in the middle of the channel. The adjacent bed feature, a mirror image of its neigh- bor, would begin from the opposite wall a short distance downstream from the first feature. (Similar features also were found under certain conditions after the water had been drained from the flume.) With further increase in flow strength the meandering scars disappeared except in the downstream part of the fiume (run 4). At the same time .(run 4) symmetrical antidunes of very low amplitude appeared throughout most of the flume, though present only in the center of the channel in a single row. The distinguishing feature of antidunes is an inphase relation between sand crests and water-surface crests. These initial antidunes had wavelengths of about 0.5 foot. In subsequent runs the meandering scars disappeared entirely and only antidunes were present. With continued increase in flow strength, two or possibly three rows of antidunes occurred side by side in the flume simultaneously. Adjacent lines of these bed form's had staggered sand crests and troughs, so that a checkerboard pattern formed. Some rhythmic pe- riodicity occurred in the formation and disappearance R H FIGURE 17.——Pattern of typical meandering scars. TRANSPORT or A COARSE SAND B21 of water surface irregularities (waves). At the highest flow strength examined at 0.1-foot depth, the antidunes were mostly flattened out, and so was the water sur- face. This rather flat bed was only occasionally interrupted by a short train (3—10 ft long) of antidunes, moving downstream. All the antidunes traveled downstream. At depths of 0.3 and 0.5 foot, dunes were the initial bed configuration (except in the first run at 0.3-ft depth, during which the bed remained flat). The distinguish- ing characteristic of dunes as opposed to antidunes is an out-of-phase relation between the sand crests and the water-surface crests. (Ripples are generally less than 1 ft in wavelength, and the present features had an average minimum wavelength of 1.5 ft). These dunes were noticeably asymmetrical from a side view; they were characterized by a long upstream side, a crest which varied from angular to somewhat rounded with increasing flow strength, and a relatively short and steep downstream face. At low transport rates the upstream face was extremely long, in comparison with the downstream face, and the downstream face seemed to be about at the angle of repose. The spacing of well-defined crests under these conditions was some- what irregular downstream, and the crests were usually perpendicular to the flume walls and extended across the whole channel. As flow strength was increased, three particular changes were observed in the dunes: (a) the length of the upstream face progressively de- creased, and that of the slip face increased; (b) the angle of the slip face tended to decrease as the sand grains began to be propelled down the slip face rather than sliding down under their own weight; and (c) the angle between the dune crests and the flume walls changed—though still extending from wall to wall, the crests began assuming irregular and curving fronts and reached the opposite wall 1 or 2 feet farther downstream from their origin. Furthermore, the water surface became increasingly irregular. (At D=0.5 foot the maximum flow capacity of the flume was reached, while the dunes were beginning to be inclined to the walls and were showing some irregularity in crest directions.) The characteristics just described probably represent a transition from dunes to antidunes. This transition evolved gradually; no tendency to develop a plane bed was observed. Clearly defined antidunes, as indicated by an inphase relation between bed and water-surface crests, were recognizable in the final three runs at the 0.3-foot depth. For the complete series of runs at the 0.3-foot depth the bed-form heights and rates of travel consistently increased with increase in flow strength, except, possibly, the travel rates of the antidunes. When antidunes began to form, the water surface be- B22 came smoother than in the preceding runs and Showed rather symmetrical waves. With further increase in flow strength these water-surface waves tended to break occasionally on the upstream side of the wave crest. In the final run the surface waves extended almost completely across the channel and broke with consider- able turbulence just upstream from the crest. The antidunes (a) were almost symmetrical from a side view, (b) possessed well-rounded crests that extended across most or all of the channel and were perpendicular to the flume walls, and (0) moved downstream. With antidunes the water-surface waves and sand waves were not always well developed throughout the flume length; rather, any given segment of the flume would possess well-developed waves during one period, and poorly developed ones during another period. 'IVvo or three segments of well-formed waves existed in the flume at any one time; the length of time such a train of well-developed waves persisted ranged from a fraction of a minute to several minutes. Because of the variations in appearance and measure- ments of bed forms, the minimum of information which will adequately describe bed conditions must include a description of the features (rather than a single name) in addition to some measurements of bed-form heights, wave lengths, and rates of travel. The characteristics of the water surface must also be noted, especially the phase relation between bed-form crests and water— surface crests. The recording of this information should be a standard practice in flume studies. During the experiments it became evident that the description and measurement of bed features after the water has drained from a flume should be undertaken only with great caution. No significant difference was found in dune wave lengths during the run and after the run, in those runs for which both measurements were taken. However, bed features existing after the water was drained were frequently quite unlike those that existed during the run. Some examples of feature changes are the following: (a) All antidunes were obliterated as the water left the flume; (b) the general bed-form appearance as well as the heights were often modified as the water drained; (c) whenever the depth was relatively shallow or the bed was somewhat .flat during the run, a peculiar type of bed feature (the meandering scars of fig. 17) appeared as the water receded. In many runs the peculiar features did not form until the flume was drained. No sound explana- tion can be offered for the formation of these features, but the writer suspects that they are associated with deflection of the water by the fixed walls of the flume. INTERRELATIONS BETWEEN CHARACTERISTICS The rate of bed-form movement (0), average bed- SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS form length (l), and average height (h) are given in table 4. Heights of well-developed antidunes were generally fairly constant for any given run. The range in dune heights during runs under given flow conditions was small in some runs and several fold in others. The determination of dune lengths was occasionally a subjective procedure. As reported in other studies, dunes under certain conditions are continually dying out, reforming, and overtaking other dunes. In many studies the dunes do not extend very far laterally, and the crests frequently trend diagonally downstream. In the present study, extremely low dune crests which were a few grain diameters high were disregarded. Such incipient bed forms were more common at low sediment-transport rates. In spite of occasional sub- j ectivity in obtaining the values, they should be fairly representative of the prevailing bed forms. No well-defined relation was obtained between bed- form height and length. The antidunes at D=0.1 TABLE 4.—Bed-form measurements [No data for runs 1-3] Length (It) Run Height (ft) Velocity (ft per sec) During run Dried bed 0.1—ft depth 1 4 ____________________ O. 5 ______________________ 15 __________ 0 021 . 5 __________ 0 0200 1 6 __________ . 042 6 __________ 0216 1 7 __________ . 083 7 __________ 0300 18 __________ 053 1 0 __________ 0683 1 9 __________ 073 6 __________ 0683 0.3—ft depth 10 ____________________________________________________ 11 ___________ . 021 ____________________ 0007 12 _____________________________________________________ 13______-____ . 042 8.9 __________ 0017 14 ___________ . 042 5. 8 __________ 0027 15 ___________ 053 4. 8 __________ 0015 16 ___________ 063 4. 3 __________ 0035 17 ___________ 042 3. 6 __________ 0050 18______-__-_ 053 3. 5 __________ 0027 19 ___________ 053 __________ 2. 3 0075 20 ___________ . O53 __________ 2. 4 0117 21_________-_ .063 __________ 2. 0 0158 22 ___________ 073 1. 8 1. 9 0267 23 ___________ 104 1. 9 2 0 0167 24 ___________ . 167 1. 3 1 9 . 0250 25 ___________ 125 1. 5 1 0 . 0384 26 ___________ . 167 1. 5 .......... . 0083 27 ___________ 250 1. 6 __________ . 0400 28 ___________ 250 1. 6 __________ . 0350 0.5—1”; depth 29 ___________ . 083 5. 2 4 6 . 0012 30 ___________ . 042 3. 9 4. 6 . 0007 31 ___________ 104 3. 7 3. 5 . 0017 ‘ 32 ___________ . 063 2. 8 3. 0 . 0018 33 ___________ 042 2. 0 2 7 . 0022 34 ___________ . 063 2. 5 __________ . 0020 35---_____-__ .167 2.0 2.2 .0072 36 ___________ . 167 2. 2 1. 8 . 0063 37 ___________ . 167 1.8 1. 8 .0217 1 Antldunes. FLUME EXPERIMENTS ON THE foot tended to increase in height as their length in- creased, but dunes increased in height as length de- creased. Height and length relations alone could not distinguish dunes occurring at a depth of 0.3 foot from those occurring at a depth of 0.5 foot. The data further indicate that bed-form height in- creased as rate of travel increased. The relation between either height or wavelength and bed-form velocity serves to distinguish the runs roughly on the basis of flow depth. Although the point scatter pre- cludes a precise relation, figure 18 suggests that for a given dune height the rate of movement downstream is slower at a greater depth. The wavelength versus bed-form velocity relations (fig. 19) show that as dune velocities increased the wavelengths gradually de- creased, apparently reaching a limiting minimum value of about 1.5 foot. The wavelengths of the antidunes at D=0.1 foot generally increased as bed-form velocity increased. CHARACTERISTICS RELATED TO FLUID FLOW STRENGTH When antidunes at depths of 0.1 and 0.3 foot became clearly recognizable, the Froude number, representing the ratio of inertial to gravity forces, was about the same for both depths (F~O.85). The value of the fluid flow strength was considerable greater, however, at a depth of 0.3 foot at the onset of formation of anti- TRANSPORT OF A COARSE SAND B23 different characteristics; at the 0.1-foot depth they were much smaller in size, more symmetrical in all directions, and usually did not exist near the flume walls. Also, trains formed side by side in runs at a depth of 0.1 foot, but not at a depth of 0.3 foot. Prior to the antidune stage, dunes existed at depths of 0.3 and 0.5 foot but not at a depth of 0.1 foot. Further- more, the dunes at the two greater depths were rather similar in appearance. This similarity, in contrast to the complete absence of dunes at the shallowest depth, seems rather suggestive of a depth effect on type of bed form. Unless wall drag or some other factor had a great influence on the bed forms which occurred in these experiments, it appears that the depth of flow caused substantial differences between bed forms occurring at the shallowest depth and bed forms of the two deeper depths. Apparently, somewhere between the 0.1 and 0.3-foot depths a critical depth existed below which the bed features, especially dunes, were greatly inhibited in their formation by shallow depth. Thus, flow depth may place certain limitations on bed-form characteris- tics. The existence of these limitations, such as on maximum attainable heights of bed forms, has been suggested by various investigators. Height In figure 20 the average height of the bed forms is dunes. The antidunes at the two depths had somewhat plotted against mean velocity, surface velocity, shear, I | I I | I I I I | | | | I | I I _I | I I I T T I I — EXPLANATION Symbol Depth. 0 o in feet — A 0.1 // — / / o 0.3 D o o // D o // / ,_ u 0.5 // // m / / Lu / / O u. 0K / / 5 K0// ’0/ E 0.1 I— D 407 / _ . _ D / / _ I- / / I __ El // / A _ 9 // x // o A LU "— / «0° / _ I / D u o 029/ o _ / 4 _ E // D// a: / 0 o / o 0 A E b // // _ a _ / E! o /,cr/o o A __ 3 // / _ // _ // // 0.01 I I I | I | | | I I I | I I I I I | I | I I I l I | 0.001 0.01 0.1 TRAVEL VELOCITY, IN FEET PER SECOND FIGURE 18.-——Variation in bed-form height with travel velocity. B24 SEDIMENT TRANSPORT IN » ALLUVIAL CHANNELS l | 10 — _ ‘— o _ \ — \ _ \ a \\ t' — \F I O \ E \\ 0 Z _ El \ D \\ _. \\\ I \\ 0 I I- — \ u \ g D ‘\ \\ Lu 0 \\ \\ o d \\ 0 I \\ i _ \¢‘\ \\ .8 o. O 3 I \“:\~:I o .2. . Trek LIE-I EXPLANATION 0 Symbol Depth. 1 _ in feet A _ : A 0.1 /// o 0.3 // — o 0.3 (after draining water) A/ _ D 0 5 V/ A . /f I 0.5 (after draining water) — | | l l | | | | l l l i | | l I l l | | | | l 1 0.001 0.01 0.1 TRAVEL VELOCITY, IN FEET PER SECOND FIGURE 19.~—Variation in bed-form wavelength with travel velocity. and power. (The constant 7 is dropped in the compu- in depth from 0.3 to 0.5 foot apparently did not affect tation of shear and power. The fitted lines do not include the antidunes at D=0.1 ft.) The heights of the bed features increased progressively with increase in flow strength. Dune heights grew with about the 3.2, 3.2, 1.2, and 0.9 powers of mean velocity, surface velocity, shear (either definition), and power, respectively. The antidunes at D=0.1 foot differed from the bed forms at greater flow depths whose heights were greater for a given flow strength. In spite of the point scatter, there is no clear indication (except possibly with the V, plot) that the heights of the dunes occurring at the 0.3-foot depth were significantly different from those at the 0.5-foot depth. Length The relation of mean wavelength to each of the measures of flow strength is shown in figure 21. p The antidunes that formed at the shallow flow depth had short intervals and are separated from the other bed forms. Also, the lengths of these antidunes increased, Whereas those of the dunes decreased, as flow strength increased. The curves indicate that a fair estimate of flow strength could be obtained from a determination of mean dune wavelength. The antidunes that formed at a depth of 0.3 foot (the last few runs) did not show any significant change in wavelength with increase in fluid flow strength. For a given flow strength, a change the mean dune wavelengths. Velocity The relation of rate of bed-form travel to the various measures of flow strength is presented in figure 22. The velocity of the bed features increased with greater flow strength. A slight increase in flow strength caused a relatively large increase in rate of bed—form movement. The rate of bed-form travel varied approximately with V”, Vs”, (RS)2'6, (08)”, and (QS)‘~5. Liu found in certain flume experiments using finer sand that bed- form velocity is proportional to V5. The depthefi'ect can be distinguished on the DS and Q8 diagrams. As indicated earlier on the sediment— transport diagrams (figs. 2, 3), the amount of sediment transported, at a given D8 or QS value, increased as the water depth decreased, within the range of flow con- ditions studied. Figure 22 is consistent with this trend; it shows that the bed forms moved downstream faster as depth decreased when DS and Q8 were the measures of flow strength. As can be seen in the diagrams, the lines for the various depths are farthest apart on the power plot. They are closer together on the DS diagram, and the plots of bed-form velocity versus RS, V, and V3 prac- tically eliminate the effect of depth. FLUME EXPERIMENTS ON THE TRANSPORT OF A COARSE SAND B25 | I | | I | I I I I I I | I I | I I | I | 7 o ' o EXPLANATION _ 0-2— Symbol Depth, in feet a no ED 5 A 0.1 Lu 0 0.3 Id. E 0.1— D 0-5 — F _ Z I _ (5 _ _. a I _ _ E 0.05— 0 l1. _ _ D m m _ _. 0.02 — _ I I I I I I I I I I I I I l I I I I I I I I I 0.0002 0.001 0.001 0.01 DS QS I I o 0.2 _ .— m E 0.1 _ E _ +—’ _ I _.. 9 Lu / _ I 2 0.05 _ n: O _ "I' 0 Lu _ m 0.02 __ I I | | I I I I | I I | | | I I MEAN VELOCITY. IN FEET PER SECOND SURFACE VELOCITY, IN FEET PER SECOND 0.001 0002 RS FIGURE 20.—Bed-form height versus measures of flow strength. (Lines exclude D=0.1 ft.) CHARACTERISTICS RELATED TO SEDIMENT-TRANSPORT RATES The general trend of bed-form measurements with increase in transport rate can be seen in' table 4. The bed-form length versus transport relation is virtually the same as that shown by the plots of wavelength versus flow strength. Bed-form height increased con- sistently with increase in transport rate (fig. 23). The point scatter precludes, and indeed the accuracy of the height values does not warrant, an attempt to fit an extremely accurate line to the data. The approximate relation for the bed forms at. depths of 0.3 and 0.5 foot is [Lotto-4°. The same remarks also apply to the bed-form velocity versus transport diagram (fig. 24), where the general relation is about 0003““. Bed-form heights, wavelengths, and velocities are frequently not constant from one bed form to the next, within a given run. In both the h/t' and c/i diagrams there is a faint suggestion that if more accurate means of measurement were available it might be possible to draw a separate line for each flow depth. The bedload equation proposed by Simons, Richard- son and Nordin (1965b), based on ripple and (or) dune heights and rates of travel, was tested on the present data. The authors cited used the equation for sand ranging from 0.19 to 0.93 mm in median fall diameter. B296 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 10 |I|||I IIIII U. /. /. BED-FORM WAVELENGTH, IN FEET III III» I I \ \ ||I|I| I IIIIII | | O O 1111 l l 0.5 - _ _ EXPLANATION '— Symbol Depth, Symbol Depth, in feet in feet _ A 0.1 o 0.3 (after draining water) 0 0.3 CI 0.5 I 0.5 (after draining water) I I I I ll |||ll|I| I 111111 I I [III I |l||I||| 1 2 3 4 2 3 4 0.0005 0.001 0.0005 0.001 0.003 0.001 0.005 0.01 MEAN VELOCITY, SURFACE RS DS QS IN FEET VELOCITY. PER SECOND IN FEET PER SECOND FIGURE 21.—Bed-form wavelengths versus measures of flow strength. — I IIIIIII I IIIIIII | I|||II | I IIIIII— : A A A — _ o __ o 0 o o— 2 _ o 0 Lu — _ (I) 0: Lu 0. ._ 0.01— : LU — _. m __ L _ _ E I I E — _ O _ o _ _I M > _ _ E e EXPLANATION a 0.001: Symbol Depth, 2 Lu — in feet : m I A 0.1 _ __ o 0.3 _ I: 0.5 I II I | I llllllll I IIIIIII I llIIII | l||I|l|| I 2 3 4 2 3 4 0.0005 0.001 0.0005 0.001 0.001 0.01 MEAN VELOCITY, IN SURFACE VELOCITY, RS DS QS FEET PER SECOND IN FEET PER SECOND FIGURE 22.—Bed-form velocity versus measures of flow strength. Their data were Obtained in the laboratory in a large the bed forms Of the present experiments. Since tri- recirculating flume. A basic assumption in the deriva- tion of the equation was that the bed forms are triangu- lar from a side View. This was true for only some Of angular bed forms are restricted to a very limited range within the spectrum Of bed configurations, it would seem that bedload equations which depend on the BED—FORM HEIGHT, IN FEET BED-FORM VELOCITY. IN FEET PER SECOND FLUME EXPERIMENTS ON THE TRANSPORT OF A COARSE SAND I | I I I I | I I l I l | | I I | | I I I I I I II I I F EXPLANATION _ Symbol Depth, 0 O — in feet _ 0.1 D D D o 0.3 05 ° . A“ 01— ° _ A I _ o A _ _ A : _ A _ ~— A _ 0.01 I I I I I I I I | | I | I | | | | | I I | I I I I I I 0.001 0.01 0.1 SEDIMENT—TRANSPORT RATE, IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH FIGURE 23.—Re1ation of bed-form height to sediment-transport rate. | | I I I I | I I I | I I l I I | I I | I I I I I I I : A _ - EXPLANATION o o “ Symbol Depth, A _ _ in feet 0 A 0.1 :90 — o 0.3 A _ D 0.5 o 0.01 — : : o A 0.001 — : I | | | | I I | I I I | I | | I I I I | I l I I I | I 0.001 0.01 0.1 SEDIMENT—TRANSPORT RATE. IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH FIGURE 24.—Variation in bed-form velocity with sediment-transport rate. B28 existence of an ideally shaped bed form will have a rather limited application. The equation is q.=(1—x) 92540. where qb=volume rate of sediment transport (ft3 per sec per ft width), )\ =porosity of sand bed, c=average bed-form velocity (ft per sec), h=average bed-form height (ft), and 01=a constant of integration, considered equal to zero as long as the bed is entirely covered with ripples or dunes. Volume rate of sediment transport can be changed to weight rate by dividing by the measured unit (specific) weight of the quartz sediment (91.5 lbs per cu ft). This dry weight in turn can be changed to immersed weight, the latter being WXMW weight)=0.624><(dry weight). By making these changes and using the measured porosity value of 0.445, the above equation can be reduced to the form ic=15.8 ch, where 736 is the computed sediment-transport rate in pounds (immersed weight) per second per foot of chan- nel width. (The constant 01 in the original equation can be taken as zero.) Although the equation was not intended to apply to antidunes, those runs which produced antidunes were included in the present computations merely out of curiosity. A comparison of all the computed versus measured bedloads is shown in figure 25. The amount of point scatter is probably not excessive in view of the uncertainties involved in measuring bed-form heights and rates of travel. CONCLUSIONS For the sediment, flow conditions, and flume of the present study, the following conclusions were drawn: 1. Scatter of points in the sediment-transport diagrams is vastly reduced and existing relations are clarified by keeping water depth constant for a series of runs—that is, by using depth as a third variable. 2. If shear, expressed as 7 RS, is used as the measure of flow strength in computing the sediment-transport rate, all the runs can be described by a single curve in which shear is uniquely related to transport rate. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 3. Mean velocity, stream power, shear expressed as 7 DS, and a regime bed factor are uniquely related to sediment-transport rate only for a constant water depth. Two corollaries of this conclusion are: (a) If depth is permitted to vary, the transport rate increases as depth decreases for a given value of any of these four measures of flow strength. (b) The critical or threshold flow strength required to initiate sediment transport, as expressed by these four measures, varies with water depth, rather than being uniquely determined by the sediment characteristics and bed slope. 4. The interrelationships between discharge, slope, and sediment-transport rate are uniquely defined only for a constant water depth. 5. If water depth is known, surface velocity is the only other measurement needed to determine the values of all other major variables. Surface velocity may be very useful in this respect because it is so easily measured. 6. The Gilbert-Murphy data for a comparable grain size are in substantial agreement with the present data. 7. A Critical water depth somewhere between 0.1 and 0.3 foot exists in the formation of bed forms. At depths shallower than this critical depth, the bed features have distinctly different characteristics than do features formed at greater depths. DESCRIPTION OF BED CONFIGURATION. BY RUN The following are partial descriptions of the bed configurations that formed during each run (numbered). The depth of water for each set of runs is indicated by centerhead. 0.1-foot depth 1. Flat bed. 2. Almost flat bed, although some barely perceptible features were present. These features were meandering scars which began at the wall and curved diagonally outward in a downstream direction; they generally faded out com- pletely in the middle of the channel. Their points of origin alternated systematically from wall to wall. The amplitudes (heights) of the features were on the order of a few grain diameters. There was a downstream distance of about 2 feet from the start of one scar to the start of its neighbor at the opposite wall. 3. Same as previous run. 4. Bed almost flat, although two different types of bed features were faintly discernible: (a) Symmetrical antidunes down much of the flume length but not present near the walls. Crests of these bed forms corresponded to crests of water- surface crests immediately above. Amplitudes of antidunes were too small to measure accurately; wavelength estimated to be 0.5 foot. NOTE :——These features disappeared as the water was drained from the flume at the completion of the run. COMPUTED TRANSPORT RATE, IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH FLUME EXPERIMENTS ON THE TRAN-SPORT OF A COARSE SAND B29 EXPLANATION Symbol Depth. in feet A 0.1 0.3 05 0.1 — 0.01 — 0.001 — l I I I 0.001 0.01 MEASURED TRANSPORT RATE. IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH 0.1 1.0 FIGURE 25.—Comparison of computed versus measured transport rates. (b) Meandering scars, like those formed in the previous runs, were present, but only downstream. Heights of scars were as much as a quarter of an inch at flume walls but'decreased toward the center of the channel, where the bed was almost flat. Down- stream distance between successive scar inceptions was about 1 foot. NOTE :—After the water drained from the flumc, features of the latter type were found throughout most of the fiume. Rather than fading out in the middle of the channel, each one curved from its point of inception, at a wall, downstream and over to the opposite wall, at which point a similar feature began. Downstream distance between these two inception points averaged 1.5 feet. 6. Symmetrical antidunes like those in the previous run, but formed in two rows in a longitudinal direction rather than in a single row. An alternating pattern existed whereby one sand crest was closer to one flume wall and the next crest downstream was closer to the opposite wall. The distribution of sand crests and troughs was so regular that it resembled a checkerboard pattern.- The water surface was correspondingly rippled in two rows, with neighboring crests staggered relative to each other, in a downstream direction. The amplitude of these water-surface waves was higher than that of the bed forms. The distance from one sand crest to the downstream range of its ofl’set neighbor (parallel to flow) was about 0.35 foot. All these bed features were smoothed out and dis- appeared as the water drained from the flumc. 5. Rather symmetrical antidunes (crests were directly beneath the crests of the ripply water surface). As the water drained from the flume, these bed forms disappeared, and meandering scars appeared. 7. Same as preceding run. 8. Antidunes (sand crests directly beneath water-surface crests) in a single row; moved downstream in groups or trains. A single sand crest sometimes extended across B30 10. ll. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. the channel width but at other times occupied only about 0.4 foot in the middle of the channel. At times the bed forms were almost obliterated (latter phenomenon was possibly more common in the first 10 ft and in the last 10 ft of the flume). All bed features were regularly spaced throughout the fiume length. The water surface was ripply but irregular. . Mostly flat bed; an occasional train of antidunes generally about 3 feet long but sometimes as much as 10 feet long. Water surface mostly rather smooth except where ripply above antidunes; inphase relation between water and sand crests, where such crests existed. 0.3-foot depth Flat bed. Smooth water surface. movement. Almost flat bed; one or two widely spaced bed features (dunes). Water surface smooth. Almost flat bed; an occasional small dune. Dunes, with fronts higher in center of channel than near walls. Wavelengths of dunes increased systematically in downstream direction. When bed-form observations were made, five dunes were present in the flumc. Dunes, many of which were poorly defined. Fronts gen- erally perpendicular to flow direction across whole channel width, and higher in channel center than near walls. Dunes. Wavelengths irregularly spaced. Dunes, with fronts normal to flow and wavelengths not consistent in downstream direction. Dunes, irregularly spaced and possibly tending to have longer wave lengths downstream. Dunes, generally with well-defined fronts and perpendicular to flow. Wavelengths not consistent throughout flume. Same as previous run. Wide range of wavelength magnitudes. Same as previous run. Dunes, with crests often curving irregularly across the channel rather than normal to flow. Fronts continually grew higher, receded, and moved downstream at various rates. Wavelengths were longer and more inconsistent in the downstream half of the flume length, but were regularly spaced in the upstream half of the flume. Dunes, with very irregular crests that generally curved from one wall downstream to the opposite wall. Small parts of the dunes were normal to the flow direction near walls. Bed forms and water surface became increasingly rougher downstream. Dune lengths more variable in downstream part of flume. Dunes, with very irregular and poorly defined crests, par- ticularly upstream. Dune heights and wavelengths vary- ing considerably in magnitude. Possible tendency for dune lengths to cluster, so that reaches of short wave- lengths alternated with reaches of longer wavelengths. Dunes, very irregular in cross-sectional and top views but rather evenly distributed throughout flume length. Same as previous run. Water surface very rough and irregular. Antidunes, with sand crests directly beneath water~surface crests. Wavelengths rather constant throughout flume length. Bed-form crests more rounded and water surface smoother than in the runs immediately preceding this. No'rnz—Bed forms were considerably smoothed out after water drained from flume and bore little, if any, resemblance to the features that were present during the run. Very little sediment 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS Antidunes, with very well rounded crests; consistent in wavelength. As water drained, bed forms were consider- ably smoothed out, and many meandering scars (run 4b) appeared. Antidunes, rather evenly spaced along the flume and rather symmetrical in form from a side view. Crests very well rounded. Water surface consisted of rough waves whose crests were inphase with the dune crests. These water waves were distinctive because they broke on the upstream side of the wave crest or peak. 0.5-foot depth Dunes, whose fronts were almost normal to flow direction except near flume walls. Water surface smooth. Dunes, irregularly spaced in downstream direction. surface rather smooth; very minor undulations. Dunes, with very well defined angular crests that extended completely across flume width, normal to flow. Water surface rather smooth. Dunes, with crests nearly perpendicular to flow from wall to wall. Crestline slightly irregular. Downstream dunes regularly spaced; upstream dunes not as regularly spaced and generally closer together. Dunes, with well—defined crests normal to flow; dunes irregu- larly spaced relative to one another. Some possible tendencies of clustering of similar dunc lengths. Minor undulations in water surface. Dunes, with well-defined angular crests normal to flow direction; not very regularly spaced in downstream direc- tion. Rather smooth water surface, with very minor undulations about 1 foot long. Same as previous run, except less variation in dune lengths. Dunes, with crests sometimes curving downstream from one wall to the other and at other times perpendicular to the flow direction. Possible tendency for clustering of similar dune lengths. Water surface had undulations about 1 inch high and 1 foot long. No discernible relation between water-surface crests and bed-form crests. Dunes, some with crests straight acorss channel (possibly more common upstream), and others with crests curving downstream from wall to wall (mostly in downstream hall of flume). Dunes tended to be regularly spaced along flume. Undulating water surface, with troughs directly over dune crests. Water REFERENCES Brooks, N. H., 1954, Laboratory studies of the mechanics of streams flowing over a movable bed of fine sand: Pasadena, California Inst. Technology Ph. D. thesis, 248 p. 1958, Mechanics of streams with movable beds of fine sand: Am. Soc. Civil Engineers Trans, v. 123, p. 526—549. Colby, B. R., 1964a, Practical computations of bed-material discharge: Am. Soc. Civil Engineers Proc., v. 90, no. HY2, p. 217—246 1964b, Discharge of sands and mean-velocity relation- ships in sand-bed streams: U.S. Geol. Survey Prof. Paper 462—A, 47 p. Colby, B. R., and Scott, C. H., 1965, Effects of water tempera- ture on the discharge of bed material: U.S. Geol. Survey Prof. Paper 462—G, 25 p. Einstein, H. A., 1942, Formulas for the transportation of bed load: Am. Soc. Civil Engineers Trans, no. 107, p. 561—577. FLUME EXPERIMENTS ON THE Gilbert, G. K., 1914, Transportation of debris by running water: U.S. Geol. Survey Prof. Paper 86, 263 p. Langbein, W. B., 1964, Geometry of river channels: Am Soc. Civil Engineers Proc., v. 90, no. HY2, p. 301—312. Liu, H. K., 1958, in discussion to “Mechanics of streams with movable beds of fine sand,” by N. H. Brooks: Am. Soc. Civil Engineers Trans, v. 123, p. 568. Simons, D. B., Richardson, E. V., and Nordin, C. F., Jr., 1965a, Sedimentary structures generated by flow in alluvial channels, in Soc. Econ. Paleontologists and Mineralogists, Primary sedimentary structures and their hydrodynamic interpretation—a symposium: Soc. Econ. Paleontologists and Mineralogists Spec. Pub. 12, p. 34—52, 253—264. TRANSPORT or A COARSE SAND B31 1965b, Bedload equation for ripples and dunes: U.S. Geol. Survey Prof. Paper 462—H, 9 p. Sundborg, 3., 1956, The river Klaralven—a study of fluvial processes: Geog. Annaler, v. 38, p. 127—316. U.S. Inter-Agency Committee on Water Resources, 1957, Some fundamentals of particle size analysis, in A study of methods used in measurement and analysis of sediment loads in streams: Washington, U.S. Govt. Printing Office, Rept. 12, 55 p. Vanoni, V. A., and Brooks, N. H., 1957, Laboratory studies of the roughness and suspended load of alluvial streams: California Inst. Technology Sedimentation Lab. Rept. E—68, 121 p. U.S. GOVERNMENT PRINTING OFFICE : 1967—0-248-1 17 ¢ “TH '175 W 7 DAY é ‘ , ezw SPLAY The Behavior of Large Particles Falling in Quiescent Liquids kg GEOLOGICAL SURVEY PROFESSIONAL PAPER 562—0 ~ ‘ ~ ; 37%\N Si . .. . “QR ‘\ F DP 9 lifhffil / 3} . :§‘\ / x,¢§sriyr DOCUMENTS DEPARTMENT APR 7 7989 LIBRARY _ unwmsm o; Muronum UoSIS‘D? The Behavior of Large Particles Falling in Quiescent Liquids By G. E. STRINGHAM, D. B. SIMONS, and H. P. GUY SEDIMENTiTRANSPORT IN ALLUVIAL CHANNELS GEOLOGICAL SURVEY PROFESSIONAL PAPER 562—C UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1969 UNITED STATES DEPARTMENT OF THE INTERIOR STEWART L. UDALL, Secretary GEOLOGICAL SURVEY William T. Pecora, Director For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 — Price 55 cents (paper cover) CON TENTS Page Abstract ___________________________________________ Cl Fall behavior parameters—Continued Introduction _______________________________________ 1 Choice of characteristic diameters and velocitie5_ _ _ _ Problem and scope ______________________________ 1 Particle steadiness ______________________________ Drag concepts __________________________________ 2 Particles, liquids, equipment, and procedure ____________ Shear drag _________________________________ 2 Particles _______________________________________ Pressure drag ______________________________ 2 Liquids ________________________________________ Total drag _________________________________ 2 Equipment _____________________________________ Historical development of drag concepts ___________ 3 Procedure ______________________________________ Mathematical development __________________ 3 Experimental results ________________________________ Experimental development ___________________ 3 Description of findings __________________________ Acknowledgments _______________________________ 5 Spheres ____________________________________ Fall behavior parameters ____________________________ 5 Disks _____________________________________ Variables affecting particle behavior _______________ 5 Oblate spheroids ____________________________ Fluid variables _____________________________ 5 Cylinders __________________________________ Variables associated with particle motion ______ 5 Prolate spheroids ___________________________ Geometric variables _________________________ 7 Comparison of behavior among all particles ________ Dimensional analysis ____________________________ 7 Interpretation of results _________________________ Coefl‘icient of drag versus Reynolds number--- - 8 Parametric relationships _____________________ Shape factor _______________________________ 9 Patterns of fall _____________________________ Frequency numbers _________________________ 9 Shape factors _______________________________ Stability numbers ___________________________ 9 Summary and conclusions ____________________________ Force number ______________________________ 10 References cited ____________________________________ ILLUSTRATIONS Page FIGURE 1. Sketches showing vortex pattern of an oscillating disk ____________________________ Ce 2. Sketches of circular fluid flow around a particle __________________________________ 7 3. Graph showing coefficient of drag as a function of Reynolds number for fixed disks, spheres, and airship hulls ___________________________________________________ 8 4. Sketch showing forces on a falling disk __________________________________________ 11 5. Photographs of particles used in experiments ____________________________________ 14 6. Graph of kinematic viscosity of glycerine-water mixtures as a function of temperature- _ 14 7. Graph of density of glycerine-water mixtures as a function of temperature ---------- 15 8. Schematic diagram of fall column ______________________________________________ l5 9. Sketch showing distortion of light rays caused by fluid refraction and the curved surface of the fall column ___________________________________________________ 16 10. Graph of coefficient of drag as a function of Reynolds number and force number for falling and fixed spheres ____________________________________________________ 21 11-15. Sketches showing fall pattern of a disk: 11. Steady ______________________________________________________________ 21 12. Regular oscillation ____________________________________________________ 21 13. Entering glide-tumble _________________________________________________ 22 14. Leaving glide-tumble _________________________________________________ 23 15. Tumble _____________________________________________________________ 23 16. Graph showing regimes of fall for a free-falling disk ______________________________ 24 17—19. Graphs showing velocity-time relationship of falling disk for— 17. Aluminum in an oscillatory pattern _____________________________________ 25 18. Aluminum in a glide-tumble pattern ____________________________________ 26 19. Lead in a tumbling pattern ____________________________________________ 26 III Page C10 11 12 12 12 13 15 16 16 16 17 27 27 31 31 32 32 32 33 35 36 CONTENTS Page FIGURES 20—21. Graphs showing comparison of maximum and nominal particle diameter for coefficient of drag as a function of Reynolds number for falling disks, SF¢=0.1, based on— 20. Path velocity ________________________________________________________ 028 21. Vertical velocity ______________________________________________________ 29 22. Graph showing coeflicient of drag as a function of frequency number for falling disks, SF a: 0.1 __________________________________________________________________ 30 23—24. Graphs showing coefficient of drag as a function of Reynolds number, SFC=0.5, for— 23. Falling oblate spheroids _______________________________________________ 30 24. Falling cylinders _____________________________________________________ 31 25. Graph showing coeflicient of drag as a function of frequency number for falling cylinders, SF 0: 0.5 __________________________________________________________________ 32 26. Graph showing coefficient of drag as a function of Reynolds number for falling prolate spheroids, SFC=0.71 _______________________________________________________ 33 27. Composite graphs of coefficient of drag as a function of Reynolds number for falling spheres, disks, oblate spheroids, cylinders, and prolate spheroids based on maximum and nominal particle diameter and path velocity ______________________________ 34 TABLES Page TABLE 1. Particle properties, measured and computed _____________________________________ 012 2—6. Drop data for— 2. Spheres ______________________________________________________________ 17 3. Disks ________________________________________________________________ 18 4. Oblate spheroids ______________________________________________________ 19 5. Cylinders _____________________________________________________________ 20 6. Prolate spheroids ______________________________________________________ 22 7. Frequency of oscillation of unstable particles falling in water-glycerine mixtures ______ 27 SYMBOLS Symbol Definition A A characteristic area of the particle (cmz). In this paper it is the maximum projected area of the particle. A" The area projected on the basis of the nominal diameter (cm2). 01. . Dimensionless coefficients. CD Coefficient of drag. 0L Coefficient of lift. D Drag forces (dynes). F Driving force defined by (p,—p,)¥g (dynes). I Moment of inertia of the particle (dyne—cm-sec’). L Lift force (dynes). M Virtual mass (dyne-secz/cm). N 2 Number of corners. 0. Volume of a sphere circumscribing a particle (cma). 0c Circumference of a circle of area equal to the plane area of the particle (cm). 0, Circumference of a particle (cm). R Reynolds number based on particle size (pfwd/M). R, Resistance due to pressure. R. Resistance due to shear. R. Total resistance. S Surface area of the particle (cma). SF Shape factor. SF; Corey shape factor (ch/(Th). SF m Corey shape factor modified by Alger. SFd Dynamic shape factor (w/w,)3. S, Surface roughness. 45 Volume (ems). SYMBOLS Definition Bouyant weight of the particle (gm). Maximum diameter of the particle (cm). Intermediate diameter of the particle (cm). Minimum diameter of the particle (cm). A characteristic diameter of the particle (cm). Diameter of fluid container. Surface diameter (cm), the diameter of a sphere with surface area equal to that of the particle. Diameter of a circle of area equal to the maximum cross-sectional area of the particle (cm). Nominal diameter (cm), the diameter of a sphere of volume equal to that of the particle. Sedimentation diameter (cm), the diameter of a sphere that has the same specific gravity and the same terminal uniform settling velocity as the given particle in the same sedimentation fluid. Sieve diameter (cm), the length of the side of the smallest square opening of the sieve through which a given particle will pass. Frequency of oscillation or tumbling. Acceleration of gravity (cm/sec“). Arbitrary constants. Distance from center of gravity to the center of pressure. Bouyant mass of the particle (dyne-secfl/cm). Added mass. Mass of accelerating fluid (dyne-secz/cm). Mass of the particle (dyne-secz/cm). Radius of curvature of a corner on a particle (cm). Radius of the maximum inscribed circle in a particle (cm). Time. Horizontal velocity of the particle (cm/sec). Verticle velocity of the particle (cm/sec). Frequency number (fd/w). . . 1r p, 6 Stability number (51 E 5 Force number (F/pfvz). Circularity. Roundness. Density-frequency number (f 2pfd‘lF) . Sphericity. Angle of attack (radians), the angle between disk trajectory and disk. Angle between vertical and particle trajectory (randians). Dynamic viscosity (dyne-sec/cm”). Kinematic viscosity (cmzlsec). Density of the fluid (dyne-sec2/cm4). Density of the particle (dyne-secz/cm’). Time interval < t. Path fall velocity of the particle (cm/sec). Fall velocity of a nominal sphere (cm/sec). SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS THE BEHAVIOR OF LARGE PARTICLES FALLING IN QUIESCENT LIQUIDS BY G. E. STRING-HAM, D. B. Swans, and H. P. GUY ABSTRACT The free-fall behavior patterns of specific idealized particles falling singly in quiescent liquids were observed with respect to fall patterns, fall velocity, and travel path. Particle shapes and densities were chosen to represent the limiting conditions of natural gravel-sized sediment found in alluvial channels. The liquids used in the fall column were water, various mixtures of water and glycerine, and pure glycerine. The particles were dropped in a vertical clear plexiglass fall column 3 meters high and 40 cm in diameter. Two 16-min movie cameras set at right angles to each other and focused on a timer and a 1-meter test section of the column recorded the particle behavior. The horizontal and vertical coordinates of the particles were established by projecting the image of the particles moving through the test section onto a grid. The spheres usually fell in a straight vertical path, but some5 times the nylon or teflon spheres falling in pure water exhibited: small erratic horizontal movements. Disks, on the other hand, exhibited four types of fall behavior: (1) steady-flat fall——ma2xi-— mum projected area perpendicular to the axis of the fall when the Reynolds number R< 100; (2) regular oscillation—oscillation occurred about a diameter perpendicular to the direction at fall, and there was very little horizontal translation; (3) glides» tumble—the frequency of oscillation was less than regular oscillation, the amplitude increased until the disks fell vertically on edge part of the time, and sometimes tumbling occurred at the end of each glide; and (4) tumble—the axis of the fall path was virtually a straight inclined line, the disk continually rotated, and the frequency of rotation approached the frequency of oscillation in the oscillation behavior pattern. The steadiness of a falling particle is dependent upon the: stability of the resultant of the pressure forces in the wake of‘ther particle. Shape of the particle and the Reynolds number both affect the distribution of the pressure forces in the wake with extremes in shape and high R causing the resultant force to be- the least stable. Thus, the fall pattern of a disk, which is in effect a two-dimensional particle, is much less steady than the. fall pattern of a three-dimensional sphere. The ratio of the path length to vertical distance through which the particle falls is also related to the steadiness of the particle, the more unsteady the particle, the greater the path length. The effect of particle-fluid density ratio and the thickness- diameter ratio of the particle on its fall velocity and steadiness can be expressed by a dimensionless stability number I. The frequency of oscillation can be related to the fall velocity and particle diameter by a dimensionless frequency number 9. INTRODUCTION The fall velocity of a sediment particle, defined as the rate at which the particle settles through a fluid, is one of the most important, factors affecting the credibility and movement of earth material, the time that a. particle will remain in suspension in streamflow, and. the nature of deposition and bed roughness formed in moving: and quiet waters. The fall velocity for a given particle depends on its shape, size, and density as well as on the physical properties of the fluid. All these factors, individually or in combination, may affect the stability and the fall path of the particle. Other properties, such as roughness, roundness, or concentration of particles, and turbulence in the fluid, may also be important. PROBLEM AND SCOPE A particle moving relative to a fluid is acted upon by a drag force whose magnitude is a. function of the relative velocity between fluid and particle, fluid density, and particle size and shape. The drag force is - usually expressed as a function of the particle velocity - and size and in terms of the fluid properties. The relationship is not unique, however, and must be correlated by means of a coefficient of drag OD. The . coeflicient of drag is, in turn, related to the Reynolds number R. The relationship between 0D and R can be ‘ shown graphically by plotting CD. as a function of R . on logarithmic paper. Such a diagram will be referred , to as the 0D~R diagram. For some idealized cases, the relationship between 0D and R, at small values of R, can be determined mathematically. Generally, however, it must be established experimentally. The relationship between the coefficient of drag and the Reynolds number is often established with the particles rigidly mounted in, a moving fluid. Different and more complicated is. the case of freely moving Cl C2 particles in either a quiescent or a moving fluid. The resistance forces on a free particle cannot be measured directly but must be estimated from limited mathe- matical theory and from tests on mounted particles. Thus, the effects of rotation, density, and inertia in the unsteady fall path of a particle cannot be con- sidered if the particle is not free to respond to the unbalanced forces which may develop around it. This paper is a report of a study made to investigate some aspects of free-fall phenomena. The scope of the study was limited to the examina— tion of the free-fall behavior patterns of specific idealized particles falling singly in quiescent liquids. Its purpose was to evaluate the steadiness of particles with respect to orientation, fall velocity, and path of travel at Reynolds numbers greater than 10. The particles used were spheres, oblate and prolate spheroids, cylinders, and disks. The specific gravity of the spheres ranged from 1.14 to 14.95. The specific gravities of the other shapes ranged from 2.81 to 10.15. These shapes and specific gravities were chosen because they represent limiting conditions of natural gravel-sized sediment particles commonly found in alluvial channels. In addi- tion, the liquids used were water, various mixtures of water and glycerine, and pure glycerine with kinematic viscosities ranging from 0.010 to 3.59 sq cm per sec, respectively. DRAG CONCEPTS The energy imparted to a fluid by a particle falling in the fluid is either transmitted to the boundaries of the fluid or is dissipated in heat. The internal resistance Within the fluid to fluid motion is transmitted to the particle, in accordance with Newton’s third law of motion, and is called drag. According to Albertson, Barton, and Simons (1960) , this drag, or fluid resistance, is of two general types: shear drag, the tangential component of the resistance, and pressure drag, the normal component of resistance. SHEAR DRAG A shearing force related to the viscosity of the fluid occurs within the fluid as the molecules attracted to the particle move past those of the surrounding fluid. The magnitude of the resistance due to shear can be defined by 2 R,=0.s ”I“ ; 2 (1) Where 01=a dimensionless coefficient, S=surface area of particle (cm2), p,= density of the fluid (dyne-secz/cm“), and w=path fall velocity of the particle (cm/sec). SEIDIMEN'I‘ TRANSPORT IN ALLUVIAL CHANNELS Equation 1 is a function of the Reynolds number wd which can be defined as the ratio of the fluid inertia forces to the fluid viscous forces and where d=characteristic length of the particle (cm) and v=kinematic viscosity (cmZ/sec). At very small R, the shear force is the result of the shear stress acting over the entire surface of the particle and is distributed throughout the fluid. If the fluid is of finite extent, the stress is transferred to its outer bound- aries. On the other hand, at large R, separation occurs on the lee side of the particle, causing a wake to develop. The formation of the wake decreases the surface area over which the shear force acts. At the same time, the velocity around the particle increases, which tends to increase the shear drag. Then, at large R, the most concentrated stresses are confined to the boundary layer near the surface of the particle and to the wake of the particle. Most of the energy imparted to the fluid is dissipated in the wake. PRESSURE mm; The resistance to movement of the mass of fluid in the path of a particle causes a positive pressure in front of, and a negative pressure behind, the particle. This pressure differential is the resistance to fall due to pressure drag and can be defined by 2 3.: 02A ”% (3) where 02=a dimensionless coefficient and A=the projected area of the particle (cmz). At small R, the pressure changes systematically around the particle in accordance with the relative acceleration and deceleration of the fluid. The pressure force is distributed throughout the fluid. On the other hand, at large R, a wake develops behind the particle. The pressure in the wake is virtually that found in the boundary layer at the point of separation. As in shear drag at large R, the pressure forces are confined to the boundary layer and the wake of the particle. TOTAL DRAG The surface area of a particle 8', used in equation 1, can be expressed as the product of some constant and the projected area of the particle A used in equation 3. When the total resistance R , of a freely falling particle becomes equal to the buoyant weight or total driving THE BEHAVIOR OF LARGE PARTICLES FALLING IN QUIE‘SCENT LIQUIDS force F of the particle, equations 1 and 3 may be written in the form 2 7 (4) R,=F=0DA ”’2‘” where 0D: 01(constant) + 02: coefficient of drag, F=¥g (Pp—P!) in dynes, g=acceleration of gravity in cm/secz, Sol=particle volume in cm", p,=fluid density in dyne-secz/cm4, and pp=particle density in dyne-sec2/cm4. This is the general form of the law of resistance to motion of solids in a fluid as expressed first by Newton (Prandtl and Tietjens, 1934). At small R (less than 0.5), Stokes’ solution (Lamb, 1932) for resistance to flow around spheres shows that two-thirds of the total resistance is due to shear, and one-third is due to pressure. The drag at small R is sometimes called deformation drag because the shear and the pressure forces are distributed throughout the fluid and thus “deform” the fluid. At large R, the shear drag becomes insignificant, and the total drag becomes predominantly pressure drag. HISTORICAL DEVELOPMENT OF DRAG CONCEPTS The present knowledge of resistance to motion experienced by a solid particle falling through a fluid has been developed largely within the past 125 years. Both mathematical and experimental studies have contributed to this fund of knowledge. MATHEMATICA L DEVELOPMENT From the Navier—Stokes equations, rather concise equations have been developed that define the nature of flow around particles for Reynolds number R less than about 0.5. However, solutions to the Navier— Stokes equations have not been found for flow con- ditions where R>>0.5 as in this study; hence, the Navier-Stokes equations are not applicable herein. For values of R greater than the Stokes range, concepts will be based on the Lagrangian description of flow phenomenon, or from the point of view of an observer traveling with the particle through a sta— tionary fluid. For unsteady motion of a particle in a fluid, Stelson and Mavis (1957) show that the force required to cause acceleration is greater than the force required to accelerate the mass of the particle m,, and that the mass of the displaced fluid m, must be con- sidered. The mass of the fluid that must be considered is related to the shape as well as the size of the particle. The total mass, or virtual mass M is, therefore, the sum of the particle mass and an appropriate fluid mass. 307—965 0—69—2 C3 The character of the resistance of an accelerating particle is defined by Brush (1964) on the basis of Basset’s equations. When the nonlinearity of the resistance term, for motion beyond the Stokes range, is accounted for, the equation becomes: ‘dw Md—“~ —0 "d2”! | 3W" WT alt—pm”; 1’8wa «pqu‘lE (5) where g=acceleration of gravity (cm/sec2), d=a characteristic diameter of the particle (cm), u=dynamic viscosity (dyne-sec/cmz) t= time (sec), —r=time interval S t, M = virtual mass (dyne—secZ/cm), mp=mass of the particle (dyne-secz/cm), and m ,=mass of the accelerating fluid (dyne-secz/cm). For steady motion, equation 5 reduces to equation 4. A solution to equation 5 was presented by Brush in the form of series expansions, which is suitable for computer analysis. Odar and Hamilton (1964) also worked with Basset’s equation. They expanded its range of applicability into the nonlinear zone by accounting for the ratio of the convective to local acceleraaion. EXPERIMENTAL DEVELOPMENT The flow characteristics around a particle become so complex when R>1 that resistance to motion and the behavior of the falling particle must be determined experimentally. Thus, Newton’s law of resistance, equation 4, has been used as the basis of experimental development. The experimental development has been achieved by determining CD from measurements of the fluid and particle properties as needed in equation 4 and from measurement of the particle velocity relative to that of the fluid. Pernolet (Wadell, 1934), a French engineer, made some of the first experiments on fall velocity in 1851. He discovered that the fall velocity of lead particles of similar weight varied with shape. Among the first contributors to use a systematic approach to deter- mine the effect of shape on fall velocity of a particle included Rubey (1933) Zergrzda (Schulz and others, 1954) and Wadell (1932). Included in Wadell’s (1932, C4 1933, 1934) work were the following particle descriptive parameters: 1. The nominal diameter dn, the diameter of a sphere having a volume equal to the volume of the par- ticle 41, 9f 1|" 1/3 d’Fl (6) 2. The degree of sphericity \II, the cube root of the ratio of the volume of the particle to the volume of the circumscribing sphere 0,, .rz 0., 1/3 w: (7) 3. The degree of roundness T, in a plane with reSpect to the particle, the ratio of the sum of the ratio of the radius of curvature of the corner 1', to the radius of the maximum inscribed circle 9”, to the number of corners N c, T 2:7: (8) 4. The degree of circularity E, the ratio of the length of the circumference of a circle of area equal to the plane area of the particle 06 to the length of the circumference of the particle 0,, 0c 3:6; (9) Of these four shape parameters, the nominal diameter has greatest application because of the relative ease of making the necessary measurements. It is used extensively as the characteristic length in computa- tions of the Reynolds number. In addition to Wadell’s nominal diameter, two other particle diameter concepts are commonly used and defined by B. C. Colby (in US. Inter-Agency Comm. Water Resources, 1957). 1. The sedimentation diameter d, is the diameter of a sphere that has the same specific gravity and same terminal uniform settling velocity as the given particle in the same sedimentation fluid. The sedimentation diameter varies with the viscosity of the fluid. Chatuthasry (1961) studied the sedi- mentation diameter as a function of the nominal diameter and found that the ratio ds/dn tended to decrease when R increased beyond 100. 2. The sieve diameter Cl,e is the length of the side of the smallest square opening of the sieve through which the given particle will pass. Serr (1948) proposed SEDIMENT TRANSPORT IN ALLUVI-AL CHANNELS that the ratio dse/d, be used as a measure of par- ticle shape. Shape description was advanced independently by Corey (1949) and McNown and Malaika (1950) with an expression of the ratio of the three mutually per- pendicular axis lengths, 6 SFc=—’ M (10) Where a=maximum diameter of the particle (cm), b=intermediate diameter of the particle (cm), and c=minimum diameter of the particle (cm). It was soon learned that this relationship did not ade- quately relate the fall velocity of all sizes and shapes of particles to that of the fall velocity of a sphere. Alger (1964) used the ratio of the diameter of a sphere Whose surface area is equal to that of the particle to the nomi- nal diameter of the particle, dA/dn, to modify equation 10. In a study of the various shape parameters affecting fall velocity, Wilde (1952) found that the maximum projected area of a particle could be closely approxi- mated by the product of the lengths of the major and intermediate axes. He also found that the fall velocity increased greatly with the roundness of a particle. Roundness has not been used extensively because it is diflicult to measure. A dynamic shape factor SF, has been derived by Briggs, McCullock, and Moser (1962) by solving equa- tion 4 for wz, dividing both sides by the square of the fall velocity of a nominal sphere 0),, and combining terms to obtain w2 8 F 1 SET—7? ,7; CTR ‘11) At large R, the fall pattern of particles is usually irregular. Wilmarth, Hawk, and Harvey (1964) studied the fall pattern of disks in various fluids and found that the dimensionless mass moment of intertia I of disks correlated with particle stability. The inertia term “I,” referred to in this paper as the “stability number,” is defined by: (12) where I = the mass moment of inertia of the particle (dyne-cm-sec 2). Experimentally, I determines a point on the OD—R diagram at which a particle would no longer be steady in orientation. Disks, for example, were found to be stable with the maximum area per- pendicular to the fall line when R is less than 100. At THE BEHAVIOR OF LARGE PARTICLES FALLING IN QUIEISCENT LIQUIDS R>100 the orientation of the disk and its path of travel were no longer constant. Once oscillation of the particle began, Wihnarth, Hawk, and Harvey found that I could be correlated with a dimensionless “frequency number” defined by 9:13, (13) Where f is the frequency of oscillation or tumbling. The relation between I and 0 is linear for a given R. It is evident from this summary of previous work on particle behavior that parameters controlling stability of the free falling particle have received too little attention, and therefore, should receive further atten- tion in this paper. ACKNOWLEDGMENTS This report is a modification of a Ph. D. dissertation presented to Colorado State University by the senior writer (Stringham, 1965) while employed by the US. Geological Survey. Notable among those giving counsel and guidance during the study were Professors M. L. Albertson, R. S. Creely, and E. J. Plate, of Colorado State University, and E. V. Richardson, of the US. Geological Survey. Ashok Kumar, Anwiya Andrews, Reinhard Weiss, and Darell Zimbelman assisted with data collection and the reduction of voluminous raW data to a usable form. Appreciation is extended to P. C. Benedict, R. W. Carter, B. C. Colby, B. R. Colby, J. V. Skinner, G. P. Williams, and F. Witzigman in connection with review of this paper. FALL BEHAVIOR PARAMETERS In accordance with the scope of this paper, it is necessary to understand how the various parameters involved in fall velocity phenomenon at R > 10 operate. A discussion of the major fall velocity param—. eters as deduced from dimensional analysis is presented. The general form of the resistance equation is that of equation 4. VARIABLES AFFECTING PARTICLE BEHAVIOR The three major kinds of variables which affect the behavior of a freely falling particle are fluid properties, particle motion characteristics, and particle character- istics. Acceleration or deceleration, as expressed in equation 5, occurs if the drag forces do not balance the buoyant weight. When drag and buoyant weight balance, the motion is steady and is governed by equation 4. It should, therefore, be possible to define all types of falling particle behavior, including fall velocity, acceleration, and pattern of fall, in terms of the force balance between buoyant weight and drag. C5 FLUID VARIABLES Fluid variables of concern are density and viscosity. The density ratio between particle and fluid p,/p,, is a measure of the driving force and hence the fall velocity of the particle. The fall velocity increases with the density ratio. The coefficient of drag 0D, the Reynolds number R, and the stability number I are also functions of fluid density. Both shear and pressure forces are dependent upon the viscosity of the fluid. The magnitude of the shear force is a direct function of viscosity. Viscosity controls the pressure force to the extent that it affects the nature of the boundary layer and the point at which the boundary layer separates from the particle. As discussed earlier, the point of separation affects the pressure within the wake behind the particle, and hence affects the pressure drag. It has been noted, as will be discussed later, that patterns of fall for some particles are dependent upon their fall velocity. It is probable that changes in the fall velocity, because of viscous changes in the fluid (brought about usually by temperature changes), can significantly affect the fall pattern of the particle. As mentioned in the introduction, the fall velocity of sediment particles found in the bed of an alluvial channel is one of the factors which control the bed form of the channel. Fahnestock and Maddock (1964) note that the bed form of the Rio Grande near El Paso, Tex., changes with the annual fluctuation of the water temperature and the corresponding change in viscosity. VARIABLES ASSOCIATED WITH PARTICLE MOTION Velocity, vortex formation and shedding, and circu- lation are the variables considered which affect fall pattern. In accordance with equation 5, resistance to motion is a function of the square of the velocity. Both shear and pressure drags increase with increasing velocity. Vortex formation and shedding When separation occurs behind an object moving in a fluid, vorticies form in the wake. The vorticies re- main bound to the particle under certain conditions, and under other conditions they are shed. Prandtl and Tietjens (1934) have shown that in a two-dimensional flow around a cylinder, at a certain value of R, the vorticies are alternately shed, first from one side of the cylinder, and then the other, at regular periodic intervals. At greater R, the periodicity disappears, but the shedding continues. This process of vortex shedding, radically changes the pressure distribution in the wake, which, in turn, may cause oscillation of the cylinder. Wilmarth, Hawk, and Harvey (1964) painted some of their disks with a water-soluble dye. As the disk 06 dropped through the water, the dye in the wake re- mained giving a visible trace of the wake and its as- sociated vorticies, which they photographed. Pictorial conception of those photographs is given in figure 1. At small R where the disk orientation was stable, the wake formed a straight streak behind the particle. When oscillation first began, (for R z 100), and motion was close to vertical with very little lateral translation, a complete horseshoe-shaped vortex ring was shed at the end of each swing (fig. 1A). At greater R, when A SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS lateral translation was associated with the oscillation, vortex trails formed on the edges of the disk on the ends of a diameter perpendicular to the direction of motion much the same as occur on wing tips of aircraft (fig. 13). At the apex of each swing, a vortex was shed from each end of the perpendicular diameter. Particles of other shapes will have different vortex patterns. The vortex pattern and the associated pressure distribution is one of the major factors controlling particle orientation and path of travel. B FIGURE 1.—Vortex pattern of an oscillating disk. After Wilmarth, Hawk, and Harvey, 1964. A, Oscillation accompained by very little horizontal translation, path of travel almost vertical. B, Oscillation accompanied by horizontal translation, path of travel almost parallel to disk face. THE BEHAVIOR OF LARGE PARTICLES FALLING IN QUIEISCENT LIQUIDS Circulation Circulation can be considered as a circular fluid flow around a submerged particle (fig. 2A). If circular flow is superimposed on the steamline flow (fig. 2B), the streamlines will be distorted (fig. 20). This distor- tion of the flow pattern causes a nonsymmetrical pressure distribution around the particle and gives rise to lateral thrust and a lift force, which combines with the drag force to resist motion. Wilmarth, Hawk, and Harvey (1964) also show that circulation exists around the disk when lateral trans- lation occurs. The combination of circulation of the fluid and translation of the particle is the cause of the vortex trails mentioned in the preceding section. The circulation produces a lift force on the particle similar to that associated with the aerodynamic effects upon which atmospheric flight depends. Thus, through at least part of the oscillation of the disk, its motion is controlled by a force system similar to the system which controls flight. Circulation may have some small effect on the shear drag, but this effect would be small in comparison to its effect on pressure drag. GEOMETRIC VARIABLES The geometric variables that affect particle behavior are shape, roundness, surface roughness, and orienta- tion with respect to the direction of motion. The density of the particle affects the buoyant weight as indicated in the discussion of fluid density. The relative lengths of the three mutually per- pendicular axes of a particle are used as an index of the particle shape. The shape of the particle controls the geometry of fluid flow. The fluid flow geometry afl'ects the shear and pressure drag by controlling the contact area between the fluid and particle, the pressure distribution around it, and the point of separation of the wake. If a particle is not symmetrical, the shape, with reference to the direction of motion, will vary with variation in the orientation of the maximum cross- C7 sectional area. Resistance will be controlled by the geometry of flow as discussed in the preceding section. The roundness of a particle modifies the effect of shape on the point of separation. Sharp corners cause separation at smaller Reynolds numbers than rounded ones, and a wake develops at lower velocities. The development of the wake increases the pressure drag. Rounded particles, therefore, will have less resistance to motion; hence greater free-fall velocities than sharp- cornered ones with similar characteristics such as size. Surface roughness of a particle may increase or decrease the resistance to motion. Shear drag will be increased by roughness if the roughness protrudes beyond the laminar boundary layer. Prandtl and Tietjens (1934) show that separation around a sphere is controlled by flow conditions in the boundary layer. When the flow in the boundary layer changes from laminar to turbulent, the point of separation moves from the upstream to the downstream side of the sphere. This reduces both the size of the wake and the pressure drag. The total drag will be affected to the extent that the balance between shear and pressure drag is affected. DIMENSIONAL ANALYSIS Measurable variables pertaining to the resistance to motion of a single particle falling at a uniform velocity in a quiescent fluid include: w=fall velocity (cm/sec), p,=fluid density (dyne-secz/cm‘), p=dynamic viscosity of the fluid (dyne-sec/cmz), pp=particle density (dyne-secz/cm“), a=major axis of the particle (cm), b=intermediate axis of the particle (cm), c=minor axis of the particle (cm), F= driving force (dynes), f=frequency of oscillation or tumbling (cycles/ sec), S,=surface roughness (cm), and S=surface area (cm2). A B /\—/\ /\—/\ /\ _//\—) FIGURE 2,—Circular fluid flow around a particle. A, Pure circulation. B, Pure translation. 0, Circulation and translation. C8 These variables can be expressed in the functional equation: ¢1(wy pf! ”’1 Pp; a: by C, F’f’ ST; S)=0 (14) Selecting w, a, and p, as the repeating variables, the following groupings can be established: pxwa,_F_,,,,a21§§,f_a_0 (15) u azpfw2 pfaaa/(L2 w ¢2 Because surface roughness will not be considered now, Sr 3 can be neglected. Then, combining: c . c 8—” and — to obtain 373 and —— Pr (1 Pf a E and g to obtain % and Q a a a (1 results in: ppccch’Lfa Wpfaa ca” w prwa F M @29er (16) 3 If the repeating variables used are a, p,, and F, a functional equation similar to equation 16 results and and is expressed as: p, 0 ob S fzp,a4_ F_pr F _,,__,_,__ 2 17 Ta2pfw2p,fl2aaa2 F () ¢4 b 9' . Because %’ 5’ and i, are functlons of the geometry of the particle, they can be combined into a term called the shape factor SF. Assuming terminal fall velocity: M 0: R ——Reynolds number [4 F 0,sz 2 oc C’D—coefiicient of drag 33 2 oc I—Wilmarth’s stability number Pf pr F —2=—2 cc A—force number pv fa 3 cc B—frequency number f 2p “4 ~ “F— o: 1,000 (fig. 3, upper curve). The curve for fixed disks represents an extreme condition in which the drag force is almost entirely pressure drag; it occurs when the size and shape of the wake are fixed by separation of the fluid from the boundary of the 10 l||| llll I III I | \R Fixed disk 1_ _ , \ WP: _ \——’ _. 0.1 I l I I I | I I I I l I Airsi‘im 10 102 103 104 105 DIMENSIONLESS COEFFICIENT OF DRAG (CD) REYNOLDS NUMBER (R) FIGURE 3.—Coefificient of drag as a function of Reynolds number for fixed disks, spheres, and airship hulls. After Rouse, 1946. THE BEHAVIOR OF LARGE PARTICLES FALLING IN Q‘UIEISCENT LIQUIDS particle at a fixed place around the particle periphery. Because shear drag is a function of velocity, as is the Reynolds number, the fact that OD does not increase with R indicates the minor role played by the shear in the total drag on a disk at high Reynolds numbers. The relationship of 0D to R for a smooth sphere (fig. 3‘, lower curve) is typical for flow conditions around a particle Where a combination of both shear and. pressure forces are significant for greater Reynolds numbers than for conditions previously discussed. Here, the place of separation is affected by flow conditions in the boundary layer as well as by shape. The relationship of CD to R for an airship hull (fig. 3, lower right corner) mounted with the long axis parallel to the flow may be considered a case where the resistance to flow is due almost entirely to shear drag on the surface of the hull for all ranges of R. The hull is a streamline shape, and separation does not occur except at the extreme downstream end. SHAPE FACTOR The shape factor combines the lenghts of the three mutually perpendicular axis into one parameter. The particular form that will be used in this study is the Corey shape factor as defined previously (equation 10). FREQUENCY NUM BERS Two numbers which are functions of frequency of oscillation or rotation are deduced from the dimensional analysis. The frequency number 0 has been used by Wilmarth, Hawk, and Harvey (1964) and others in studies of resistance to motion. This number is a sig- nificant factor only when cyclic oscillations or complete rotation occurs. The density-frequency number reflects the density ratio between the fluid and the particle. Logically, density should affect the frequency of oscillation through the inertial forces; this number, therefore, may be significant. STABILITY NUMBERS The steadiness of a particle does not influence re- sistance to motion in studies on rigidly mounted par- ticles, nor on particles which maintain a stable orientation during free fall. For freely falling disks, the stability number I can be used in conjunction with the Reynolds number to define a region of stable fall, and hence is termed a “stability number” (Wilmarth and others, 1964). Since particles with shapes other than disks are used in this study, the number will be spe- cifically defined for each shape on the basis of the definition for disks as a pattern. The stability number for disks, as defined by Wil- marth, Hawk, and Harvey, is the ratio of the mass moment of inertia of a thin disk about its diameter to '09 a quantity proportional to the mass moment of inertia of a rigid sphere of fluid of the same diameter as that of the disk about its diameter. Or, in equation form: I I = mar” (22) where a? 7r 4 I pp-V 16 ’61 ppa c (23) then 1:.1 & E. (24) Thus, it can be seen that I is a constant multiplied by the density ratio of the disk and the fluid in which the particle is submerged and by the thickness-diameter ratio of the disk. The stability number for oblate spheroids is defined in the same way as for disks. Therefore, with: (12+ 62 I = pp-IZ T, (25) the stability number becomes: _£ a2+62 p, _a5 20 3' (26) The stability number for cylinders is defined as the ratio of the mass moment of inertia of a cylinder about an axis perpendicular to its major axis to a quantity proportional to the mass moment of inertia of a rigid disk of fluid whose diameter is equal to the length of the cylinder about an axis perpendicular to the diameter of the fluid disk. Therefore, with: c2 a2 I—Pp'lz fi+1_2- ’ (27) the stability number is: _-V 02 a2 p,, _a E 12 p, (28) The stability number for prolate spheroids is defined in a manner similar to the stability number for cylin- ders. The moment of inertia is: (:2 a2 1:”ng (29) and the stability number becomes: _£ 62+az £13. I—a5 20 p, (30) 010 The stability number for spheres, if defined in terms of the moment of inertia of the sphere and the moment of inertia of the associated fluid sphere of the same diameter, is the density ratio of the sphere and the fluid. FORCE NUMBER The force number, known as a size coefficient by other investigators, has been used to estimate fall velocity of a nominal sphere in fall-velocity studies. Not only does it come from the dimensional analysis, but it can be derived from Newton’s drag equation. By proper manipulation of equation 4, and assuming the area term A can be written as some constant k times a characteristic diameter, the drag equation can be written as: 2 F='£‘;—”f 0,, R2, (31) 01‘ £2:ch R2: (32) where k is [cl/2. Since F is the buoyant weight of the particle, for any discrete particle falling in a fluid of constant density and viscosity, the force number )\ is unique. This indicates that the product ODR2 is constant, and that a line of constant A on the OD—R diagram should have a slope of —2. The unique nature of the relationship among )\, CD, and R indicates to some extent the influence that shape, diameter, and velocity have on the position on the UD—R diagram for any discrete particle. If for any given value of )\ equation 32 is rewritten as: k=0D R2- (33) 0D is replaced by its definition as derived from equation 4, and the Reynolds number is written in accordance with its definition, then [C is: _2_F 1 (weir, —Apf .072 U2 (34) or by letting A=k1d2, then __E l (and)? k‘klmwdr v2 (35) In equation 35, note that wd is common to both the Reynolds number and the coefficient of drag. There— fore, any factor which affects either to or d affects both 01) and R, changing the individual terms, but not the SEDIMENT TRANSPORT IN ALLU'VIAL CHANNELS constant-product relationship. If by some [means the shape of a particle could be changed while maintaining the same buoyant weight, the relationship of 0D to R for the particle would shift on the OD—R diagram to a new position along the line of constant A. Any other parameter which might affect velocity, such as rough- ness or roundness, would also simply change its position along the line of constant )\. In the literature, the question as to what diameter should be used in computing OD and R for irregularly shaped particles is discussed. Equation 35 indicates that the only effect of picking one particular diameter over another would be to shift position on the OD—R diagram on a line of constant ). To be specific, because the area associated with the nominal diameter of a nonspherical particle is less than the maximum pro- jected area of the particle, its characteristic diameter is the smaller for the same particle. Hence, the point based on the nominal diameter plots at a greater value of 0D and a lesser value of R than the point based on the characteristic diameter associated with the maxi- mum projected area, but both points are on the same A line. CHOICE OF CHARACTERISTIO DIAMETERS AND VELO CITIES The computations for CD and R require the use of a characteristic length and velocity. Two characteristic diameters and two characteristic velocities are used in this report. The characteristic lengths are the maximum diameter dm and the nominal diameter d”. The diameter dm is the diameter of a circle which has an area equal to the maximum projected area of the particle. When 10100 will be used as an example (fig. 4). When the plane of the disk face is neither perpen- dicular nor parallel to the direction of motion, the re— sultant pressure force opposing motion acting normal to the face of the disk has both horizontal and vertical ”7.47 FIGURE 4.—Forces on a falling disk. Component L is the lift force normal to the drag, and component D is the drag force parallel to the direction of travel. See text for description of symbols. 307—965 0—69—3 Cll components. The vertical component resists the vertical fall of the disk, whereas the horizontal component causes its horizontal movement. If, as a. result of circu- lation or the nonsymmetrical formation of the trailing vortex, the center of pressure does not act through the center of gravity of the disk, a torque will be exerted on the disk. The magnitude of the torque will be equal to the product of the magnitude of the resultant pressure force and the distance along the disk between the center of pressure and the center of gravity (fig. 4). The plane of the disk face must continually change because there is no movement to counterbalance the torque. This change in the angle of inclination is the reason that an oscillating disk swings through curvilinear arcs. With reference to figure 4: mg: buoyant weight of the particle, D= drag force, L= lift force, l=distance between the center of gravity and center of pressure, u=horizontal velocity of the particle (cm/sec), v=vertical velocity of the particle (cm/sec), a=angle of attack or the angle between the plane of the disk face and direction of travel, and B=angle between direction of travel and the vertical. By appropriate substitutions, the differential equations of motion for a freely falling disk can be written: mg-t—mg-l-D cos B+L sin [3: 0, (36) du . m (it-+0 sm fi—L cos (i=0, and (37) lA— ”f2“ (Opsin «+0. cos zoo—Id d:,_ =.0 (38) At the instant an oscillating disk stops at the apex on one of the arcs, the plane of the face is inclined with the horizontal, and the disk weight is the onlyforce acting on it. Once motion begins, the horizontal com— ponent of the resultant pressure changes the horizontal position, the vertical component opposes the motion, and the torque changes the angle of inclination, turning the disk towards the horizontal. This process continues until the apex at the opposite end of the arc is reached. This apex is reached rather abruptly once the angle of inclination is upward, because the resultant force and the weight of the particle combine to reduce the velocity of the disk and cause it to stall. It is then in a position to begin its next arc of motion. The net result of all the forces acting on a disk is a dynamic situation involving the momentum of the 012 disk, and the horizontal, vertical, and torque compo- nents of force acting on it. All these variables continually change with time. PARTICLES, LIQUIDS, EQUIPMENT, AND PROCEDURE PARTICLES The particles studied included spheres, cylinders, disks, and oblate and prolate spheroids. Oblate spheroids are solids of revolution generated when an ellipse is rotated about its minor axis. The maximum projected area of an oblate spheroid is circular. Prolate spheroids are solids of revolution generated when an ellipse is rotated about its major axis. The maximum projected area of a prolate spheroid is elliptical. Nylon spheres, teflon spheres, and steel spheres, of three sizes and one tungsten carbide sphere were used (fig. 5). The diameters of the nylon, teflon, and steel spheres were 1.91, 2.54, and 3.81 cm, respectively. The tungsten carbide sphere SErDIMENT TRANSPORT IN ALLU'VLAL CHANNELS was 2.54 cm in diameter. In all, there were 10 spheres, no two being alike in both material and size. The other dimensions and properties of the spheres are given in table 1. Three sizes of cylinders, disks, oblate and prolate spheroids were machined from lead and aluminum, making a total of 24 nonspherical particles, no two being the same size, shape, and density. The lengths of the major axes were 1.91, 2.54, and 3.81 cm. The thickness to diameter ratio was 0.1 for the disks and 0.5 for the oblate spheroids. The length to diameter ratio was 4.0 for the cylinders and 2.0 for the prolate spheroids. Additional properties of these particles are also summarized in table 1. LIQUIDS Seven different liquids, pure glycerine, water, and five different mixtures of glycerine and water were used in the experiment. Percentages of glycerine used to TABLE 1.—Particle properties, measured and computed Measured Length Maximum Maximum Volume Surface area Particle No. Material and Specific gravity Wei ht Ratio projected projected V S shape 1 (:5 Maximum Minimum c/a 8,14% diameter a c m (cm (cm) (cm 2) (cm) (cm s) (cm 2) 1 N—S 1. 14 4. 17 1. 91 1. 91 1. 00 2. 86 1. 91 3. 64 11. 46 2 N—S 1. 14 9. 87 2. 54 2. 54 1. 00 5. 08 2. 54 8. 61 20. 25 3 N—S 1. 14 33. 22 3. 81 3. 81 1. 00 11. 40 3. 81 28. 96 45. 53 4 T-S 2. 15 7. 82 1. 91 1. 91 1. 00 2. 86 l. 91 3. 63 11. 44 5 T—S 2. 15 18. 60 2. 55 2. 55 1. 00 5. 09 2. 55 8. 64 20. 41 6 T—S 2. 15 62. 92 3. 82 3. 82 1. 00 11. 43 3. 82 29. 07 45. 78 7 SrS 7. 68 27. 76 1. 91 1. 91 1. 00 2. 85 1. 91 3. 62 11. 40 8 SrS 7. 68 65. 68 2. 54 2. 54 1. 00 5. 07 2. 54 8. 58 20. 25 9 SrS 7. 90 229. 56 3. 80 3. 80 1. 00 11. 36 3. 80 28. 84 45. 28 10 Tc—S 14. 95 128. 34 2. 54 2. 54 1. 00 5. 06 2. 54 8. 58 20. 25 11 L—OS 10. 15 21. 38 1. 91 1. 04 . 54 2. 88 1. 91 2. 11 8. 20 12 L-OS 10. 15 45. 30 2. 49 1. 33 . 53 4. 87 2. 49 4. 64 13. 86 13 L—OS 10. 15 156. 85 3. 85 1. 89 . 49 11. 62 3. 85 15. 45 31. 89 14 L—PS 10. 15 9. 94 1. 91 . 96 . 50 1. 44 1. 35 . 98 4. 79 15 L—PS 10. 15 23. 26 2. 52 1. 28 . 51 2. 54 1. 80 2. 29 8. 71 16 L—PS 10. 15 76. 52 3. 85 1. 92 . 50 5. 81 2. 72 7. 54 19. 9 17 L—C 10. 15 3. 88 1. 91 . 48 . 25 . 91 1. 08 . 33 3. 24 18 L—C 10. 15 8. 12 2. 54 . 63 . 25 1. 61 1. 43 . 80 5. 49 19 L—C 10. 15 27. 49 3. 81 . 95 . 25 3. 63 2. 15 2. 71 12. 79 20 L—D 10. 15 5. 50 1. 91 . 19 . 10 2. 87 l. 91 . 54 6. 28 21 L—D 10. 15 13. O7 2. 54 . 26 . 10 5. 08 2. 54 1. 29 12. 20 22 L—D 10. 15 44. 20 3. 81 . 38 . 10 11. 42 3. 81 4. 35 26. 13 23 A—OS 2. 81 5. 60 1. 91 . 99 . 52 2. 85 1. 91 1. 99 8. 02 24 A—OS 2. 81 12. 66 2. 50 1. 31 . 52 4. 90 2. 50 4. 51 15. 63 25 A—OS 2. 81 45. 05 3. 78 1. 96 . 52 11. 21 3. 78 15. 99 31. 7O 26 A—PS 2. 8] 2. 48 1. 83 . 95 . 52 1. 37 1. 32 . 88 4. 72 27 A—PS 2. 81 5. 98 2. 50 1. 27 . 51 2. 49 1. 78 2. 13 8. 52 28 A~PS 2. 81 20. 00 3. 78 1. 88 . 50 5. 57 2. 67 7. 11 19. 06 29 A—C 2. 81 . 90 1. 91 . 47 . 25 . 94 1. 09 . 32 3. 17 30 A—C 2. 81 2. 15 2. 54 . 64 . 25 1. 62 1. 44 . 76 5. 76 31 A—C 2. 81 7. 62 3. 81 . 96 . 25 3. 64 2. 15 2. 71 12. 74 32 A—D 2. 81 1. 54 1. 91 . 19 . 10 2. 87 1. 91 . 55 6. 87 33 A—D 2. 81 3. 62 2. 54 . 26 . 10 5. 08 2. 54 1. 29 12. 17 34 A—D 2. 81 12. 27 3. 81 . 38 . 10 11. 39 3. 81 4. 37 27. 39 1 N, nylon; T, teflon; Sc, steel; T., tungsten carbide; L, lead; A, aluminum; S, sphere; OS, oblate spheroid; PS, prolate spheroid; C, cylinder; D, disk. THE BEHAVIOR OF LARGE PARTICLES FALLING IN QUIE‘SCENT LIQUIDS (313 TABLE 1.—Particle properties, measured and computed—Continued Computed Nominal Nominal Surface Shape Stability number 1X10z Particle No. diameter area diameter Ratio factor Sphericity dn An dA dA/dn SF ‘1’ Percent glycerine (cm) (cm 2) (cm) 0.0 70.0 83.3 90.1 95.2 98.0 100.0 1 1. 91 2. 86 1. 91 1. 00 1. 00 1. 00 ________________________________________________________ 2 2. 54 5. 08 2. 54 1. 00 1. 00 1. 00 ________________________________________________________ 3 3. 81 11. 4O 3. 81 1. 00 1. 00 1. 00 ________________________________________________________ 4 1. 91 2. 86 1. 91 1. 00 1. 00 1. 00 ________________________________________________________ 5 2. 55 5. 09 2. 54 1. 00 1. 00 1. 00 ________________________________________________________ 6 3. 82 11. 00 3. 82 1. 00 1. 00 1. 00 ________________________________________________________ 7 1. 91 2. 85 1. 91 1. 00 1. 00 1. 00 ________________________________________________________ 8 2. 54 5. 07 2. 54 1. 00 l. 00 1. 00 ________________________________________________________ 9 3. 80 11. 36 3. 80 1. 00 1. 00 1. 00 ________________________________________________________ 10 2. 54 5. 06 2. 54 1. 00 1. 00 1. 00 ________________________________________________________ 11 1. 59 1. 99 l. 62 1. 02 . 54 . 83 16. 8 13. 9 13. 6 13. 4 13. 3 13. 3 13. 2 12 2. 04 3. 27 2. 10 1. 03 . 53 . 82 16. 8 13. 9 13. 6 13. 4 13. 3 13. 3 13. 2 13 3. 09 7. 46 3. 17 1. 03 . 49 . 80 16. 8 13. 9 13. 6 13. 4 13. 3 13. 3 . 13. 2 14 1. 23 1. 19 1. 24 1. 01 . 71 . 64 8. 38 6. 90 6. 80 6. 70 6. 64 6. 64 6. 60 15 1. 64 2. 12 1. 67 1. 02 . 71 . 60 8. 38 6. 90 6. 80 6. 70 6. 64 6. 64 6. 60 16 2. 43 4. 63 2. 52 1. 04 . 71 . 63 8. 38 6. 90 6. 80 6. 7O 6. 64 6. 64 6. 60 17 . 86 . 58 1. 02 1. 18 . 50 . 43 4. 38 3. 65 3. 56 3. 50 3. 47 3. 47 3. 45 18 1. 15 1. 04 1. 32 1. 15 . 50 . 44 4. 39 3. 65 3. 56 3. 50 3. 47 3. 47 3. 45 19 1. 73 2. 36 2. O2 1. 17 . 50 . 43 4. 39 3. 65 3. 56 3. 50 3. 47 3. 47 3. 45 20 1. 01 . 80 1. 41 1. 40 . 10 . 53 4. 98 4. 21 4. 10 4. 02 3. 99 3. 97 3. 96 21 1. 35 1. 42 1. 97 1. 46 . 10 . 53 4. 98 4. 21 4. 10 4. 02 3. 99 3. 97 3. 96 22 2. 03 3. 22 2. 88 1. 42 . 10 . 53 4. 98 4. 21 4. 10 4. 02 3. 99 3. 97 3. 96 23 1. 56 1. 90 1. 60 1. 03 . 50 . 83 4. 65 3. 88 3. 80 3. 74 3. 71 3. 71 3. 68 24 2. 05 3. 30 2. 23 1. 09 . 5O . 82 4. 65 3. 88 3. 80 3. 74 3. 71 3. 71 3. 68 25 3. 12 7. 63 3. 16 1. 01 . 50 . 82 4. 65 3. 88 3. 80 3. 74 3. 71 3. 71 3. 68 26 1. 19 1. 12 1. 23 1. O3 . 72 . 65 2. 32 1. 95 1. 90 1. 87 1. 86 1. 86 1. 84 27 1. 60 2. 00 1. 65 1. 03 . 71 . 64 2. 32 1. 95 1. 90 l. 87 1. 86 1. 86 1. 84 28 2. 39 4. 47 2. 46 1. 03 . 7O . 63 2. 32 1. 95 1. 90 1. 87 1. 86 1. 86 1. 84 29 . 84 . 56 1. 00 1. 19 . 49 . 43 1. 22 1. 02 1. 00 . 98 . 97 . 97 . 96 30 1. 13 1 00 1. 36 1. 20 . 5O . 43 1. 22 1. 02 1. 00 98 97 . 97 96 31 1. 73 2 34 2. 03 1. 17 50 . 40 1 22 1. 02 1. 00 . 98 . 97 . 97 . 96 32 1. 02 . 82 1. 48 1. 45 . 10 . 53 1 38 1 16 1. 13 1. 11 1. 10 1. 10 1. 09 33 1. 35 1. 43 1. 97 1. 46 . 10 . 53 1 38 1 16 1. 13 1. 11 1. 10 1. 10 1. 09 34 2. 02, 3. 22 2. 95 1. 46 . 10 . 53 1 38 1 16 1. 13 1. 11 1. 10 1. 10 1 09 define the specific mixtures were determined by weight. The glycerine and water were mixed with a large paint mixer for 5—10 minutes in two large interconnected barrels. During the mixing process the fluid was cir- culated from one barrel to the other to insure a homo- geneous fluid. When mixing was completed, the fluid was pumped into the fall column. The viscosities of the liquids (fig. 6) were measured with calibrated Cannon- Fenske viscometers. The densities of the liquid mixtures were taken from standard density tables (fig. 7). Temperatures were measured at the top, center, and bottom of the test section at the beginning of each day and periodically throughout the day. Rarely did the temperature vary more than 05° C through the test section or more than 02° C throughout the day. EQUIPMENT The fall column was a vertical clear plexiglass cylindrical column 3 meters high and 40 cm in diameter (fig. 8). The wall thickness was 0.625 cm. A 1-meter test section was located near the bottom of the column to allow the particles to fall through the liquid for about 1.5 meters to ensure that they reached terminal fall velocity before they entered the test section. The test section was circled with black plastic tape at 10 cm intervals. The clear plexiglass column and the fluid made it possible to see the tape on the back of the column and permitted a close approximation of the vertical position of the particle. After the experiments were started, a mirror was added at the bottom of the column to reflect the top light. Then, both the top and the bottom of the particle were illuminated. A wire basket was suspended below the test section to retrieve the particles. Periodically it was withdrawn from the column and the particles removed. A mini- mum of 10-15 minutes was allowed for the fluid to Cl4 SEDIMENT TRANSPORT IN ALLUVLAL CHANNELS FIGURE 5.——Particles used in experiments. Particles were marked with black stripes to make rotational behavior observable. A, Nylon, teflon, steel, and tungsten carbide spheres in order from top to bottom. B, Aluminum disks, oblate spheroids, prolate spheroids, and cylinders in order from left to right. return to equilibrium after the particles had been retrieved. Photographs of each drop were made with two 16-mm reflex movie cameras equipped with 10—mm wide-angle lenses and set 90° to one another with respect to the column (fig. 8). The speed of each camera could be varied from 8 to 64 frames per second. All drops were made at 16, 32, or 64 frames per second, depending on . the rate of particle fall and detail required to define particle behavior. A 10-second sweep timer was used to obtain direct readings to 0.1 second and estimated readings to 0.01 second. The timer was mounted at the side of the column and set level with the center of the test section. It was illuminated by two 100-watt incandescent light globes shielded to protect the film from direct exposure by this source. One camera photographed the timer directly, the other photographed an image of the timer reflected to it by a mirror. Thus, a reference time image was recorded on the pictures obtained with both cameras. 0.1 KINEMATIC VISCOSITY (11), IN SQUARE CENTIMETERS PER SECOND 0.01 0.005 20 25 30 35 40 TEMPERATURE, IN DEGREES CELSIUS FIGURE 6.—-—Kinematic viscosity of glycerine-water mixtures in terms of percent glycerine as a function of temperature. Fluid 1 was 100 percent water. Two 500-watt photo floodlights and a BOO-watt in— candescent lamp were suspended at the top of the column to direct light down through the column. The lights were turned on only during the run to prevent excess absorption of heat in the top layers of the fluid. The developed pictures were projected onto a grid to make the necessary particle location measurements. The projector was equipped with a single or multiple framing switch and a reverse switch that enabled the operator to change the pictures one frame at a time, watch a series of pictures as a slow-motion movie, or to reverse the film thus permitting “re-runs” of short sections. These switches were mounted in a remote control box to enable the operator to control the projec— tor from a position near the grid. The grid was a sheet of 10- by 10-to-the-inch graph paper. The projector was positioned to give a projection THE BEHAVIOR OF LARGE PARTICLES FALLING IN QUIEISCENT LIQUIDS 1.27 \ \\ 100 \ flnt \ 980 \ \”t\ \ \ 52 ”Green: \ n: 1.25 E \\ E \\ E 90'1 Derc int LIJ \ o \ 2 \ "a” O 1.23 n: E \ w \ 83 q 3 “’°‘"r\ a: c: \_\ .2. >- 1.21 I: m z LIJ o 9 :3 _I U. 1.19 \ \ \Mint \ \ 1.17 10 15 20 25 30 35 TEMPERATURE, IN DEGREES CELSIUS FIGURE 7.—Density of glycerine-water mixtures in terms of percent glycerine as a function of temperature. scale of 1 inch on the grid for 10 cm of the fall column. This arrangement permitted reasonably accurate esti- mates of the particle position at any time. PRO CEDUBE A permanent record was made of each drop of each particle with the two 16-mm movie cameras. The motion pictures thus made permitted a more accurate visualization of particle behavior and fall pattern than could be obtained with still pictures. The cameras were adjusted so that the camera lens were level with the center of the test section. The distance from the camera to the fall column was 7.5 feet for the first series of tests and 6 feet for the last series. The distance was changed to get better lighting characteristics. The cameras were manually operated throughout the experiment, and the particles were dropped by hand. 01?) Clock Test tube Camera PLAN VIEW ALights Tube Grid Camera SIDE VIEW FIGURE 8.—Schematic diagram of fall column. Determination of path and vertical drop lengths required measuring the distances between the positions of the particles in successive pictures as they were projected onto the grid. Inherent in this procedure is the assumption that the particle fell in a plane through the center line of the 016 column perpendicular to the camera. Generally, this was not the case. However, when the angle from the camera to the top or bottom of the measured section and the angle of refraction of the light in the fluid were considered, a maximum error of 16.5 to i825 percent in water and i595 to i7 .45 percent in glycerine can result. No attempt was made to compensate for the error in defining particle behavior. The distortion of the curved surface of the column was neglected. The error thus caused was affected by the position, parallel to the line of sight, of the particle in the column (fig. 9). The three-dimensional length of the fall path of the particle was determined by taking the x and 2, or the horizontal and vertical, coordinates from one camera and the y coordinate, from the other camera. The square root of the sum of the squares of the differences in position of successive pictures, summed for the entire measurable length, determined the length of the fall path. The vertical path was measured by taking the difference in the z coordinates of the particle at the beginning and end of the run. Except for disks, the fall and vertical paths were usually identical. The path and vertical velocities of the particles were determined by dividing the path and vertical distance by the elapsed time of fall. Some of the drops for disks required special analysis to determine the fall velocities. For example, during the drop through the test section, a disk would often tumble from one side of the column to the other, strike the wall, bounce along it for a short distance, then move away and begin a tumbling descent through the remainder of a test section. In these cases, only those parts of the drop where the disk was away from the wall were used in the computations. To arrive at a GI ' ycerlne KWall of fall column ———-— Water a _____ M x.\ ........ Light ray :i§\ ““““““ \\ \\\ K \ \\ \ \\ \ \\ / \ O 10 20 CENTIMETERS |__|_J FIGURE 9.——Distortion of light rays caused by fluid refraction and the curved surface of the fall column. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS single value of the velocity for that run, the distances which the particle fell in the center of the column were added and the sum divided by the elapsed time for falling that distance. For example, if a particle fell through the first 18 cm in 2 seconds and then struck the wall, fell down the wall for 10 cm, and then fell freely for 52 cm in 5 seconds before striking the opposite wall, the length of the fall path was treated as being 70 cm, elapsed time as 7 seconds, and the velocity as 10 cm/sec. If the same disk was dropped in the same fluid more than once, then the aggregate free-fall distance of all drops was divided by the accumulated free-fall time to determine the single velocity used in computations of 0D and R for that disk in that fluid. The procedure outlined above gave the greatest weight in the averaging process to the longest free-fall distance. EXPERIMENTAL RESULTS In the presentation of results, a few symbols have been changed from those common to current literature. Fall velocities and resistance to fall are expressed in terms of the coefficient of drag and the Reynolds number diagrams. The basic drop data and some param- eters computed therefrom are given in tables 2—6 for spheres, disks, oblate spheroids, cylinders, and prolate spheroids. The results for each differently shaped particle are plotted separately to avoid obscuring any significant relationships in a maze of points. The curves thus developed are later plotted together for compar- ison. The curves of the relation of 0D to R for fixed spheres and for disks, and a curve computed from Stokes’ equation, are plotted on all diagrams for ref- erence. The particular curves for fixed disks and spheres were taken from Rouse (1946). ' DES CRIPTION OF FINDINGS Terms relating to orientation, velocity, and path of travel of a particle need to be clearly defined. When a particle falls with its maximum projected area perpen— dicular to the direction of fall, in a straight vertical path at a constant velocity, the particle is said to be steady, and the condition of the fall is stable. When the particle orientation, direction of path, and velocity change during fall, the particle is said to be unsteady, and the condition of fall may be either stable or un- stable. Reference to fall patterns of particles and their effect on the appropriate descriptive parameters will be made in these terms. SPHERES Generally, the spheres fell in a straight, vertical path. Exceptions were small erratic nonrepeating horizontal movements exhibited by two or three of the nylon and teflon spheres as they dropped in water. The THE BEHAVIOR OF LARGE PARTICLES FALLING IN QUIElSCENT LIQUIDS TABLE 2.—Drop data for spheresl CD and R values for Travel Mean Run No. 2 distance velocity ”M and ‘1'- (cm) (cm/sec) 09 R X 10‘2 1-1—10 ______________ 100. 0 303. 0 0. 51 927 2—1—9 _______________ 103. 4 258. 6 . 51 1, 180 102. 7 209. 6 . 49 641 102. 0 185. 4 . 51 426 100. 6 192. 8 42 461 104. 6 94. 7 . 64 435 101. 6 98. 4 . 60 453 102. 6 87. 5 . 51 268 100. 1 29. 9 . 42 69 102. 5 80. 0 . 46 184 102. 4 39. 0 . 39 179 101. 5 34. 4 . 43 105 100. 0 24. 9 3 81 18 100. 0 44. 5 1 79 48 100. 0 83. 9 1 80 45 99. 0 114. 0 l. 29 . 80 100. 0 180. 0 . 82 1. 85 102.0 151. 0 . 96 1. 55 98. 0 206. 0 1. 07 1. 46 100. 0 22. 0 4. 05 . 15 100. 0 31. 4 2. 42 . 29 100. 0 49. 6 l. 47 . 64 100. 0 91. 0 1. 54 . 62 101. 0 122. 0 1. 14 1. 11 98. 1 184. 5 . 78 2. 51 98. 1 190. 0 . 74 2. 58 98. 0 202. 0 . 88 1. 84 100. 0 25. 0 2. 90 . 21 100. 0 35. 0 1. 98 . 39 100. 0 56. 0 1. 16 . 93 125-4—7 _______________ 99. 1 101. 0 1. 26 84 126-4-8 _______________ 98. 1 134. 0 . 94 1. 48 128—4—9 _______________ 69. 7 201. 0 . 66 3. 33 129-4—10 ______________ 97. 8 231. 0 . 87 2. 55 153—4-9 _______________ 91. 3 197. 0 . 69 3. 25 183—5—4 _______________ 100. 0 37. 0 1. 34 . 59 184—5—5 _______________ 99. 0 48. 8 1. 03 1. 03 185—5-6 _______________ 100. 3 70. 2 . 76 2. 22 190—5-9 _______________ 100. 8 252. 0 . 42 7. 75 194—5—7 _______________ 100. 1 129. 8 . 76 2. 05 195—5-10 ______________ 77. 0 256. 5 . 56 5. 39 240—6-4 _______________ 100. 5 45. 7 . 91 1. 40 241-6—5 _______________ 61. 2 55. 6 . 83 2. 27 243-6~6 _______________ 100. 9 80. 8 . 59 4. 95 247—6—7 _______________ 101. 5 145. 2 . 62 4. 45 248-6-8 _______________ 97. 4 198. 2 . 44 8. 05 249—6—9 _______________ 98. 2 233. 0 . 51 14. 1 250—6—10 ______________ 102. 7 267. 0 . 53 10. 8 251—6—7 _______________ 101. 3 158. 3 . 53 4. 85 343—7-4 _______________ 101. 8 67. 1 . 45 7. 64 344—7—5 _______________ 101. 1 77. 4 . 40 11. 7 345—7—6 _______________ 95. 6 101. 0 . 41 23 346—7—7 _______________ 97. 1 162. 5 . 50 18. 5 347—7—8 _______________ 100. 2 208. 0 . 40 31. 4 348-7—9 _______________ 96. 7 263. 0 . 41 58. 5 349—7—10 ______________ 100. 3 305. 0 . 40 46 1 The vertical and path data for travel distance, velocity, CD and R are identical for spheres. 2 The run number is a combination of drop number, fluid number (fig. 6), and particle number. 017 horizontal movements increased the fall-path length a maximum of 3 percent. Average increase in length was 1 percent. Occasionally, a steel sphere exhibited a horizontal translation as it fell through the test section. This translation also increased path length to a maxi- mum of 3 percent. Specific characteristics of this un- stable condition could not be repeated with other drops. ‘ Only one sphere exhibited any perceptible rotation. The 3.81-cm teflon sphere falling in water rotated approximately 45° during the last 50 cm of fall. The CD—R curve for the falling spheres was virtually the same as for spheres rigidly mounted in a moving fluid (fig. 10). The scatter in the data can be ascribed to experimental error. DISKS Several broad systematic patterns of fall existed for a freely falling disk. Steady-flat tall When the Reynolds number for a falling disk was less than 100, the disk fell at a uniform velocity with the maximum projected area perpendicular to the direc- tion of fall and had no tendency to oscillate. This in- dicated a very stable condition because oscillations caused by some outside influence damped out with time and distance. The stable fall pattern of a falling disk is typified in figure 11. Drawings from successive pic- tures of the movies are used to represent the steady-flat fall pattern (fig. 11). Regular oscillation At Reynolds numbers slightly greater than 100, the disk oscillated about a diameter perpendicular to the direction of fall. Very little horizontal translation was associated with the oscillation (fig. 1). As R increased, the amplitude of the oscillation and the horizontal translation increased. The path of travel was almost parallel to the face of the disk, and the drag was mainly shear drag (figs. 1, 12). In theory, the amplitude of the are through which the disk oscillates is a function of the balance between the weight of the disk and the lift and drag forces acting on it. The greater the lift force with respect to the disk weight and the drag force, the greater will be the amplitude of the are through which the disk oscillates. Wilmarth, Hawk, and Harvey (1964) found that the amplitude of the arc was inversely proportional to the stability number I of the disk. Because I is the product of (a) the density ratio of the disk and the fluid and (b) the thickness-diameter ratio of the disk, decreasing I merely decreases the ratio of the weight to area of the disk. Therefore, assuming a constant velocity, decreasing I will increase the lift-weight ratio of the 018 TABLE 3.-—Drop data for disks SEDIME'NT TRANSPORT IN ALLUVLAL CHANNELS Travel distance Velocity CD and R values [or d... On and R values for dn Run No.l _ Stability2 Path Vertlcal Path Vertical Path Vertical ath Vertical (cm) (cm) (cm/sec) (cm/sac) Co nxm—z CD 11le Up Rxl 0;) 19—1—34--- 121.8 70.5 86.5 50.2 0.28 324 0.54 231 0.98 172 1.93 123 GT 20—1—33--- 61.8 31.0 74.3 37.1 .16 226 .66 114 .59 121 2.34 60.4 GT 21—1—32___ 95.0 46.5 58.0 28.4 .20 133 .85 65 .72 70.5 3.02 34.6 GT 23—1—33- _ _ 30.4 21. 0 73 . 5 50.9 . 17 224 .35 155 .60 120 1 . 24 83 . 0 GT 24-1—33--- 129.0 91.5 58.5 41.6 .26 179 .48 134 .94 95.4 1.86 67.9 GT 25—1—32--- 121.2 69.5 70.5 40.5 .14 163 .42 93.4 .48 86.6 1.47 49.7 GT 42—1—21--- 51.7 33.5 76.2 49.8 .79 234 1.84 1.53 2.80 124 6.55 81.0 T 43—1—22- _ _ 102.9 67 .5 102.5 67.5 .65 472 1 .52 310 2 .33 250 5 .40 164 T 73—2—20___ 100.0 100.0 26.2 26.2 3.82 .14 ________________ 13.6 .07 ________________ S 74-2—21--- 100.0 ________ 36.2 ________ 2.68 .26 ________________ 9.56 .14 ________________ S 75—2-22--- 100.0 ________ 53.9 ________ 1.82 .57 ________________ 6.45 .30 ________________ S 87—2—34--- 100.0 ________ 17.4 ________ 3.05 .19 ________________ 10.8 .10 ________________ S 106—3—20--- 100.0 ________ 29.4 ________ 3.04 .20 ________________ 10.9 .11 ________________ S 107—3—21--- 80.0 ________ 42.0 ________ 2.00 .38 ________________ 7.15 .20 ________________ S 108-3—22--- 100.0 ________ 61.0 ________ 1.42 .83 ________________ 5.05 .44 ________________ S 119-3—33--- 100.0 ________ 12.2 ........ 4.16 .11 ________________ 14.7 .06 ________________ S 120-3—34- _ _ 100. 0 ________ l9 .6 ________ 2 .44 . 27 ________________ 8 .60 . 14 ________________ S 121—3—34--- 100.0 ________ 20.2 ________ 2.28 .28 ________________ 8.05 .15 ________________ S 143—4—33--- 100.0 ________ 13.6 ________ 3.38 .15 ________________ 11.8 .08 ________________ S 144—4—34--- 100.0 ________ 20.4 ________ 2.26 .34 ________________ 7.97 .18 ________________ S 145-4—20--- 101.0 ________ 33.8 ________ 2.31 .28 ________________ 8.30 .15 ________________ S 146—4—21--- 100.0 ________ 46.1 ________ 1.67 .51 ________________ 5.96 .27 ________________ S 147—4—22--- 99.0 ________ 67.9 ________ 1.16 1.12 ; _______________ 4.11 .60 ________________ S 148—4—22--- 99.0 ________ 66.0 ________ 1.22 1.09 ________________ 4.36 .58 ________________ S 156—5—32--- 100.0 ________ 14.2 ________ 2.33 .22 ________________ 8.23 .12 ________________ S 157—5—33- _ _ 100. 0 ________ 18 .7 ________ l .80 . 39 ________________ 6 .40 .21 ________________ S 158—5—34--- 100.0 ________ 27.4 ________ 1.28 .79 ________________ 4.53 .42 ________________ S 159—5—20- _ _ 100. 0 ________ 45. 0 ________ l .30 .70 ________________ 4.63 . 38 ________________ S 160—5—21--- 100.0 ________ 56.9 ________ 1.11 1.20 ________________ 3.94 .64 ________________ S 161—5-22--- 78.0 61.0 95.1 74.5 .60 3.00 .97 2.35 2.10 1.60 3.44 1.25 GT 162—5—22--- 91.6 72.5 92.3 72.5 .64 2.90 .99 2.28 2.24 1.55 3.48 1.22 GT 169-5—22--- 75.2 60.0 94.0 75.0 .61 2.96 .96 2.36 2.16 1.58 3.38 1.26 GT 170—5—22--- 83.4 70.0 100.5 84.4 .54 3.17 .76 2.68 1.89 1.69 2.68 1.42 GT 186—5—22___ 119.5 100.0 87.5 73.2 .70 2.76 1.01 2.30 2.50 1.47 3.57 1.22 GT 187—5—22--- 121.0 96.5 97.0 77.4 .57 3.06 .90 2.44 2.03 1.63 3.20 1.30 GT 188—5-22--- 118.4 78.5 101.8 67.7 .52 3.20 1.17 2.13 1.84 1.71 4.14 1.14 GT 189—5—22--- 68.2 52.0 89.1 67.8 .68 2.80 1.17 2.14 2.42 1.49 4.16 1.14 GT 192—5—22--- 103.2 74.5 102.0 73.5 .52 3.21 1.00 2.31 1.84 1.71 3.52 1.23 GT l93—5—22--- 104.4 80.5 99.2 76.4 .55 3.12 .92 2.40 1.94 1.67 3.26 1.28 GT 196—1—32--- 93.3 56.5 57.5 34.8 .20 108 .56 65.6 .72 57.8 1.95 35.0 GT 197—1—32___ 58.0 26.5 56.9 26.0 .21 107 1.00 49 .73 57.1 3.50 26.1 GT 198—1—33--- 114.5 63.5 75.0 41.5 .16 187 .52 104 .57 99.5 1.86 55.1 GT 199—1—33- _ _ 58 .9 39.0 93 . 7 62. 1 . 10 234 . 23 155 .36 124 .83 82 .4 GT 200—1—34--- 147.6 74.5 78.5 39.8 .22 294 .86 149 .78 156 3.05 79.0 GT 201—1—34--- 55.5 30.0 99.7 54.1 .14 373 .47 203 .48 198 1.65 108 GT 202—1—20--- 76.8 43.0 51.4 28.8 1.29 97.6 4.09 54.1 4.66 51.2 14.65 28.6 T 203—1—20--- 74.0 42.0 78.8 44.8 .54 148 1.69 84.2 1.95 78.6 6.04 44.7 T 204—1—21--- 64.0 45.5 66.8 47.3 1.02 168 2.02 119 3.64 88.9 7.25 63.0 T 206—1—22_ _ _ 72.9 59.0 109 . 2 88. 5 . 62 409 .88 332 2.23 222 3 . 11 177 GT 207—1—22- _ _ 98. 6 66. 5 91 . 5 61 .8 .82 343 1 .80 232 2.90 183 6.36 124 GT 224—6—32--- 101.0 ________ 17.1 ________ 1.56 .52 ________________ 5.46 .27 ________________ S 225—6—33- _ _ 100. 0 ________ 22. 2 ________ 1 .32 .90 ________________ 4.69 .48 ________________ S 226—6—34--- 99.5 ________ 29.3 ________ 1.15 1.79 ________________ 4.06 .94 ________________ S 227—6—20___ 115.8 100.0 53.5 46.7 .94 1.64 1.24 1.43 3.40 .86 4.46 .75 0 228—6-21--- 112.4 76.5 78.6 53.5 .59 3.20 1.27 2.18 2.10 1.70 4.55 1.16 T 229—6—34--- 80.0 ________ 30.0 ........ 1.09 1.83 _________________ 3.86 .97 ________________ S 230—6—20--- 111.9 100.5 50.9 44.6 1.05 1.51 1.43 1.37 3.76 .82 5.14 .72 O 231—6—21___ 89.0 66.5 79.1 59.1 .58 3.22 1.04 2.40 2.08 1.71 3.72 1.28 T 232—6—22--- 101.2 68.0 79.5 53.4 .87 4.84 1.93 3.24 3.08 2.58 6.85 1.73 GT 233—6—22--- 96.4 66.5 94.5 65.4 .61 5.76 1.28 3.98 2.18 3.07 4.56 2.12 GT See footnotes at end of table. W """‘&Wfi£fii¥e§‘¢.t§{1V"..} 2‘1.-- 1 THE BEHAVIOR OF LARGE PARTICLES FALLING IN QUIESCENT LIQUIDS 019 TABLE 3.—Drop data for disks-«Continued Travel distance Velocity CD and R values for d... On and R values for d. Run No. 1 . Stability 7 Path Vertical Path Vertical Path Vertical Path Vertical (cm) (cm) (cm/sec) (cm/sec) CD RXIM CD RXIO—2 09 ino—2 On Bx10—2 244—6—34--- 100,0 ________ 30.6 ________ 1.05 1.86 ________________ 3 71 0.99 ................ S 245—6—20--- 111.2 100.0 51.2 46.8 1.04 1.56 1.24 1.43 3 71 .83 4.44 .76 O 246—6-21--- 102.1 69.0 87.5 59.1 .48 3.55 1.04 2.40 1 71 1.89 3.72 1.28 T 356—7—32--- 146.8 100.0 26.3 18.1 .74 3.03 1.57 2.08 2 66 1.61 5.50 1.11 OR 357—7—32--- 120.2 101.0 22.8 19.8 .99 2.62 1.31 2.28 3 55 1.40 4.69 1.21 0 358-7—20--- 57.1 35.5 66.9 41.4 .63 7.70 1.63 4.76 2 26 4.06 5.88 2.52 T 359—7—20--- 82.5 57.5 57.9 40.4 .83 6.65 1.72 4.65 3 01 3.51 6.18 2.45 T 366—7—33--- 132.8 100.5 28.8 21.8 .87 4.46 1.52 3.38 3 08 2.39 5.37 1.81 O 367—7—21___ 93.4 50.5 89.0 48.0 .48 13.8 1.63 7.45 1 70 7.31 5.81 3.94 T 375—7—34___ 186.1 100.0 47.1 25.1 .46 10.9 1.63 5.83 1.64 5.82 5.75 3.10 O 376-7—22--- 108.9 60.0 107.9 59.5 .49 25.0 1.60 13.8 1.74 13.4 5.70 7.37 T l The run number is a combination of drop number, fluid number (fig. 6), and particle number. 2 G, glide fall; ’1‘, tumbling fall; S, stable orientation and path; 0, regular oscillation; R, rotation about vertical axis. TABLE 4-—D’0P dam for Oblate Sphermdsl oscillation, gliding, and tumbling (figs. 13, 14). In the 2 Em“, v1 1 on fidgvalues CD aquigvaiues st glide-tumble pattern, the amplitude of the disk 0s- R'm N°' d :3?“ .332ng ___£’_’”__ #— me'a cillation increased until the lane of the disk face was ( ) ( / ) c ino—2 o ino-2 y D ” almost vertical at the end of the arc. At this point, the 38-1-33 ........ 133.2 3.13 mg 3% 0.3:; :3: 8% disk fell vertically, on edge. The torque caused by 34—1-25? 10221 78:6 '83 358 1122 296 0 c' ' ' ‘ ' 354%-" 103.4 89.6 41 270 .61 221 T 1rculation then changed the angle of inclination from 45-1-12.-. 101.2 168.9 58 506 86 415 S vertical to horizontal and to vertical again. Associated i353 131: 1'53 342 2'35 285 52 g with the change in angle of inclination was a chan c 10020 13515 399 1'45 1:56 117 s . . . . g. 1&8 3111.; if): 19 3.81 .152 g In path d1rect10n from vertically downward to hori- 97—3-11 ________ 1330 74.0 1&6 ' 50 367 '43 E zontal to vertically upward. When the drag and gravity ”'3'” -------- 198:3 1%.? 1:979 1:89 1:2? 1;;3 S forces stopped the upward motion of the disk, the 100.0 22.4 3.39 .15 5.06 .13 S . 100.0 31,5 2.32 .23 3,44 .23 s cycle was repeated. Whether or not the particle con- 100.0 48.8 1.47 .66 2.16 .55 S ' ' ' ' ' 100.0 25.3 2.75 .21 4' 13 .17 s tinued in the same horizontal direction on the next arc 133:3 :13 {832 :33 fig :3}, g or returned on its path depended on the position of the 133‘: 123': 1:; 1:: 1:: g: 2 disk at the end of the arc. If, for example, the disk 101:1 146:5 :87 2:45 1:35 1:96 8 ‘ 99.0 36.2 1.32 .57 1.99 .47 s approached the end of the arc from the right and £23 3% {$2 13% {g3 13;; g stopped With the angle of 1nclination slightly to the 1%.; 12.8% 5752 ”a “g 3 right of the vertical, it would move back to the right 13823 1226:; :33 (152%? 112$ 3.3; 5 on the next arc (see upper half, fig. 13). If the disk 101-5 534 ~83 2-13 1-23 1.75 S stopped with the angle of inclination to the left of the £33 15313 333 3.1.33 113.7; 31?: 3 vertical, it would move on to the left in the succeeding 97.6 139.2 .68 5.56 1.01 4.55 S . . 101.6 177.5 .63 10.6 .98 8.56 s are (see lower half, fig. 13). The oscfllation frequency of 100.0 54.1 .64 6.22 .99 5.08 S . . . 31.5 139.0 '56 16 .80 13.3 s the disk was much less during the glide-tumble fall 18ng 12:1; :23 29'85 :33 12:88 3 pattern than during the regular oscillation fall pattern. 96.5 177.8 .63 41.5 .97 33.4 S 97.5 81.2 .59 18.8 .86 15.5 S Tumble l’I‘h rtll lit! lit , 1,0, 1: 5.51 . . . . .. for 0.1:.Z°SD§;.?3§ pat d“ "mm ‘13 8““ “:th D an: ‘2'“ e)" 1°: With further increases in R, the disks exhibited a 2 The run number is a combination of dro nun; er, fluid iium er fig. 6 , an particle number.. , , p _ _ fourth fall pattern, the tumble pattern. In the tumble 3 0, regular osmllation; T, tumbling fall; S, stable orientation and path. _ fall pattern, the disk rotated through 360° at a nearly disk because the lift is directly proportional to the constant angular velocity, and the path of travel was area. Hence, the amplitude of oscillation should in- nearly a straight line inclined at an angle with the hori- crease with I, as observed. zontal (fig. 15). The tumble fall pattern is a stable one Gnde_mmme where the frequency of angular rotation approaches the The third general fall pattern which the disks ex- frequency of oscfllation 1n the regular oscillation hibited as R continued to increase was a combination of pattern. C20 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS TABLE 5.—Drop data for cylinders Travel distance Velocity CD and R values for d... On and R values for d, Run No. 1 Path Vertical Path Vertical Path Vertical Path Vertical Stability 1 (cm) (cm) (cm/sec) (cm/sec) CD Rxlo-2 CD litxlo-2 Co R><10—2 CD lkxlo—2 32—1——3l___ 106.1 100.0 60.5 57.1 0.73 157 0.81 41.5 1.14 126 1.27 118 OR 33—1—30--- 104.1 100.0 47.3 45.5 .76 82 .83 79. 1.22 64.6 1.32 62.1 OR 38—1—29--- 103.9 100.0 39.0 37.6 .80 51.5 .86 49.6 1.33 40 1.43 38.6 0 50—1—19___ 103.1 100.0 164 0 157.0 .50 425 .55 407 .77 341 .85 326 0 51—1—18--- 89.1 85.0 137 0 130.5 .48 236 .52 225 .74 191 .81 182 0 71—2—18___ 100.0 ________ 42.6 ________ 3.78 .17 ________________ 5.85 .14 ________________ S 72—2—19--- 100.0 ________ 67.8 ________ 2.32 .40 ________________ 3.58 .32 ________________ S 84—2—31--- 100.0 ________ 18.8 ________ 5.06 .12 ________________ 7.85 .09 ________________ S 103~3—l7___ 100.0 ________ 33.1 ________ 4.64 .13 ________________ 7.31 .10 ________________ S 104-3—18___ 100.0 ________ 46.1 ________ 3.27 .24 ________________ 5.02 .19 ________________ S 105—3—19--- 100.0 ________ 65.4 ________ 2.44 .50 ________________ 3.74 .40 ________________ S 117—3—31--- 100.0 ________ 21.3 ________ 4.00 .16 ________________ 6.16 .13 ________________ S l49—4—19--- 99.0 ________ 77.4 ________ 1.73 .72 ________________ 2.63 .58 ________________ S 150—4—18___ 100.0 ________ 52.1 ________ 2.56 .32 ________________ 3.96 .26 ________________ S 151—4—31--- 100.0 ________ 23.6 ________ 3.27 .22 ________________ 5.09 .18 ________________ S 154—4—17--- 100.0 ________ 38.8 ________ 3.41 .18 ________________ 5.33 .15 ________________ S 171—5—29--- 100.0 ________ 14.4 ________ 4.11 .13 ________________ 6.86 .10 ________________ S 172—5-30--- 100.0 ________ 19.7 ________ 3.02 .23 ________________ 4.86 .18 ________________ S. 173—5-31--- 100.0 ________ 31.9 ________ 1.82 .57 ________________ 2.80 .46 ________________ S 174—5—17--- 99.0 ________ 50.7 ________ 2.02 .45 ________________ 3.17 .36 ________________ S 175—5—18--- 100.0 ________ 66.7 ________ 1.58 .79 ________________ 2.44 .64 ________________ S 176—5-19--- 100.0 ________ 102.0 _________ 1.01 1.82 ________________ 1.58 1.46 ________________ S 208-1-18--- 33.1 31.0 132.4 124.0 .51 187 .58 175 .79 150 .90 140 OR 209—1—19--- 106.4 100.0 152.2 143.0 .58 322 .65 303 .89 260 1.01 244 OR 210—1—31--- 111.4 98.5 66.5 58.8 60 141 76 125 92 113 1 18 100 OR 212—6—29--- 100.2 ________ 18.6 ________ 2.51 .32 ________________ 4.22 .25 ________________ S 213—6—30--- 100.0 ________ 24.9 ________ 1.96 .57 ________________ 3.17 .45 ________________ S 214—6-31--- 100.0 ________ 39.7 ________ 1.22 1.37 ________________ 1.89 1.10 ________________ S 215—6—17--- 101.1 ________ 60.6 ________ 1.44 1.05 ________________ 2.26 .83 ________________ S 216—6—18--- 99.0 ________ 82.6 ________ 1.05 1.89 ________________ 1.62 1.52 ________________ S 217—6—19___ 100.0 ________ 111.2 ________ .87 3.82 ________________ 1.33 3.08 ________________ S 350—7—29--- 100.0 ________ 29.6 ________ 1.04 1.94 ________________ 1.75 1.50 ________________ S 351—7—17--- 102.8 99.5 90.0 87.2 .67 5.85 72 5 66 1.07 4.65 1 14 4 51 O 360—7—30--- 100.0 ________ 37.2 ________ .92 3.27 ________________ 1.49 2.56 ________________ 361—7—18--- 51.1 50.0 105 6 103.0 .66 9.19 .69 8.96 1.02 7.40 1.07 7 21 O 369-7—31--- 100.7 100.0 50.3 50.0 .79 6.60 .79 6.55 1.22 5.30 1.24 5.26 O 370~7—19___ 54.41 52.5 146 2 141.2 52 19 2 .56 18 5 79 15.4 .85 14 9 O (11 T3? run number is a combination of drop number, fluid number (fig. 6), and particle number. 2 0, regular oscillation; R, rotation about vertical axis, S, stable orientation an pa . THE BEHAVIOR OF LARGE PARTICLES FALLING IN QUIE'SCENT LIQUIDS CZ]. FORCE NUMBER Ox) 103 104 105 106 107 108 109 1010 1° \ \ I\' '\ T\' '\"l\' '\“ \“ ‘ Falling sphere F' _o-_ Ixed Sphere ‘~O O 0 ||O - ‘. / °E l I l l I I DIMENSIONLESS COEFFICIENT OF DRAG (CD) >-—\ ' 10 102 103 104 105 REYNOLDS NUMBER (R) FIGURE 10.—Coefiicient of drag as a function at Reynolds number and force number for falling and fixed spheres. 9 FIGURE 12.—-Regular oscillation fall pattern of a disk. The example is from drop 375 consisting of an aluminum disk FIGURE 11.—Steady fall pattern of a steady disk. The example with d,,.=3.81 cm in a fluid of 70 percent glycerine and is from drop 107 consisting of a lead disk with d,,,=2.54 cm showing a. time inverval of 0.055 sec. Path parameters are in a fluid of 98 percent glycerine and showing a time interval w=47 .1 cm/sec, R: 1,092, CD=0.46. Vertical parameters of 0.075 sec. Path parameters are (0:42 cm/sec, R=38, are w=25.1 cm/sec, R=583, CD=1.63. Shaded surface is CD=2.00. Shaded surface is bottom of disk. bottom of disk. 022 TABLE 6.—Drop data for prolate spheroids 1 Travel Co and R values On and R values Run No.2 distance Velocity for d... for d. Sta- (cm) (cm/sec) — bility 3 CD RXIO‘2 C’D [1X10-2 104. 1 85. 5 0. 63 275 0. 78 245 UO 103. 1 65. 7 . 53 104 . 66 940 U0 100. 4 75. 2 . 54 159 . 67 145 S 103. 7 89. 5 . 57 288 . 71 258 U0 104. 3 65.2 . 54 104 . 68 93. 3 U0 104. 4 174. 0 .54 378 . 65 344 R 52. 2 196.0 . 61 644 . 76 572 R 105. 2 178.0 . 52 386 . 67 352 R 100. 0 57. 2 2. 88 21 3. 49 . 20 S 100. 0 81. 3 1.89 41 2. 26 37 8 69—2—16 ________ 100. 0 114. 2 1. 38 .87 1. 72 . 78 S 81-2—28 ........ 100. 0 33. 6 2. 71 . 25 3. 38 . 22 S 100—3-14 ........ 100. 0 62. 1 2. 46 . 30 2. 99 . 27 S 101—3—15 ________ 100. 0 85. 5 1. 71 .55 2. 08 .50 S 102-3—16 ........ 100. 0 128. 0 1.10 1. 24 1. 38 1. 11 S 113—3-27 ________ 100. 0 24. 3 3. 50 .54 4. 39 . 14 S 114-3-28 ........ 100. 0 42. 5 l. 72 . 40 2. 14 . 36 S 136-4—16 ........ 100. 0 141.0 . 91 1.66 1.14 1. 49 S 137—4-15 ........ 100. 0 96. 5 1. 35 .76 1. 62 .68 S 138—4-14 ________ 100. 0 66. 7 2. 13 55 2. 59 3 6 S 100. 0 26. 6 2. 82 .21 3. 50 .19 S 100. 0 42. 0 1. 79 .49 2. 20 . 44 S 100. 0 27. 6 2.10 . 30 2. 62 .27 S 100. 0 37. 2 1. 55 .55 1.92 . 49 S 100. 0 55. 6 1.01 1. 23 1.26 1. 11 S 100.0 94.4 1 09 1.06 1. 32 .96 S 99. 0 122.0 86 1. 82 1.03 1. 65 S 97. 2 165. 8 .67 3. 73 .84 3. 34 S 100. 0 35. 7 1. 31 .75 1. 60 . 68 S 101.0 47. 8 96 1 36 1.19 1.22 S 100. 0 65.0 .79 2. 77 .96 2. 49 S 100. 0 108. 5 .83 2. 34 1. 00 2.14 S 102. 2 132. 8 . 73 3. 82 . 88 3. 48 S 99.6 175. 3 .61 7. 63 . 76 5. 82 S 352—7—26 ........ 100. 5 50. 2 . 69 4. 00 . 48 3. 40 S 353-7-14 ........ 92. 5 138.0 . 53 11.2 . 64 10. 2 S 362—7-27 ........ 100. 0 61. 5 . 63 6. 67 . 80 6. 0 S 363—7-15. . . _ 72. 0 164. 5 . 50 18.0 .59 16. 4 S 371-7-28. . . _ . 101.5 81.9 51 13. 3 .64 12.0 S 372-7-16 ........ 90.0 210.0 43 34.8 .54 31. 2 S I The vertical and path data for travel distance, velocity, 00 and R are identical for prolate spheroids. 2 The run number is a combination of drop number, fluid number (fig. 6), and particle number. 3 S, stable orientation and path; 0, regular oscillation; U, unstable path; R, rota- tion about vertical axis. * In summary, the four general fall patterns for disks are: 1. Steady-flat 2. Regular oscillation 3. Glide-tumble, and 4. Tumble. Except for the boundary between steady-flat fall and regular oscillation, no definitive boundaries between each pattern exists. Instead, there was a progressive transition from one pattern to another. All the disks did not exhibit all the patterns described as a result of the step-changes in the viscosity of the fluids and the subsequent step-changes in the Reynolds number. The lead disks exhibited the glide-tumble fall pattern at much smaller Reynolds numbers than did the aluminum disks, indicating that the stability num- ber I was a significant parameter in defining the fall pat- terns of disks. Since the thickness-diameter ratio of all the disks was the same, the apparent affect of I must be due solely to the density ratio of the disk and the fluid. SE‘DIMENT TRANSPORT IN ALLUVLAL CHANNELS ®®©©© @ Q FIGURE 13.—Fall of a disk just after entering the glide-tumble pattern. The example is from drop 24 consisting of an alumi- num disk with d,,,= 2.54 cm in a fluid of water and showing a time interval of 0.051 sec. Path parameters are w=58.5 cm/sec, R: 17,900, CD=O.26. Vertical parameters are w=41.6 cm/sec, R= 13,400, 00:0.48. Shaded surface is bottom of disk. Changes in I as a result of changes in the thickness- diameter ratio of the disk would produce similar changes in fall patterns if the density ratio of the disk and fluid were kept constant. Further evidence of the importance of the density ratio will be discussed in connection with the OD—R diagrams in a following section. Regimes or fall As the Reynolds number for a falling disk was further increased, the fall of the disk changed from a stable pattern of steady-flat fall, through a period of transition until the disk reached a second stable condition of con- stant angular rotation or tumble. Thus, the patterns of fall for a disk can be divided into three regimes: a steady regime, where a stable pattern of steady-flat fall exists; the transition regime which includes the oscillation and glide-tumble fall patterns; and the tum- ble regime where a second stable condition exists as a uniform tumble and constant angular rotation. THE BEHAVIOR OF LARGE PARTICLES FALLING IN QUIESCENT LIQUIDS fig FIGURE 14.—Fall of a disk just before leaving the glide-tumble fall pattern. The example is from drop 161 consisting of a lead disk with d,,.=3.81 cm in a fluid of 90.1 percent glycerine and showing a time interval of 0.029 sec. Path parameters are w=95.1 cm/sec, R=300, CD=0.60. Vertical parameters are w=74.5 cm/sec, R=235, 09:0.97. Shaded surface is bottom of disk. The regime classification is dependent, not only upon the coefficient of drag 0D and the Reynolds number R, but also upon the stability number I and the frequency number 0. Thus, the regimes of fall can be related to the C’D—R diagram (fig. 16). (ID-R curves and fall regimes The steady regime exists when 10 2,000. The tumble regime consists of the upper branch 023 FIGURE 15.—Tumble fall pattern of a disk. The example is from drop 204 consisting of a lead disk with dm=2.54 cm in a fluid of water and showing a time interval of 0.03 sec. Path param- eters are w=66.8 cm/sec, R=16,800, CD: 1.02. Vertical pa- rameters are w=47.3 cm/sec, R=11,900, 09:2.02. of the (ID—R curve of figure 16 where the angular velocity is nearly constant. Unsteady conditions The preceding discussion on the fall pattern and regimes of disks makes it clear that the velocity of a disk is not constant once oscillation begins. The disk, thereafter, continually accelerates or decelerates in a vertical direction, angularly, or both. The method of data collection permitted both vertical and path velocities to be determined for short periods of time, that is, periods down to less than 0.015 second. Graphs of the time-variation of velocity were obtained plotting the incremental velocities against time for several of the drops (figs. 17—19). The three horizontal lines on the graphs represent the average velocity of fall through the entire test section. The long-dashed line represents the vertical fall velocity of the disk, the short-dashed line represents the path velocity, and the large solid dots represent the three-point moving average of the path velocities. The three-point moving average was determined by plotting the average of three consecutive path velocities at the midpoint of the three. When the data were taken from the film, movements of less than one—half centimeter were difficult to measure. Because of the high speed of the camera and slow speed of some of the particles, movement of that magnitude was not uncommon. It should also be noted that a gradual change over two or three consecutive intervals was recorded in one interval because the minimum length recorded was one-half centimeter. When the lengths were converted to ve- locities, a sudden change seemed to have occurred at 024 'SEDMENT TRANSPORT IN ALLUVIIAL CHANNELS I I I I l I I I I l I I I I I l l l I 10 — n _\\\ __ \\ \\\\\\\\ :\ \\\\\\ _ ’3. \\\\\\\\\\ 9 \ _ \ \\\\ \\\\\ \\\\\\\ (D \\\\ \ \\\\ < \\\\ \\\\ \ O: _ \ \\ \ \\\\\ __ Q \\\\\ \\ \\ \ \\\ \ \. s \\\:\ \ +— 11: Fixed disk E 1.0 — \ O _ E LL LIJ — O U m _ 8 2‘ Steady-flat 0 <7) . . E ._ Transmon 2 0 Tumble VIII/A 0.1 - I I I I l l J 10 102 103 104 105 REYNOLDS NUMBER (R) FIGURE l6.—Regimes of fall for a free-falling disk. such intervals. Therefore, the three-point moving accelerate or deoelerate, tends to justify this ap- averages should better represent path velocity than the singly determined values shown by the short-dashed line. When a disk falling in a glide-tumble pattern (fig. 18) is accelerating vertically (positive slope on the velocity- time curve), the vertical and path velocities are iden- tical. When the path of travel is not vertical, the velocities are no longer identical and the vertical velocity decreases earlier in time than does the path velocity. After a disk begins a regular tumble (fig. 19), it moves laterally across the column throughout the entire fall. Therefore, the path velocity is always greater than the vertical velocity. The cyclic nature of the velocity-time relationship is typical for all disks in all fall patterns except the steady-flat fall pattern. Several times, particularly in the glide-tumble pattern, negative vertical velocities were recorded. By definition, the path velocity is always positive except at the apecies of the arcs where it goes to zero. Average velocities Current methods of expressing resistance to motion do not account for accelerating motion because average velocities are used. The apparent cyclic nature of the fall of disks, indicating that the disk does not continually proximation. In all tests in the transition and tumble regimes, the average path velocity was greater than the average vertical velocity (see heavy horizontal lines, figs. 17—18). In one test the average path velocity was 81 percent greater than the average vertical velocity. The path velocity of a falling disk will generally be greater than the velocity of a fluid, of the same density and viscosity as the one in which the given disk is falling, flowing past a rigidly mounted disk, of the same cross—sectional area as the falling disk, which would exert a force on the fixed disk equal to the weight of the falling disk. Such a velocity can be computed from the CD—R diagram for fixed disks and from the force number of the falling disk (see heavy broken lines, fig. 17—19). Frequency of oscillatlon Two variables which affect the frequency of oscillation or rotation are disk size and density. If the density- frequency number (1) previously derived by dimension- less analysis is written as: fZZcpIi—LPJEQ, 4 p, aa it is evident that for a constant thickness—diameter ratio of the disk, the square of the frequency is inversely THE BEHAVIOR OF LARGE PARTICLES FALLING IN QUIEISCENT LIQUIDS 180 T I F I I I I T I I I I I I I I I I I I r I l I I I D 160 -' '— Z ' DROP NUMBER 366 O . . a - co CD R - a: 120 — Path 28.8 0.87 446 """""" Path - E ' Vertical 121.8 1.52 338 —————— Vertical : w _ Fixed 20.0 1.82 308 o o o Three-point - E - moving average _ >- 80 — “J _ E _ ,_ . . E - II , A Path average - 0 40 L .I \‘ l ‘ 0/ ‘1‘ /\ / — Z L. I _ ; I ," ., . -- 1 . . +77 X. . , ..’ . .; x, 1+1 rm ‘. v-v = . ‘ . 7‘ .+ ___T .._ . v _ v r . V t ,‘ _ __ . u __ E _ I \ 5,7, \ / \ / \/ \ /, Fixed dlsk \\ / Vertical average V/ ' o O _ , \_‘v/ \/ \/ \ a _ ._ _I LLJ _ .. > _ _4O - I I; J l I l l I I I I l I I I I I I I I l I I 1 I I 0 0.5 1.0 1.5 2.0 2.5 TIME, IN SECONDS A 180 I l i I I l I i I I i i I I I I I i I I I I I I I a 160 “‘ ---------- Path “ z " DROP NUMBER 366 - 8 _ ——~— Vertical ' Lu — _ w 120 — o o o Three-point _ '1 moving average _ E _ _ U) — E _ i— 80 — _ Lu _ _ E i— — _ z 8 — _ 4O — _ Z _ _-—- Path average A“ _ ; ~:‘_ —’—— ¢\‘ Q;_ - —/—.¥‘~‘ §:“‘ \” I __________ \~ , / I m“ '— ‘ 4 ~\/ / ‘\’/ E ‘ Vertical average\ — 9 o — — “J '_ _ > — — _40 l i l l | | l | | I I l i | I 1 1 i l I I I l l I l 0 0.5 1.0 1.5 2.0 2.5 TIME, IN SECONDS B FIGURE 17 .-—Velocity-time relationship for a 2.54-cm aluminum disk falling in an oscillatory pattern. The time interval between successive position of the disk is five times longer in (B) than in (A). proportional to the diameter of the disk and directly Pp—Pf proportional to - For example, the 3.81 cm (di- / ameter) aluminum and lead disks falling in water at average vertical velocities of 50.2 and 67.5 cm/sec, had rotational frequencies of 0.6 and 2.9 revolutions per second, respectively. Table 7 summarizes the frequency of oscillation for each experimental drop. (JD—R curves and fall velocity Four diagrams (figs. 20, 21) present the C’D—R relationships for disks. Particle identity is maintained by use of different symbols as indicated in the legend. The stability number I and the frequency number 0 appear beside each point in figures 20A and 21A Where the disks were unsteady. C26 SEIDIMENT TRANSPORT IN ALLUVIAL CHANNELS 180 I j I I I I T I I I I I I I I I I I ‘T l I 1 I l I — DROP NUMBER 24 ‘ 0160 —- a) CD R _ Z ’ Path 58.5 0.26 17,900 -------- Path ' g L Vertical 41.6 0.48 13,400 —~—— Vertical ”1120 _ Fixed 26.6 1.10 8,560 O 0 O Three-point A __ a: _ moving average \ _ E A, l.’. ' \ _ _7 \— ‘ U) 1‘ O I s» _ E . L‘w "IA.- |— 80 i‘ .,’ _. L” '1 . .' I a E ‘ I .fgl' Path average ‘ Y ‘ \ E \ i, 0 o 1 \ l Vertical average “ 0 40 l 1‘ a \r m E \ ‘i L I Fixed disk , _ ‘. ,‘l ' _ E \\ I"l/ _ O J O _ a O \VF - > _40 I I I l 1 I 1 l l l I I 1.5 2.0 2.5 2.7 TIME, IN SECONDS FIGURE 18.—Vclocity-time relationship for a 2.54-cm aluminum disk fallin in a lide-tumble attern. g g P 180 l I.. I . I I I HT ' | I I I i I I I - l l {I , I I' _ II I'- D 160 H II II DROP NUMBER 43 I I I I ,_ Z : A IIOII l * II I 1 II i\\ _ 8 /I III I {III )7) l II [III II II I\\ ll“ m r l ,i l l l l l ' o u) I I l I .II I «120* ’l il i M? r l r JIII°'/l\\lll .i-l Wit E ' In ’J II 'AII \ ——\ I Path ave'age .. \ ' ' ll“ r H" ". Il‘iui - l l " ""I" ‘ D ‘ I’ ' H11 \"ol “I "i‘ I‘” " g _ I iII.I/\II\\\, l I I“ 4 I‘ll \‘Illb 1*I III-Io II Ivl I' L|J Cl“, 6 CI \ F' dd'k I II I ‘ ‘1‘.' "I II :I: l— 80 — I Pi lmj I I II ll . 'Xe '5 _ -_E-_‘_'i_.:I__rp.\ . E — L‘H I'll lr" ' i l-i i'hi‘.‘ L \OII l‘, '1 ,l’ ,I I V, l— \l ‘,'/— _ ; _ ‘K I I,” I ”BI/30' Vertical average \ II \ I], III I \ I II ll _ z \I " \ V V/ ‘l v, v v/ II I /l 8 _ \ III / I I / I I I ‘ Z 40 — \__I \__I \v I \ _1 \__I I_/ — r>—: ' a) CD R — Z3 _ Path 102.9 0.65 47,200 --------- Path _. a O — Vertical 67.5 1.52 31,000 ————— — Vertical —' > : Fixed 76.0 1.18 35,000 I 0 C Three-point _ movmg average -—4O _ I I l I 1 I l I l 1 I O 0.2 0.4 0.6 0.8 1.0 1,2 1.3 TIME, IN SECONDS FIGURE 19.—Velocity-time relationship for a 3.81-cm lead disk falling in a. tumbling pattern. (Break in curve occurs where the disk fell down the wall of the column.) When 10 < R < 2,000, the curve for the relation— ship of OD—R for falling disks is approximately the same as the O’D—R relationship for fixed spheres (fig. 20A). For 10 < R < 120, the relationship is well established because the disks fell vertically, at a constant velocity without oscillation and with their maximum projected area perpendicular to the direction of fall. The re- lationship is not so well defined in the range between 120 < R < 2,000, where the disks were unsteady. Here, the data are more sparse, the points scatter more, and the stability and frequency number are beginning to influence the OD—R relationship. At R equal to about 10,000 for the given disks of this experiment, the OD—R relationship is no longer unique, but has two values. The only difference be— tween the disks used to develop the nonunique re— lationship is the density of the disks. The lead disks have a greater 0D value for a given value of R than do THE BEHAVIOR OF LARGE PARTICLES FALLING IN Q‘UIESCENT LIQUIDS TABLE 7,—Frequency of oscillation of unsteady particles falling in water—glycerine mixtures, in cycles per second [Particles falling in mixtures of 94.24 percent or more of glycerine were always stable] A, aluminum; 0, cylinder; D, disk; GT, glide tumble; L, lead; 0, oscillation; OS, oblate spheriod; PS, prolate spheroid; R, rotation; S, steady fall; T, tumble; U, undetermined. Particle material, shape, Percent glycerine and Size 90.1 83.33 70.00 0.00 4.0—0 4.2—GT 4.2—T 2.9—GT 3.6—GT 3.9—T 2.6—GT 2.9—GT 2.9—T S 2.8~O 1.4—GT S 2.2—0 1.2—GT S 1.6—0 .6—GT S S S S S S S S U . S S 4.6—T A—OS—2.50 ___________ S S S U A—OS-3.78 ___________ S S U 2.66—0 L—PS—1.91 ___________ S S S U L—PS—2.52 ___________ S S S 4.81—0 R L—PS—3.85 ___________ S S S 4.0—0 R A—PS—l.83 ___________ S S S 3.5—0 A—PS—2.50 ___________ S S S S A—PS—3.85 ___________ S S S 2.69—0 L—C—1.91 ____________ S S 3.2—0 U L—C—2.54 ____________ S S 2.4—0 2.0—0 R L—C—3.81 ____________ S S 2.0—0 2.0—0 R A—C—1.91 ___________ S S S 2.3—0 A—C—2.54 ___________ S S S 2.0—0 R A—C—3.81 ____________ S S 1.6-0 1.7—0R the aluminum ones. Thus, somewhere between a Reynolds number of 2,000 and 10,000, the resistance to motion for a disk becomes a function of the density. ratio between it and the fluid as well as Reynolds number and shape factor. The division of the OD—R relationship into two branches on the basis of the stability number I further emphasizes the importance of the density ratio between the disk and the fluid on the behavior of disks at certain values of R. The shape of the curve representing the OD—R diagram is not affected by the choice of characteristic diameter used in the computations. The position of the curve OD—R diagram, however, is the result of using different characteristic diameters (fig. 20). Associated with the effect of I on resistance to motion is the effect of the frequency number 0. 0D increases with 0 independently of R (fig. 22). Thus, it is evident that the stability number I and the frequency number 0 are important parameters in describing the behavior of freely falling disks. The solid lines in figures 22A and 223 represent the relationship for the glide-tumble and tumble patterns of fall. Insufficient data were available for the oscillating pattern of fall to establish a definite trend in the relation of 0D to 0; therefore, the broken lines, which represent that fall pattern, were arbitrarily drawn parallel to the solid ones. The position of the lines indicate, however, that the drag for a given frequency C27 number is greater when the disk tumbles or glides than when it oscillates. OBLATE SPHEROIDS The fall pattern of the oblate spheroids was steady throughout most of the range of Reynolds numbers covered in the experiment. The only exceptions occurred for the aluminum and the largest lead spheroids falling in water. Of the aluminum spheroids, only the smallest one tumbled, whereas the largest one oscillated in a vertical plane about a horizontal diameter. The two smallest lead spheroids were per— fectly steady while falling in the water. The middle- sized aluminum particle and the largest lead one, for which the data were insufficient to make computations of 0D and R, had a tumbling pattern. The fact that the lead spheroids were steady whereas the aluminum ones were not, at least for the drops having valid data, is again evidence that the density ratio of the particle and fluid is an important parameter in particle behavior. As expected, the oblate spheroids were steady over a larger range of Reynolds number than disks were. When. 10400, the cylinders oscillated in a vertical plane about a horizontal axis normal to the major axis of the cylinder. At R> 8,000, another oscillation was superimposed on the first, an oscillation in a horizontal plane about a vertical axis. The frequencies of oscillation for cylinders are sum- marized in table 7. The curve representing the relationship of 0D to R for cylinders is higher on the CD—R diagram than for spheres (fig. 24). The two curves slowly diverge to R~400, after which the increased rate of divergence is coincidental with the increased oscillation in the C28 SEDIMENT TRANSPORT IN ALLUVLAL CHANNELS FORCE NUMBER Ox) 103 104 105 106 107 108 109 1010 10 \ I I \ o I \ — Alumi— Major _ num axis Lead 0 1.91 o A u 2.54 - fl 9? A 3.81 . o < O: —1 D ‘* ——————————————— ‘\\ “- 004/ \\ O 50 \‘\\\“ Fixed disk ’— \ 0.0/2 00/? 0050 ‘ 0.04/ E 1 _ \\ 0.2/7 0 /94 0 //5 '0/48 0050 — G - \ o D ' ,x’ '0 050 I Ol/3 - E \ Falling disk-rim ‘ 0042 // O /29 0,050 0050 “J ~ \ ' /’ 0./3 — 0 \\L3\ 0. /02/,/ _____________ O \(o . ’ \\\\A :’ _ ” ——————— \49 009’ “~~- \ FIxed spheLe ______ — "’ P “5‘ 00/2 ------- ~ --------- — (I) \ e \\ Lu \% 0./29 \ —I \e,, \\ 5 \’°/; \\ 00/8 0 0/4 _ \ ‘\ 0.046 0.039 (I) \\ \\ o a A — E I— \ 010/4 A0.0/4 ‘ o E \\ 00047 0, 0/4 D 0044 D \ 0042 00/4 \ 0038 _ 0.1 — \\\ ——_‘fli:shi t \ ‘~\g// - \ \\ \ \~ \ 1 \ _ |\ l | \ I l I\ | ‘ I I J I | I l I \ I I 10 102 103 104 105 REYNOLDS NUMBER (R) A FORCE NUMBER (x) 1 103 104 105 106 107 108 109 1010 O ' I \ I \ \ I \ A Alumi- Major u A num axis Lead 0 1.91 0 D 2.54 I A 3.81 A DIMENSIONLESS COEFFICIENT OF DRAG (C0) 10 102 103 104 105 REYNOLDS NUMBER (R) B FIGURE 20.—Relationship of coefficient of drag and Reynolds number for falling disks having SF; = 0.1. A, Computations are based on d,” and path velocity. I and 0 are given for points where disks were unsteady. B, Computations are based on d” and path velocity. THE BEHAVIOR OF LARGE PARTICLES FALLING IN QUIEISCENT LIQUIDS 029 FORCE NUMBER 0‘) 103 104 105 106 107 108 109 1010 10 \\\\\ \ l\\\\\\\\\\l\\ \\\\l\\\ \ \ Alumi- Major num axis Lead 0 1191 o A ~ I: 2.54 I Q 0.050 U V F ||' d' k d 0229 A 3.81 ‘ O a Ing Is — m ,,'— é \ A 2%: 0.042 02430 04.2 0 022 // 0 050 D \ __ _O‘_Of£ 0/98 0 /53 // 0 /99 0050 u. \ ------ 0 “707/ 0/64“ ‘ 0‘/8§/’ 012/0 .0 ’63 O \ \ \\ ,_ \\ \\___:\ Fixed disk ‘0050 Z \ \ ' V\\ _ — 0.0/4 _B_/54 g 1 '— \\ \\\ ‘O 040 \\\ A0 075 —' E — \ \\O//8 \\ b \\ \\\ ‘\\ 00/4 0.0/4 0 — \ \\\ 00/4 0.078 00/4 0076 0 Mg; ‘\\ 0,084 007/ —————————— \O \\\ Fixed ———— to \‘Fe \~‘__$Dhere ——:r” g} ‘— \°‘ —————————— 010/4 — \0 -‘ \90 0064 Z \96. 9 \oz) m X \\ E \ — E \ o \ \ \\ 0.1— \ ‘ Airs _ _ -— \\ ““hLDJ’u/l \\ \\‘ |\ llli Txml I I III L | l\l 10 102 103 104 105 REYNOLDS NUMBER (R) A FORCE NUMBER Ox) 103 104 105 106 107 108 109 1010 10 o \ \\\ \ r\\\\ \ \ \\ \ l\\\§/‘<\ \ l\\\\ \ \\\\ //// o A I —” . . \ “Q Falllng dlsk—dfl \\\ A A v \ I l \\ 0 \\ A A \\\ Alumi- Major é \\\ \\ A num axis Lead 0 \\\ \\ o 1.91 o 8 :§\\ \\\\\\\ _______ \ \j/ Z 2-54 I ,_ \ \\ ——————— ‘\\\ 3.81 A Z \ \\ \\ El E \ \\ \\\‘_ Fixed disk _______ 9 \ \\ ______________________________ t 1 — \\ \\\ — Lu _ \ \\\ o U \S‘fof \\\\ g) — \Gé‘ \\\ \ \ _——— 3 \09 \\\ ’fl’ ....... .1 \09 ‘\\‘ Fixed sphere _____ —’ z — \\% ——————————————— — 9 \’) u) \ z \\ Lu \ 5 \ E \\ _ \ \ \ \ 01 111l\1\ l\lll\| |1||\1 1\1| ' 10 102 103 104 105 REYNOLDS NUMBER (R) B FIGURE 21.——Relationship of coeflicient of drag and Reynolds number for falling disks having SFC = 0.1. A, Computations are based on d," and vertical velocity. I and 9 are given for points where disks were unsteady. B, Computations are based on dn and vertical velocity. C30 SEDIMENT TRANSPORT IN ALLUVIIAL CHANNELS Alumi- Major 14 AlumI- Major 2.8 num aXIS Lead _ num axis Lead F 0 D’ 1.91 o . o 11 1.91 I u )1 2.54 I // u ;r 2.54 I A A 3.81 A / 1.2 _ A A’ 3.81 A 2.4 _ 9Q // 9e 0 < 1.0 — / 3 2.0 — I: / I: D / Q n. / I.._ o n/ 0 E / Li I— '3 0.8 — E 1.6 _ 2 § LL L L U. 3 “6‘ 3 0.6 — o 142 _ w 3 s _l _J z z 9 9 3 0.4 — Q 08 _ L|J Lu E E o o 0.2 - 0.4 - O I I/ | L | J O I / I l I 4| 0 0.04 0.08 0.12 0.16 020 0.24 . 0 008 0.16 0.24 0.32 0.40 FREQUENCY NUMBER (0) FREQUENCY NUMBER (0) A ‘ / B FIGURE 22.—Coeflicient of drag as a function of frequency number for falling disks having SFc = 0.1. A, Computations are based on d," and path velocity. B, Computations are based on d,,, and vertical velocity. FORCE NUMBER (M 10 103 104 105 106 107 108 109 1010 \\\\ \l\\\\\\\\ |\\\\\\\\\l\\\\ \\\\ Alumi- Major num axis Lead A 0 1.91 0 Q a 2.54 I 9 o \ A 3.81 A < 0: o s s ._ \ \______,,——-—-—~\\ Z \\\ g \\\‘__ Fixed disk _________________ \ I: \\ ——————— 0.046 — LL 1“ \ 0.0465 0./3%/// — g _ \\ .ty 0,45 // 0,046 o \‘Séf ‘Vertlcflfltv/ A0 /28 g — \ese \\\\\ ' #Path velocity 0045 _’. 2 63’s,, \‘\‘,__Fi_xed sphere _________L?—4 """ O _ \IO’) ________ — <7) \\ z \ LIJ \\ E x \ _ o \\\ \ \ 01\I |\ll|\T\ I\II|\I |\l|]\| |\[l ‘ 10 102 103 104 105 REYNOLDS NUMBER (R) FIGURE 23.—Coeflicient of drag as a function at Reynolds number for falling oblate spheroids, SFC=0.5. Computations are based on d”. and path velocity. I and 0 are given for points where the spheroids were unsteady. THE BEHAVIOR OF LARGE PARTICLES FALLING IN Q‘UIE-SCENT LIQUIDS C31 FORCE NUMBER (A) 10 103 104 105 106 107 108 109 1010 \\\ \ \\\\ \ [\\\\ \ \\\\ \ [\\\\ \ \\\\ \ p\\\ \ \\\\ Alumi- Major num axis Lead Ag 0 1.91 o 9 A n 2.54 - 2 x a: \ A 3.81 A o \\ U. E \ \\\ LIJ \ \\ F' . 5 \ \ ________ Ixed dlsk _ ____\ E _ \ 0.0/0 00/2 _ b l \\ \\ 003/A 0.036 0.028 00/2 8 _ \\Qo \ 0.0/4Famngcyund ' <0 — \48 fl V199 d A00/3 0044 \\ s . , 2' _ {’96. ‘Jflle—ri _______________ 00"" 0.0/2 __ o \9, 0.009 <7) \ z \ “J \ E \ 5 xi \ — \ \ \\ mu |\lll\l\ |\II|\| l\lll\| l\l| 10 102 103 104 105 REYNOLDS NUMBER (R) FIGURE 24.—Coefficient of drag as a function at Reynolds number for falling cylinders, SF.=0.5. Computations are based on d," and path velocity. I and 9 are given for points where cylinders were unsteady. cylinder fall pattern. At R x 12,000, the drag coefficient suddenly decreased. In all instances where the cylinders were unsteady during fall, the increase in path length due to horizontal motion was small. The resulting increase in the path velocity over the vertical velocity was a maximum of 11 percent and a minimum of 1.6 percent. Average increase was 5.6 percent. As for disks, a strong relation— ship exists between OD and 0, further evidence that resistance to motion increases as the degree of particle instability increases (fig. 25). PROLATE SPHEROIDS The prolate spheroids, a shape between the sphere and the cylinder, exhibited much the same patterns of fall as the cylinders. The first indication of instability was an oscillation in a vertical plane followed by an oscillation in both the horizontal and vertical planes as the Reynolds number increased. One particle, the 2.54 cm aluminum spheroid, exhibited a very slow rotation in the horizontal plane and no oscillation in the vertical plane. All particles were steady. for Reynolds number ranging from 10 to 8,000. For R<200, the OD—R relationship for prolate spheroids is almost identical to that for spheres (fig. 26). Differences in path and vertical velocity were small. The path velocity was greater than the vertical velocity by a maximum of 5 percent and a minimum of 2.1 percent. The average increase was 3.3 percent. COMPARISON OF BEHAVIOR AMONG ALL PARTICLES When the OD—R relationships for all particles com- puted by using dm and path velocity as characteristic parameters are compared, the relationships for spheres, oblate and prolate spheroids, and disks are almost identical in the range where 10400. The extreme shape of particles with small values of the Corey shape factor SF. causes separation of the flow and subsequent development of the pressure drag at smaller Reynolds numbers than for particles more uniformly shaped. The more rapid development of pressure drag of particles with small SF, causes the resistance to be- come independent of the Reynolds number at smaller values or R and larger values of 0D. C32 07 — 0.6 .O .0 .0 U.) A U1 DIMENSIONLESS COEFFICIENT OF DRAG (CD) .0 N 0.1 ~— O l I l l J O 0.01 0.02 0.03 0.04 0.05 FREQUENCY NUMBER (6) FIGURE 25.—Coeflicient of drag as a. function of frequency number for falling cylinders, SF¢=0.5. Computations are based on d". and path velocity. When R> 10,000, the (JD—R relationships for disks and cylinders, is not uniquely fixed by particle shape. It is a function of I, 0, and as well. When R<2,000, the curves representing the rela- tionship between 01, and R are separated according to SE, except for cylinders and oblate spheroids, on the OD—R diagram (fig. 273). The cylinders and oblate spheroids have the same shape factor, but the relation- ships do not coincide. More will be said about the effect of particle shape in the section below. INTERPRETATION OF RESULTS The foregoing discussion presented experimental findings; the following interprets these findings. PARAM ETRIC RELATION SHIPS The ratio between the maximum diameter (1,, and minimum diameter d” obviously is constant for all particles of one shape. Thus, when d,,, and d” are used to compute OD and R, the constancy of the ratio of d". and d,, preserves the “shape” of the curves repre— senting the relationship of 0D to R regardless of which SEDIMENT TRANSPORT IN ALLUVLAL CHANNELS characteristic diameter is used. Therefore, the shift in location of the respective curves on the OD—R diagram is due to particle geometry, and the choice of diameter can be arbitrary as long as it is used consistently. The difference found between the path and vertical velocities is a direct function of the effect of particle steadiness on the length of the fall path. The greater the degree of oscillation or rotation, the greater the difference between the velocities. Therefore, the OD—R curves using the respective characteristic velocities in the computations for 0,, and R, are the same as long as the particles are steady; they are different when the particles are unstable. Unlike the shift in the position of the OD—R curve because of the change of character- istic diameter, the shift due to difference in velocity changes the shape of the curve. Probably much of the scatter in the data of other investigators is due to the change in vertical velocity brought about by the un— stable condition of the particles during fall. All the given OD—R diagrams that were based on the path velocity, except for the curve for disks when R> 10,000, show a smooth curve, even when the particles oscillate and rotate. Hence, the fall velocity predicted from these C’D—R diagrams should be a close approximation of path velocity of the particle. PATTERNS OF FALL When the magnitude of the pressure drag on a particle approaches the weight of the particle, its pattern of fall is greatly influenced by small changes in the dis- tribution of the pressure forces around it. Thus, the pattern of fall is a function of the steadiness of the center of pressure on the particle. Inasmuch as the pressure drag is dependent upon the degree of wake development, particle shape affects the pattern of fall to the degree that it affects the development and stability of the wake downstream from the particle. If the wake stability is a function of the symmetry of the particle, then particles with a circular cross section should be more stable than ones with an elliptical cross section. Except for the disks, this was found to be true The oblate spheroids were more stable than either the prolate spheroids or the cylinders. The fact that the disks were the most unstable indi- cates that extremeness in shape also affects the fall pattern. That is, extreme shape causes separation and wake development, and hence full development of pres— sure drag at smaller Reynolds numbers than for parti- cles of more streamlined shapes, such as the oblate spheroids. Apparently, the fall pattern of a particle becomes more steady (less oscillation and rotation and more vertical) as the Corey shape factor increases from num- bers less than one to one. Also, the particle becomes THE BEHAVIOR OF LARGE PARTICLES FALLING IN QUIE-SCENT LIQUIDS C33 FORCE NUMBER Ox) 10 103 104 105 106 107 108 109 1010 \\\ \ \\\ \ l\\\\ \ \\\\ \ |\\\ \\\\ \ kluf11i\-\Maj\or \\\\ num axis Lead 0 1.91 o D 2.54 I \ A 3.81 A —___._._ ——-—— —‘ DlMENSIONLESS COEFFICIENT OF DRAG (CD) ._- \\ \\\\__ Fixed di_s_k_ ______________ A _‘ \ _ \ _ 38 0.0838 \‘Sfo 00232 38:60 0.0392 4 E‘ 00505 — \§S‘G Falling prolate spheroid-dm o 'n 9 0.023 ,E _ Wk, \\\\~‘_:flx_e_d_s_p_h_eg———'a7232’ _ \0 \ \ \ x, \ — \ \ \ 0.1 \l l\lli T 1\11l\1 I\ll]\l l\l| 10 102 103 104 105 REYNOLDS NUMBER (R) FIGURE 26.—Coefiicient of drag as a function at Reynolds number for falling prolate spheroids, SFc= 0.71. Computations are based on dm and path velocity. I and 0 are given for points where spheroids were unsteady. more stable as SF. approaches one because of cross- sectional changes from elliptical to circular. The effect of shape on the fall pattern of a particle is, therefore, a combination of the effects of the shape of the cross sec- tion and the extremeness of the overall shape or Corey shape factor SE. The steadiness of the fall pattern of a particle has a marked effect on the ratio of path distance to vertical distance that the particle travels. The ratio increases as the degree of steadiness decreases. The degree of un- steadiness has a greater effect on the length of the path of nonspherical particles having a circular cross section than on those having elliptical cross sections. The path of travel for both disks and oblate spheroids was in- creased more by an unsteady fall pattern than it was for cylinders and prolate spheroids. The separation of the curve into two parts in the OD—R relationship was found only for disks. It is not known whether particle shapes other than disks will become sufficiently unsteady as a result of density dif— ferences for a similar division in the OD—R relationship. Two characteristics of an unsteady particle may reduce its fall velocity in turbulent natural flow from that obtained in a quiescent fluid. As previously noted, resistance to fall increases with the frequency of oscilla- tion or rotation. If a particle, which has one fall pattern when falling in a quiescent fluid, were falling in a tur- bulent fluid, the turbulence may increase its oscillation, and hence its resistance to fall. The velocity of the parti- cle would decrease a corresponding amount. The second characteristic is the increased length of the fall path as the particle becomes more unsteady. As the path of travel increases, the particle may be exposed to more turbulent eddies, which, in turn, would increase its unsteadiness. The net result would be a slower fall velocity than the same particle would experience in a quiescent fluid. The turbulenece of a moving fluid may affect the be- havior of a particle in another manner. Since resistance to motion is a function of «)2, squaring the mean velocity plus the velocity fluctuations will give a greater number to be used in equation 4 than the square of the mean velocity. The result will be a greater mean resistance to fall and a smaller mean fall velocity. SHAPE FACTORS Of the three shape factors presented in the data (fig. 27B), the Corey shape factor SFC fits the (JD—R relationships in the most logical manner. It is still an inadequate measure because two curves having the same shape factor (cylinders and oblate spheroids) plot in quite different positions on the diagram. Alger’s shape factor SFM, which modified SF, by accounting for surface area, fits the OD—R curves (in fig. 27) except C34 SEDIMENT TRANSPORT IN ALLUVIIAL CHANNELS FORCE NUMBER (M 103 104 105 106 107 108 109 1010 1O \ \\\I\ \\\\I\\ K\Y\.\\ DIMENSIONLESS COEFFICIENT 0F DRAG (CD) DIMENSIONLESS COEFFICIENT 0F DRAG (CD) PARTICLE * Fixed disk Fixed sphere Falling disk —— 0.10 0.15 0.53 \-.\ Falling cylinder —-—-—0.50 0.59 0.43 \ Falling prolate spheroid ————-— 0.71 0.73 0.63 '-\ _/ Y Falling oblate spheroid ——————— 0.50 0.53 0.82 Falling sphere 1.00 1.00 1.00 . 0.1 . it.” . lull 1 llI\I Ill 10 102 103 104 105 REYNOLDS NUMBER (R) A FORCE NUMBER (A) 103 104 105 106 107 108 109 1010 10 \\\ I\ \ I\ \ \ \ h _\ s. \. \\\‘ \ \ PARTICLE Falling oblate spheroid Falling sphere 0.1 1 I I » Fixed disk — — Fixed sphere ----------- Falling disk —----——- 0.10 0.15 0.53 EV Falling cylinder —~— 0.50 0.59 0.43 Falling prolate spheroid —-—-— 0.71 0.73 0.63 _ ————— 0.50 0.53 0.82 1.00 1.00 1.00 10 REYNOLDS NUMBER (R) B FIGURE 27.——Composite graphs of coeflicient of drag as a function of Reynolds number for falling spheres, disks, oblate spheroids, cylinders, and prolate spheroids. A, Computations are based on d," and path velocity. B, Computations are based on d" and path velocity. THE BEHAVIOR OF LARGE PARTICLES FALLING IN QUIEISCEN’I‘ LIQUIDS for the cylinders and oblate spheroids. The larger value should be with the oblate spheroids rather than the cylinders to fit properly. Thus, the modification by Alger may overcompensate for some deficiencies of SF, for some particles. Wadell’s sphericity parameter seems to be the least significant of the three shape factors. Apparently, rough surfaces and sharp corners meas- urable increase the drag of falling particles. Compari— sons of the curves representing the OD—R relationship for crushed and naturally worn gravel particles have been made by Wilde (1952) and Colby (U.S. Inter- Agency Comm. Water Resources, 1957) for naturally worn sand and gravel. The curves for particles studied in the Wilde experiments indicate that roughness and roundness have as great an effect on particle fall velocity, if not greater, than the effects of shape. Alger (1964) shows that the modification of 0D and SF, by a factor proportional to the surface area of the particle is significant. By appropriate modification of 0D and SF, with the ratio dA/dn, Alger was able to predict the fall velocity of large concrete and steel cylinders from small aluminum models with an accuracy of about 2 percent. Alger assumed that 0,, was inde- pendent of R when R >2,000. The relationship of 0D to R for cylinders found in this study (fig. 27B) is not independent of R when R >2,000. This appears to contradict Alger’s findings. SUMMARY AND CONCLUSIONS The fall velocities of disks, cylinders, oblate and prolate spheroids, and spheres falling in quiescent fluids has been studied for the range of Reynolds numbers between 10 and 100,000. Curves that present the relationships between the coefficient of drag and the Reynolds number based on the path velocity, vertical velocity, maximum diameter, and nominal diameter as characteristic variables have been developed. These characteristic variables are used to determine the coefficient of drag and the Reynolds number which are plotted on the (JD—R diagram. Individual particles, however, plot on lines of constant force number re- gardless of which parameters are used. Curves from points based on the nominal diameter and the maximum diameter of the particles are identical in shape when the path velocity is used in the OD—R computations. The curves are also identical when the vertical velocity is used, but they are different from those for the path velocity. Curves using the path and vertical velocities are the same as long as the particles are steady, but deviate, depending on the degree of difference in velocity, when the particles become unsteady. The falling spheres exhibited very little unsteadineSs. The experimental curve based upon the data herein presented coincides with the curve for fixed spheres. C35 No rotation was apparent in any of the drops made with spheres except one that rotated through 45° during its fall in the test section. The disks were the least steady of all the particles tested. Unsteadiness first occurred in the form of os- cillations in a vertical plane about a horizontal diameter at Reynolds numbers of approximately 100. As the Reynolds number increases over its entire range, the results of the drops show a series of fall patterns ranging from a stable pattern of steady-flat fall where the disks fell vertically with their maximum projected area perpendicular to the direction of fall, to one of quasi- stable pattern of constant rotation. The patterns have been categorized in four general classifications which are, in turn, combined into three fall regimes as follows: Fall patterns Regimes Stable _________________________ Stable Oscillation } Transition Glide-tumble """"""""""" Tumble ________________________ Tumble Boundaries of the suggested regimes are defined by 0D, R, and I. The density ratio between the particles and the fluid affects fall velocity by virtue of its relation to the stability number I and to the frequency of oscillation. When R>10,000, two branches of the C’D—R curve were defined for two different stability numbers of the disks. The stability number is greater for lead than aluminum disks, and the points for the lead disks plot higher on the OD—R diagram than do the points for the aluminum ones. Since all variables of I are the same for all disks, including the thickness-diameter ratio, except the density ratio, the division in the curve must be due to particle density. The coefficient of drag is a function of the frequency of oscillation as reflected by the linear relationship between 0D and 0. Thus, it can be concluded that both I and 0 are important parameters in fall behavior studies. The studies indicated that once oscillation began, disk unsteadiness was characterized by a rather uniform cyclic frequency. The oscillations were not random with respect to time. The oblate spheroids were the most stable of the nonspherical particles. Reynolds numbers as great as 50,000 were obtained without indication of unsteadiness. When unsteadiness did develop, the patterns of fall were oscillation and tumble. Prolate spheroids and cylinders had very similar patterns of fall, except that instability began at smaller Reynolds numbers for cylinders than for prolate sphe- roids. The general pattern of unsteady fall was that of oscillation in a vertical plane about a horizontal axis C36 followed by the imposition of a horizontal oscillation about a vertical axis as Reynolds numbers increased. When all curves based on the “path velocity” and the “maximum diameter” as characteristic parameters were plotted together, it was apparent that the shape of the particle had only a small effect on fall velocity for Reynolds numbers less than 400. For R>400, the particle shape had a more pronounced effect on the location of the OD-R curves. Curves for particles with the smallest values of SF, became horizontal, or inde- pendent of R, at lower Reynolds numbers than the curves for particles with larger SF, values. When the fall patterns of all the particles were com- pared on the basis of shape, it was evident that the more extreme the shape, the greater the degree of insta- bility. When extremes were not considered, it was apparent that particles with circular cross sections were more stable than particles with elliptical cross sections of the same SFC. This study indicates that more research is needed to investigate the various problems related to the behavior of large particles falling in quiescent fluids. The fol— lowing studies would be helpful: 1. A systematic study of the effect of roughness and roundness on particle behavior. A comparison of these results with those of other investigations show that neglect of roughness and roundness may introduce errors of as much as 100 percent in estimating fall velocities. 2. A study to enlarge the concept of fall regimes to particles of shapes other than disks. 3. A more systematic study of the effect of the shape of the cross-sectional area needs to be made. The study herein reported appears to indicate that the O’D—R curve for particles with nearly circular cross section is not the same as the CD—R curve for particles with elliptical or rectangular cross section even though the Corey shape factor is the same for both particles. Therefore, a study of particle behavior as the particle shape changes through progressive stages from an oblate spheroid to a sphere as compared to the particle behavior as the shape changes from a prolate spheroid to a sphere would be helpful. 4. The steadiness of a particle is important in its be- havior. Therefore, a more detailed analysis of the equations of motion of a particle should be made. REFERENCES CITED Albertson, M. L., Barton, J. R., and Simons, D. B., 1960, Fluid mechanics for engineers: Englewood Cliffs, N.J., Prentice- Hall, 561 p. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS Alger, G. L., 1964, Terminal fall velocity of particles of irregular shapes as affected by surface area: Colorado State Univ., Ph. D. dissertation, 110 p. Briggs, L. I., McCullock, D. S., and Moser, F., 1962, The hydraulic shape of sand particles: Jour. Sed. Petrology, v. 32, no. 4, p. 645—656. Brush, L. M., 1964, Accelerated motion of a sphere in a viscous fluid: Am. Soc. Civil Eng. Jour., v. 90, no. HY 1, p. 149—160. Chatuthasry, N. C., 1961, Sedimentation diameter: SEATO Graduate School of Engineering, Bangkok, Thailand, M.S. thesis, 33 p. Corey, A. T., 1949, Influence of shape on the fall velocity of sand grains: Colorado State Univ., M.S. thesis, 102 p. Fahnestock, R. K., and Maddock, Thomas Jr., 1964, Preliminary report on bed forms and flow phenomena in the Rio Grande near El Paso, Texas, in Geological Survey research 1964, US. Geol. Survey Prof. Paper, 501-B, p. B140-B142. Lamb, Horace, 1932, Hydrodynamics, New York, Dover Publications, 378 p. McNown, J. S., and Malaika, J., 1950, Effects of particle shape on settling velocity at low Reynolds numbers: Am. Geophys., Union Trans, v. 31, p. 74—82. Odar, F., and Hamilton, W. 8., 1964, Forces on a sphere accel- erating in a viscous fluid: Jour. Fluid Mech., v. 18, pt. 2, p. 302-314. Prandtl, L., and Tietjens, O. G., 1934, Applied hydro- and aero- mechanics: New York, McGraw—Hill Book Co. Rouse, H., 1946, Elementary mechanics of fluids: New York, John Wiley & Sons, 376 p. Rubey, W. W., 1933, Settling velocities of gravel, sand, and silt particles: Am. Jour. Sci., 5th ser., v. 25, p. 325—338. Schulz, E. F., Wilde, R. H., and Albertson, M. L., 1954, Influence of shape on the fall velocity of sedimentary particles: Colorado State University and US. Army Corps of Engi- neers, MRD Sediment Ser., no. 5, 163 p. Serr, E. F., 1948, A comparison of the sedimentation diameter and the sieve diameter for various types of natural sands: Colorado State Univ., MS. thesis, 82 p. Stelson, T. E., and Mavis, F. T., 1957, Virtual mass and accelera- tion in fluids: Am. Soc. Civil Eng. Trans., v. 122, p. 518—530. Stringham, G. E., 1965, Behavior of geometric particles falling in quiescent viscous fluids: Colorado State Univ., Ph. D. dissertation, 143 p. U.S. Inter-Agency Committee on Water Resources, 1957, Some fundamentals of particle size analysis [prepared by B. C. Colby * * *], in A study of methods used in measure- ment and analysis of sediment loads in streams: Washington, US. Govt Printing Office, Rept. 12, .55 p. [1958]. Wadell, H. A., 1932, Volume, space, and roundness of rock particles: J our. Geology, v. 40, p. 443—451. 1933, Sphericity and roundness of rock particles: Jour. Geology, v. 41, p. 310-331. 1934, The coefficient of resistance as a function of Reynolds number for solids of various shapes: Franklin Inst. Jour., v. 217, no. 4, p. 459—490. Wilde, R. H., 1952, Effect of shape on the fall-velocity of gravel- size particles: Colorado State Univ., M.S. thesis, 86 p. Wilmarth, W. W., Hawk, N. E., and Harvey, R. L., 1964, Steady and unsteady motions and Wakes of freely falling disks: Physics of Fluids, v. 7, no. 2, p. 197-208. U.S. GOVERNMENT PRINTING OFFICE: 1969—0-307-955 7 i i? (A m GE 75 7 DAY Response of a Laboratory Alluvial Channel to Changes of Hydraulic and Sediment -Transport Variables GEOLOGICAL SURVEY PROFESSIONAL PAPER 562-D Response of a Laboratory Alluvial Channel to Changes of Hydraulic and Sediment -Transp0rt Variables By R. E. RATHBUN, H. P. GUY, and E. V. RICHARDSON SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS GEOLOGICAL SURVEY PROFESSIONAL PAPER 562-D A comparison of taefeeaI anaI recirculation ystenzs of flame operation for [aooratory studies of sediment transport anaI resistance to flow —I— UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1969 UNITED STATES DEPARTMENT OF THE INTERIOR WALTER J. HICKEL, Secretary GEOLOGICAL SURVEY William T. Pecora, Director For sale by the Superintendent of Documents, US. Government Printing Office Washington, DC. 20402 - Price 40 cents (paper cover) CONTENTS Page Abstract ___________________________________________ D1 Comparison of the feed and recirculation systems— Introduction _______________________________________ 1 Continued General procedures for laboratory alluvial channel Depth of flow __________________________________ experiments ______________________________________ 3 Velocity _______________________________________ Experimental apparatus and procedure ________________ 5 Responses of the flume to changes of the hydraulic and Apparatus _____________________________________ 5 sediment-transport variables _______________________ Bed material ___________________________________ 7 Advantages and disadvantages of the feed and recircula- Procedure ______________________________________ 7 tion systems _____________________________________ Comparison of the feed and recirculation systems _______ 9 Summary __________________________________________ Sediment-transport rate- _ _. ______________________ 9 Limitations and recommendations ____________________ Water-surface slope _____________________________ 10 Literature cited _____________________________________ ILLUSTRATIONS FIGURE 1. Schematic diagrams of the recirculation and feed systems of flume operation for alluvial channel experiments- 2. Schematic diagram of the experimental flume and associated equipment used in this study ................ 3—21. Graphs showing: 3. Variation with time of several variables in run 6 ______________________________________________ 4. Comparison of the unit sediment-transport rate when a change is made from the recirculation system to the feed system, runs 1—11 ___________________________________________________________ 5. Comparison of the unit sediment-transport rate when a change is' made from the feed system to the recirculation system, runs 3—6 and 8-11 __________________________________________________ 6. Comparison of the water-surface slope for the recirculation and feed systems, runs 1—11 ............ 7. Comparison of the mean depth of flow for the recirculation and feed systems, runs 1—11 ............ 8. Comparison of the mean velocity of flow for the recirculation and feed systems, runs 1—11 ........... 9—11. Response of the feed system to: . 9. An increase in sand-bed slope, run 12b _______________________________________________ 10. A decrease in sand-bed slope, run 13 __________________________________________________ 11. An increase in sediment-feed rate, run 14b ______________________________________________ 12. Response of the recirculation system to a decrease in sand-bed slope, run 15 ....................... 13. Response of the feed system to a decrease in sediment-feed rate, run 16 ___________________________ 14—16. Response of the recirculation system to: 14. An increasing sediment-transport rate, run 17b ________________ , _________________________ 15. An increase in sand-bed slope, run 18 _________________________________________________ 16. A decreasing sediment-transport rate, run 19 ___________________________________________ 17. Response of the feed system to an increase in the tail-water depth, run 20 _________________________ 18. Response of the recirculation system to a decrease in the tail-water depth, run 21- _ _ _ - - - _ - _ - _ - _ - 1 _ - 19. Response of the recirculation system to an increase in the tail-water depth, run 22 _______________ 20; Response of Ian; teed system to a decrease in tail-water depth, run 23 __________________________ 21. Mean velocity versus unit water discharge-slope product relations _____________________________ TABLES TABLE 1. Summary of experimental data for rum; 1—11 ________________________________________________________ 2. Comparison of the responses of the feed and recirculation systems to changes of sand-bed slope, tail-water depth, and sediment-transport rate when water discharge is constant _______________________________ 3. Summary of experimental data for runs 12—23 _______________________________________________________ 4- Summary of the least squares values of log, a and b _________________________________________________ III Page D11 11 13 28 30 31 31 Page Page D10 16 16 27 mymfncoapfi‘qe . on U “I<—-—— I | I Feed —————>I<—— Recirculation —-——>n| 15— ._. o | m I O \> ,, °\ k \ 771m VARIATION FROM MEAN. IN PERCENT I I I I \ , ,, \ ,3 , -5— I; — — V \ 7" — d EXPLANATION I I \ /’C\ I] Discharge H \ / *10# A Depth 1! — — \ // — o Slope \g _15 I I I L I I l I 0300 1000 1200 1400 1600 1700 0800 1000 1200 1400 1600 1700 12—28—65 12—29-65 TIME, IN HOURS FIGURE 3.——Variatlon with time of sediment-transport rate, water-surface slope, mean depth of flow, and water discharge in run 6. tion system, and there was a greater tendency for the oscillations in the sediment-transport rate to be averaged for the feed system. After the collection of sufiicient data to define the equilibrium conditions for the recirculation system, the change to the feed system was made. The water dis— charge and sediment-feed rate were set equal to the mean equilibrium values of the water discharge and sediment-transport rate for the recirculation system. Measurements of the water discharge, depth of flow, water-surface slope, sediInent-tranSport rate, water temperature, and sediment-feed rate were continued un- til suflicient data were obtained to define the equilibrium conditions for the feed system. These measurements were begun as soon as the change to the feed system was completed so that measurements would be obtained dur- ing the transition to the new equilibrium conditions if the change to the feed system resulted in new hydraulic and sediment-transport conditions. After the completion of the feed system part of the experiment, the usual procedure was to revert to the recirculation system and to continue the hydraulic and sediment-transport measurements. The purpose of this procedure was to permit a comparison of the sediment- transport rate under conditions where the sediment- transport rate was an independent or controlled variable before the change and a dependent Variable after the change. The measurements were begun as soon as the change in the method of operation was completed, and the measurements were continued until suflicieiit data were obtained to define the equilibrium conditions for the recirculation system. The second part of this study was to determine the responses of the laboratory flume systems to changes RESPONSE OF CHANNEL T0 CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES that caused nonequilibrium conditions, with the water discharge maintained at a constant value. The runs consisted in general of three parts: (1) establishment of equilibrium conditions; (2) imposition of a change, resulting in nonequilibrium conditions; and (3) reestab- lishment of equilibrium. The change imposed upon the system consisted of either increasing or decreasing the sand-bed slope by raising or lowering the upper end of the flume, either increasing or decreasing the tail-water depth at the downstream end of the flume by adjusting the tailgate, or increasing or decreasing the amount of sediment transported by changing the sediment-feed rate for the feed system and by adding sediment to the recirculating system or extracting a portion of the re- circulating sediment. These changes were imposed upon both the feed and recirculation systems in a total of 12 experimental runs. The runs were completed in a se- quence such that a run that resulted in increased values of the water—surface slope and sediment-transport rate was followed by a run that was expected to yield de- creased values of the water-surface slope and sediment- transport rate. The equilibrium conditions established at the conclusion of one run served as the initial equilib- rium conditions for the next run. Numerous measurements of the water discharge, water-surface slope, depth of flow, sediment—transport rate, and water temperature were made for both the nonequilibrium conditions and the equilibrium condi- tions. The sediment-feed rate was also checked period- ically in the feed system runs. During the initial stages of each run when the nonequilibrium conditions pre- vailed, measurements of the variables were completed as rapidly as possible. It required about 1 minute to read and record the readings of the 11 piezometers used to determine the water-surface slope, the reading of the manometer used to determine the water discharge, and the reading of the thermometer used to determine the water temperature. The depth of flow was determined from 18 measurements of the water-surface elevation and 18 measurements of the sand-bed elevation at 0.5- meter intervals along the flume centerline. The initial 2-meter section of the flume was affected by entrance conditions and was not considered in the determination of the depth of flow. The measurement of the depth of flow required about 9 minutes. For feed-system runs, the determination of the sediment-feed rate required about 2 minutes. Thus, a complete set of measurements of the variables could be obtained in about 10 minutes for recirculation-system runs and in about 12 minutes for the feed-system runs. The sediment—transport rate determinations in the recirculation-system runs were made concurrently with the other measurements. In the feed-system runs, all the sediment transported from the D9 end of the flume was collected continuously (divided into discrete increments of time), and the sediment volumes and the correSponding sediment-transport rates were determined after the completion of a run. The magnitudes of the changes imposed upon the systems during these experimental runs and the dura- tions of the runs were such that significant changes oc- curred in the sediment-transport rate, the water-sur- face slope, and the depth of flow. Significant changes generally did not occur in the resistance to flow as rep- resented by the Darcy-Weisbach resistance coeflicient. The water-discharge used in runs 12 and 13 was about 10 percent larger than the approximately constant water discharge used in runs 14—23. COMPARISON OF THE FEED AND RECIRCULATION SYSTEMS In the first part of this study, the feed and recircu- lation systems were compared under equilibrium condi- tions in 11 experimental runs that covered a wide range of flow conditions with bed forms ranging from ripples to antidunes. The mean values of the measured variables at equilibrium flow conditions and the parameters com- puted from the measured variables are given in table 1. The variations of the variables about their mean values were essentially the same for the two systems. Com- parison of the measured variables and the calculated parameters is as follows. SEDIMENT-TRAN SPORT RATE The sediment-transport rate should be one of the more sensitive indicators of any possible difl'erences be- tween the feed and recirculation systems. In the pro- cedure employed in runs 1—11, the mean equilibrium sediment-transport rate for the recirculation system was used as the sediment-feed rate when the change from the recirculation system to the feed system was made. If differences between the two systems had existed, the equilibrium conditions established in the recirculation part of the run would have been disturbed, and different values of the water-surface slope, depth'of flow, and bed roughness would have resulted. Because the sediment- feed rate was fixed, and, hence, the sediment-transport rate, a new permanent equilibrium condition could not be established. Differences between the two flume sys- tems would have been reflected in changing conditions and an inability to establish equilibrium. Changing con- ditions were not observed in any of the 11 runs, and the equilibrium conditions of the recirculation system did not change within the limits of experimental variation or error when the change to the feed system was made. Figure 4 is a comparison of the unit sediment-transport D10 SEDIIMENT TRANSPORT IN ALLU'VIAL CHANNELS TABLE 1.—Summary of experimental data for rum 1—11 l Mean Weter-eurtaee Sediment transport Run number Operational system Disc): Mean depth velocity 510 X 10' Ten rature 0/ch (cm) (em/sec) lid/m) (2°C) Rate Concentrar (Elsec/m) tlon (mg/l) 1 ____________________ Recirculation ___________ 30. 4 5. 97 50. 9 4. 13 19. 8 26. 9 885 Feed ___________________ 30. 2 6. 10 49. 6 3. 90 21. l 24. 2 798 2 ____________________ Recirculation ........... 37. 5 7. 42 50. 5 3. 22 20. 4 20. 6 550 Feed ___________________ 37. 4 7. 71 48. 6 3. 50 20. 8 16. 7 446 3 .................... Recirculation ........... 22. 4 4. 50 50. 0 5. 28 20. 7 19. 8 875 eed ___________________ 22. 7 4. 70 48. 4 4. 67 20. 5 28. 8 1, 270 Recirculation ___________ 22. 2 4. 42 50. 2 4. 87 21. 0 20. 6 925 4 ____________________ Recirculation ___________ 32. 8 5. 32 61. 4 6. 08 20. 4 55. 0 1, 680 Feed ___________________ 32. 6 5. 50 59. 4 5. 51 21. 1 50. 0 1, 540 Recirculation ___________ 32. 5 5. 14 63. 2 5. 90 21. 5 52. 9 1, 630 5 ____________________ Recirculation ___________ 24. 6 5. 63 43. 8 3. 06 24. 3 l3. 0 529 ee ___________________ 24. 7 5. 72 43. 2 3. 30 24. 7 15. 7 637 Recirculation ___________ 24. 6 5. 83 42. 2 2. 92 25. 0 11. 7 474 6 ____________________ Recirculation ___________ 37. 0 8. 41 44. 2 2. 40 25. 2 12. 4 335 ee ___________________ 37. 0 8. 59 43. 1 2. 31 25. 1 11. 8 318 Recirculation ___________ 37. 2 8. 63 43. 0 2. 25 25. 4 11. 9 320 7 ____________________ Recirculation ___________ 19. 7 6. 05 32. 6 2. 12 24. 6 2. 74 139 Feed ___________________ 19. 7 6. 12 32. 1 2. 06 23. 9 2. 73 139 8 .................... Recirculation ___________ 14. 9 4. 70 31. 7 2. 74 24. 2 2. 71 182 eed ................... 14. 9 4. 74 31. 5 2. 74 23. 9 3. 28 220 Recirculation ___________ 15. 0 4. 84 31. O 2. 83 24. 1 3. 08 234 9 ____________________ Recirculation ___________ 25. 2 3. 99 62. 8 7. 83 21. 0 , 69. 0 2, 750 Feed ___________________ 24. 9 4. 14 60. 4 7. 78 21. 2 84. 2 3, 380 Recirculation ___________ 24. 9 4. 00 62. 4 7. 82 21. 0 65. 2 2, 610 10 ___________________ Recirculation ___________ 17. 5 4. 59 38. 2 3. 24 24. O 8. 59 490 Fee ___________________ 17. 6 4. 59 38. 4 3. 19 24. 0 8. 59 488 Recirculation ___________ 17. 5 4. 60 38. 1 3. 20 24. 0 9. 00 514 11 ___________________ Recirculation ___________ 29. 4 3. 87 76. 1 8. 96 24. 0 146 4, 960 Feed ___________________ 28. 6 3. 80 75. 4 8. 78 24. 0 140 4, 890 Recirculation ___________ 27. 8 3. 70 75. 2 9. 40 24. 0 145, 5, 210 rate for the recirculation system with the unit sediment- transport rate for the feed system when a change is made from the recirculation system to the feed system. The mean sediment-transport rates for each run fall on both sides of, but near, the line of perfect agreement. The size of the rectangle about each point represents the confidence limits at the 95 percent level of significance of the mean values used to establish the point. In eight of the 11 runs (runs 1, 2, and 7 are the excep- tions), 3. change was made from the feed system to the recirculation system with only the water discharge held constant. Under these conditions, the sediment-trans- port rate changed from an independent variable to a dependent variable, and the water-surface slope, depth of flow, bed roughness, and sediment-transport rate were free to change if differences existed between the feed and recirculation systems. Figure 5 is a compari- son of the unit sediment-transport rate for the recir- culation system with the unit sediment-transport rate for the feed system when a change is made from the feed system to the recirculation system, The mean sediment- transport rates for each run fall on both sides of, but near, the line of perfect agreement. It can be concluded on the basis of the results presented in figure 5 that no significant differences at the 95 percent level of signifi- cance exist between the sediment-transport rate for the recirculation system and the sediment-transport rate for the feed system. WATER-SURFACE SLOPE The results of the comparison of the mean values of the water-surface slope for the recirculation and feed systems are shown in figure 6. Values of the water-sur- face slope for runs 1, 3, 4, and 11 were slightly larger for the recirculation system than for the feed system and values of the water-surface slope for runs 2 and 5 were smaller for the recirculation system than for the feed system. The differences in water-surface slopes were not significant at the 95 percent level of significance. RESPONSE OF CHANNEL T0 CHANGES IN HYDRAULIC AND SEDIIVIENT-TRANSPORT VARIABLES D11 SEDIMENT-TRANSPORT RATE (RECIRCULATION SYSTEM), IN GRAMS PER SECOND PER METER 1 2 4 6 8 10 20 40 60 80 100 200 SEDIMENT-TRANSPORT RATE (FEED SYSTEM), IN GRAMS PER SECOND PER METER FIGURE 4.—Comparlson of the unit sediment-transport rate when a change is made from the recirculation system to the feed system, runs 1—11. DEPTH OF FLOW VELOCITY The results of the comparison of the mean values of The mean velocity was computed from the equation the depth of flow for the recirculation and feed systems of continuity, equation 3. Because the water discharge are shown in figure 7. Mean depth of flow values were was controlled within very narrow limits, the flume in general slightly smaller for the recirculation system width was constant, and the depths of flow were, in gen- than for the feed system. The differences in depths of eral, slightly smaller for the recirculation system than flow were not significant at the 95 percent level of for the feed system, the mean velocities were slightly significance. . larger for the recirculation system than for the feed D12 1000 800 600 400 100 80 60 40 20 10 SEDIMENT—TRANSPORT RATE (RECIRCULATION SYSTEM), IN GRAMS PER SECOND PER METER 1 2 4 6 810 20 SEDIMIENT TRANSPORT IN ALLUVIAL CHANNELS 40 60 SEDIMENT-TRANSPORT RATE (FEED SYSTEM), IN GRAMS PER SECOND PER METER 80 100 200 400 600 800 1000 FIGURE 5.——Comparlson of the unit sediment-transport rate when a change is made from the feed system to the recirculation system, runs 3.6 and 8-11. system, as figure 8 shows. The difl'erences in mean veloci- ties were not significant at the 95 percent level of significance. Agreement between derived parameters, such as the Darcy-Weisbach friction factor, as defined by equation 5, and the stream power (708 V) was found for the two systems. Agreement was expected because of the agree- ment between water-surface slope, depth of flow, and mean velocity values for the two systems. On the basis of these results and the results shown in figures 5—8, we conclude that no significant difi'erences at the 95 percent level of significance exist between the equilib- rium values of the sediment-transport rate, water-sur- face slope, depth of flow, mean velocity, Darcy-Weisbach resistance coefficient, and stream power for the recircu- lation system and for the feed system. RESPONSE OF CHANNEL T0 CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES D13 10 I I I I | | | WATER-SURFACE SLOPE (RECIRCULATION SYSTEM)X103 m | I I I I I ———.——— J?- I I I l I | I | 2 I I I 2 3 4 5 6 7 8 9 10 WATER-SURFACE SLOPE (FEED SYSTEM)><103 FIGURE (i—Oomparison of the water-surface slope for the recirculation and teed systems, runs 1—11. RESPONSES OF THE FLUME TO CHANGES OF THE HYDRAULIC AND SEDIMENT-TRAN SPORT VARIABLES The second part of this study consisted of determin- ing the responses of the feed and recirculation systems of flume operation to three types of changes that caused nonequilibrium hydraulic and sediment-transport con- ditions in the flume. A series of 12 experimental runs 351—258 0—69—43 (runs 12—23) was completed, and the qualitative results of these runs are given in table 2. A summary of the equilibrium values of the variables for each run is given in table 3. The bed forms for these runs were transition (Task Committee on Bed Forms in Alluvial Channels, 1966), and the Froude number (F= V/ (gD)°-5) ranged from 0.58 to 0.86. The unit sediment-transport rate gs, D14 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 1" I I I T T DEPTH OF FLOW (RECIRCULATION SYSTEM), IN CENTIMETERS 10 11 l l l | l | 3 4 5 6 7 8 9 1o DEPTH OF FLOW (FEED SYSTEM), IN CENTIMETERS FIGURE 7 .——Oomparison of the mean depth of flow for the recirculation and feed systems, runs 1-1L ranged from 13.2 to 53.7 grams per second per meter conditions. Results from these experiments are shown and were in the middle of the range of unit sedimenta in a figure for each run (figs. 9—20 for runs 12—23, re- transport rates for runs 1—11. spectively). The following comments are applicable to Numerous measurements of the different variables these figures: were obtained during the periods of nonequilibrium 1. The rate of sediment transport from the end of the conditions as well as during the periods of equilibrium flume is represented by the use of block diagrams. RESPONSE OF CHANNEL T0 CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES D15 86 I I I 78— 70— 54— MEAN VELOCITY OF FLOW (RECIRCULATION SYSTEM), IN CENTIMETERS PER SECOND I I I I I I 46 54 MEAN VELOCITY OF FLOW (FEED SYSTEM), IN CENTIMETERS PER SECOND 62 7O 78 86 FIGURE 8.—Oomparison of the mean velocity of flow for the recirculation and feed system, runs 1—11. With the feed system, a continuous record (divided into discrete increments) of the sediment-trans- port rate was obtained. 2. The triangles represent measurements of the sedi- ment-feed rate for the feed system. 3. The horizontal lines and the numbers near the ordi- nate scale represent the variable values for the equilibrium that existed prior to the change imposed upon the system. 4. During nonequilibrium and equilibrium conditions, the depth of flow values are the average of 18 obser- vations at 0.5-meter intervals over the section of the flume from station 2.5 to station 11. During nonequilibrium conditions, local depth difl'erences D16 SEDIMCENT TRANSPORT IN ALLUVIAL CHANNELS TABLE 2,—Comparison of the responses of the feed and recirculation systems to changes of sand-bed slope, tail—water depth, and sediment- transport rate when water discharge is constant Res se Method of pen operation Variable changed Rate of and run Water-surface slope Depth of flow Sediment-transport rate approach to Equilibrium equilibrium conditions conditions Recirculation, Slope increased by raising Increased .................... Decreased .................... Increased .................... Rapid ...... New. run 18. upstream end of flume. Recirculation, Slope decreased by lowering Decreased ____________________ Increased .................... Decreased .......................... do. . Do. run 15. upstream end of flume. Feed, run 1%.. Slope increased by raising Slope was initially steeper Depth was initially shallower Sediment-transport was Slow ....... Original. upstream end of flame. and then returned to value and then returned to value initially larger and than existing before flume was existing before flume was returned to value existing raised. . before flume was raised. Feed, run 13. .. Slope decreased by lowering Slope was initially flatter Depth was initially deeper Sediment-trans ort rate was ..... do....-.. Do. upstream end of flume. and then returned to value and then returned to value initially sin er and then existing before flume was existin before flume was returned to value exist lowered. lowere . before flume was lowere . Recirculation, Sediment-transport rate Slope increased as long as Depth decreased as long as Sediment-transport rate Slow ....... Changing. run 17b increased by adding sand sediment was added. sediment was added. increased as lon as Witt]:a feeder to recirculating sediment was (led. s s m. Recirculation, Se iment-transport rate Slope decreased as long as Depth increased as long as Extracted part of sediment- ..... do ....... Do. run 19. decreased by extracting a sediment was extracted. sediment was extracted. transport rate decreased, portion of the recirculating total sediment-transport sediment. rate decreased as long as sediment was extracted. Feed, run 141).. Sediment-transport rate Slope increased until Depth decreased until Sediment-trans ort rate _____ do ....... New. increased by increasing sediment-transport rate sediment-transport rate increased unt it equaled sediment-feed rate. equaled sediment-feed rate. equaled sediment-feed rate. sediment-feed rate. Feed, run 16. .. Sediment-transport rate Slope decreased until Depth increased until Sediment-transport rate _____ do....-. . Do. decreased by decreasing sediment-transport rate sediment-transport rate decreased until it equaled sediment-feed rate. equaled sediment-feed rate. equaled sediment-feed rate. sediment—feed rate. Recirculation, Tail-water depth increased Decreased .................... Increased .................... Decreased ..................... Rapid....._. New. run 22. by adjusting tailgate. Recirculation, Tail-water depth decreased Increased .................... Decreased .................... Increased .......................... do..._. . . Do. run 21. by adjusting tailgate. Feed, run 20. . . Tail-water depth increased Slope was initially flatter Depth was initially deeper Sediment-trans rt rate was Slow ........ Original. by adjusting tailgate. and then returned to value and then returned to value initially sm er and then existing before depth was existing before depth was increased until it equaled changed. increased. sediment-feed rate. Feed, run 23. __ Tail-water depth decreased Slope was initially steeper Depth was initially shallower Sediment-transport rate was ..... do ....... Do. by adjusting tailgate. and then returned to value and then returned to value initially larger and than existing before depth was existing before depth was decreased until it equaled decreased. increased. sediment-feed rate. TABLE 3.——Summary of experimental data for runs 12-23 Mean Water- Flume-bed Tempera- Sediment transport Run Change imposed on system Operational system Disch e depth surface 310 e X 103 ture -————— (l/sec/m (an) slope x lo3 m/m) (° 0) Rate Concentra- (m/m) (slaw/m) lion (mg/l) 12a ____________________________________ Recirculation _______ 24. 5 5. 64 3. 10 3. 09 24. 0 13. 2 539 12b ______ Increase flume slope ___________ Feed _______________ 24. 7 5. 40 3. 15 4. 72 23. 8 13. 4 544 13 _______ Decrease flume slope ________________ do _____________ 24. 5 5. 56 3. 16 3. 12 24. 9 13. 2 539 14a ____________________________________ Recirculation _______ 22. 4 4. 55 4. 62 4. 76 24. O 28. 0 l, 250 14b ______ Increase feed rate _____________ Fee _______________ 22. 2 _ 4. 31 5. 91 4. 76 24. 0 39. 5 1, 780 15 _______ Decrease flume slope ___________ Recirculation _______ 22. 4 4. 62 4. 84 3. 53 24. 4 29. 1 1, 300 16 _______ Decrease feed rate _____________ Feed _______________ 22. 3 5. 00 3. 67 3. 53 24. 6 15. 2 681 17a ____________________________________ Recirculation _______ 22. 4 5. 01 3. 64 3. 73 24. 7 17. 0 760 17b ______ Add sediment ______________________ do _____________ 22. 3 4. 60 4. 95 3. 73 25. 2 32. 1 1, 440 18 _______ Increase flume slope ________________ do _____________ 22. 2 4. 28 5. 97 4. 72 24. 5 44. 2 2, 000 19 _______ Extract sediment ___________________ do _____________ 22. 3 4. 62 4. 67 4. 72 24. 6 27. 1 1, 210 20 _______ Increase depth ________________ Feed _______________ 22. 2 4. 50 4. 84 4. 72 25. 6 28. 1 1, 260 21 _______ Decrease depth ________________ Recirculation _______ 22. 2 4. 06 6. 64 4. 72 24. 2 53. 7 2, 420 22 _______ Increase depth _____________________ do _____________ 22. 4 4. 58 4. 78 4. 72 24. 1 29. 0 1, 300 23 _______ Decrease depth ________________ Feed _______________ 22. 3 4. 45 4. 85 4. 72 24. 0 28. 6 1, 280 (in the upstream or downstream flume section most afl’ected by the change) were greater than differ— ences shown by the data in the figures. 5. During nonequilibrium conditions, an abrupt change or break in the water—surface slope sometimes occurred during the initial stages of a run. This break occurred either in the upstream or down- stream section of the flume, the location depending on the type of change imposed on the system. When a break was observed, the water-surface slope calculation was based on the longer of the two sections. The shorter section was usually 23 meters RESPONSE OF CHANNEL T0 CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES in length, Initial slope differences, therefore, were greater than the differences shown by the data in figures 9—20. 6. For equilibrium conditions, water-surface-slope values were determined from the water—surface elevations measured by the 10 piezometer taps between stations 2—11. 7. The determination of when equilibrium had been established was based on the manner in which the depth of flow, water-surface s10pe, and sediment- transport rate varied with time. In the feed system, the agreement of the sediment-transport rate with the sediment-feed rate was also a necessary cri- terion for equilibrium. Runs 12—23 are discussed in detail in the following paragraphs. The water discharge was a constant or independent variable and the water-surface slope, depth . of flow, and the bed roughness were dependent variables in all the runs. The sediment-transport rate was an independent variable in the feed system runs and in two of the recirculation system runs (17b and 19) and was a dependent variable in the other four recirculation system runs. Run 12 (increase slope, feed system) .—In run 12b, after establishment of equilibrium conditions with the recirculation system in run 12a, the sand-bed slope was increased about 50 percent by raising the upper end of the flume, and the feed system was used with a sedi- ment-feed rate equal to the mean equilibrium value of the sediment-transport rate for run 12a. Figure 9 shows graphically the variation with time of the several variables during run 12b. The increase in sand-bed slope caused degradation of the sand bed in the upstream section of the flume; the degradation resulted in a flattening slope and a gradual approach to the final equilibrium value of the water-surface slope. The initial sediment-transport rate was larger and the initial mean depth of flow was shallower than the final equilibrium values of these variables. The final equilibrium values of the water-surface slope, depth of flow, and sediment- transport rate, however, were within 4.3 percent of the equilibrium values of these variables that existed before the change in sand-bed slope. The maximum diiference between initial and final equilibrium values was for the depth of flow. About 6 hours was required to achieve equilibrium after the change in slope. Rum 13 (decrease slope, feed 83/8tem).—In run 13 the sand-bed slope was decreased about 50 percent by loWering the upper end of the flume, and the feed sys- tem was used with the same water discharge and the same sediment-feed rate as in run 12b. Figure 10 shows graphically the variation with time of the several vari- ables during run 13. The decrease in sand-bed slope re- D17 sulted in aggradation in the upstream section of the flume, and the sediment-transport rate was less than the sediment-feed rate. The initial depth of flow was deeper than the final equilibrium value. As the sand bed aggraded in the upstream section of the flume, the water- surface slope increased, the depth of flow decreased, and the sediment-transport rate increased until equilibrium conditions were established. The final equilibrium values of the water-surface slope, depth of flow, and sedi— ment-transport rate were within 3.0 percent of the equi- librium values of these variables that existed before the change in sand—bed slope. About 8.2 hours was re- quired to achieve equilibrium after the change in slope. Run 1!; (increase sediment-feed rate, feed system) .— In run 14b, after establishment of equilibrium condi- tions with the recirculation system in run 14a, the sedi- ment-feed rate was set at a value 1.35 times the mean equilibrum value of the sediment-transport rate for run 14a. Figure 11 shows graphically the results of run 14b. The increased sediment—feed rate caused aggradation in the upstream section of the flume; the aggradation caused the slope to increase gradually, the mean depth of flow to decrease, and the sediment-transport rate to increase. The process of increasing slope, decreasing depth, and increasing sediment-transport rate contin— I— 40 555 | l | l | l | | all-u", u, _ _ _ _ 2g: 30 §00 “’E 250 — — —- — — — 0.50 O “1.: FW) 2.00 — -— I— ~ — — < 3 Feed Feed 150 I I I I L ' 1 Fe?“ I ' I 1200 1400 1600 1700 0800 1000 1200 1400 1000 1200 1400 1600 1700 1000 5—16-66 5-27—66 5-31-66 TIME, IN HOURS FIGURE 10.—Response of the feed system to a decrease in sand-bed slope, run 13. ued until the sediment-transport rate approximately equaled the sediment-feed rate at which time the slope and depth had also attained approximately constant values. The fluctuations of the variable values about the mean equilibrium values, which are indicated by the solid lines and the numbers near the right ordinate in figure 11, should be noted. Equilibrium was reached in about 7.5 hours after the increase in sediment-feed rate. The water-surface slope was 28 percent larger, the depth of flow was 5.3 percent less, and the mean bed-surface elevation was 0.42 cm higher than the equilibrium val- ues of these variables that existed before the increase in sediment-feed rate. Ram. 15 (decrease slope, recirculation system) .—In run 15 the sand-bed slope was reduced about 26 percent (from 0.00476 to 0.00353 m per m) by lowering the upper end of the flume. The recirculation system was used, and new equilibrium conditions were established almost im- mediately. The rapid response of the recirculation sys- tem to the decrease in flume slope is shown by the data presented in figure 12. The water—surface slope was 18 percent less, the depth of flow was 7.2 percent larger, and the sediment-transport rate was 26 percent less than the equilibrium values of these variables that existed before the decrease in sand-bed slope. Run 16’ (decrease sediment-feed rate, feed system) .— In run 16 the sediment-feed rate was reduced to about 48 percent of the mean sediment-transport rate for the equilibrium conditions at the end of run 15. Because the sediment—transport capacity of the flume system was larger than the sediment-feed rate, degradation oc- curred in the upstream section of the flume. The degra- dation caused the water-surface slope to decrease and the depth of flow to increase. The slope continued to de- crease, and the depth increased until the sediment- transport rate had decreased to a rate equal to the sedi- ment-feed rate. The mean sand-bed surface elevation decreased 0.75 cm during the run. The variation with time of the several variables during run 16 is shown in figure 13. Equilibrium was obtained about 9.2 hours after the decrease in sediment-feed rate. The water- surface slope was 24 percent less and the depth of RESPONSE OF CHANNEL '1‘0 CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES D19 50 I I I l IE—-|Ib-—.l __.I qun "Um Ema: 9.5- can” 40 l E 2‘”: _ <30: 30 a: PIN I40“ 20 — zzo I-u-z E38 0 __ Q l gét _ 0 ‘83 0! “Lu“ 230 (mm ' I O I I I I I 502233 225:22.41 000 0 00000 = ”0 ooooO _ _‘ WOOOO‘ gfizfi 22.0_ o 000 0° — — 0O 006)- — o 00 22.20- l—o O I_ O _ trio: 21.5- I I I — | _ _ I I 32% 21.0 E- “(n gt: 5.00 I 4E I I I I | L L; 450—455 0 O = _ —.4 .._ O O o: ' o o o o o o o 00 0 40.31 2 o o o E” 400 I I O I 10° I O (l to ‘ “2 o_ 6.50 I I I I I I o 6-00— ~ — ° — — W LLI O O o O dDO O 6) 2a. 5.50— 0° 0 — — 00 — — — “‘3 00000 §>< oo 0 O 0 mm 5.00— — — — — — «es LIE—I —4.62 O 0 — (to 4.50— — —— — — — 3 4.00— — — — — — It——Feed—>l I‘— Feed ———I [<— Feed —>I 350 I I I I 1 I 0300 1000 1200 1400 1500 0800 1000 1200 0800 1000 1200 6-9-66 6-13-66 6—17—66 TIME, IN HOURS Flam 11.——Response of the feed system to an increase in sediment-feed rate, run 14b. flow was 7.6 percent larger than the equilibrium values of these variables that existed before the decrease in sediment-feed rate. Ram 17 (increase sediment-tampon rate, recircula- tion system).—Run 17b was made after equilibrium conditions were determined using the recirculation sys- tem in run 17a. In run 17b sediment at a rate equal to about 65 percent of the equilibrium sediment-transport rate of run 17a was added continuously to the recircu- lating system by feeding sediment into the tailbox with the sediment feeder. Because the amount of sediment transported from the downstream end of the flume is usually the input to the upstream end of the flume in a recirculation system, the sediment added to the sys- tem resulted in a larger input of sediment at the flume inlet. This sediment input exceeded the sediment-trans- port capacity of the flume for the given hydraulic con- ditions and aggradation occurred. The aggradation caused the slope to steepen, the depth of flow to de- crease, and the sediment-transport rate to increase. As the sediment-transport rate increased, the sediment input at the flume inlet increased, and the cycle of adjustment of the water-surface slope and depth of flow in response to the increasing sediment-transport rate continued. The result was a flume system of chang- ing hydraulic and sediment-transport conditions, and it was impossible to achieve equilibrium conditions as long as sediment was being added to the system. The addition of sediment was terminated after 4.25 hours of operation. During the period of adding sedi- ment, the water-surface slope increased 36 percent and the sediment-transport rate increased 89 percent, whereas the depth of flow decreased 8.0 percent with respect to the equilibrium values of these variables that existed at the start of run 17b. Equilibrium conditions were assumed established about 1.7 hours after the ces- D20 40 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS Equilibrium -———————-——'I ‘39.5| 30—- 20—- SECOND PER METER I l I __ 29.1 SEDIMENT-TRANSPORT RATE IN GRAMS PER 23-5 I I I 23.0 —- — 22.5 — 22.0 1 ' — 21.5 ~ — 21.0 I I WATER DISCHARGE. IN LITERS PER SECOND PER M ETER N N N Oi I 5.00 I 4.00 L I I O ‘O 0—046—2 DEPTH OF FLOW. IN CENTIMETERS 6.00 5.50 — — 5.00 — — 4.50 — O — rRecircuIational _ I I I WATER SURFACE SLOPEX 103 O O 4.00 F ‘I‘——-Recirculation-———-——. | | I 3510200 1300 1500 6—20-66 1700 1800 0800 1000 1 200 1400 1 600 6-21—66 TIME, IN HOURS FIGURE 12.—Response of the recirculation system to a decrease in sand-bed slope, run 15. sation of the addition of the sediment; however, the data indicated that equilibrium was established almost immediately after the addition of sediment was stopped. The variation with time of the several vari- ables in run 17b is shown graphically in figure 14. The mean bed-surface elevation increased 0.81 cm during the run. It is interesting to speculate on the final condition of the system if the addition of the sediment had been continued. The final condition probably would have been one of large sediment-transport rate with flow in the upper regime; the final condition would have de- pended on the water discharge. Ram 18 (increase slope, recirculation system).——In run 18 the flume slope was increased about 26 percent (from 0.00373 to 0.0047 2 m per m) by raising the upper end of the flume. The change for run 18 was the con- verse of the change for run 15, and, as in run 15, equi- librium conditions were established immediately. The increase in flume slope caused a 21 percent increase in water-surface slope, a 38 percent increase in sediment- transport rate, and a 7 percent decrease in depth of flow with respect to the equilibrium values of these variables that existed before the increase in flume slope. The data from run 18 are shown in figure 15. Run 19 (decrease sedimnt-tramport rate, recircula- tion system) .—The change for run 19 was the converse RESPONSE OF CHANNEL TO CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES 40 30 20 10 0 D21 I I I I _ F— Equilibrium —'( — 23.5 23.0 22.5 22.0 IN LITERS SEDIMENT-TRANSPORT WATER DISCHARGE. 21.5 55° I I I I 5.00 — O 4.50 DEPTH 0F FLOW, PER SECOND RATE. IN GRAMS PER IN CENTIMETERS PER METER SECOND PER METER 4.00 55° . I I I 5.00 — o — 4.50 —— o 69 o — 4.00 — 3.50 —- _ WATER-SU RFACE SLOPEX 103 O 3.00 — I I—I‘Fee‘i—W o 000 00000 0 O O O O Q—O-O—o—-—O—O-D—O 3.67 ' Feed | l I _.JL 25 ' 8700 0800 1000 1200 6-22—66 1400 1500 0800 1200 1400 1600 6—27—66 1000 1800 TIME, IN HOURS FIGURE 13.—Response of the feed system to a decrease in sediment-feed rate, run 16. of the change for run 17b. A proportional sediment trap was placed in the tailbox of the flume so that about one-third of the sediment transported from the end of the flume was trapped and removed from the system. Thus the amount of sediment returned to the upstream end of the fiume was decreased. Degradation occurred because the sediment input to the flume was less than the sediment-transport capacity of the flume for the given conditions. The degradation caused a decreasing slope, an increasing depth of flow, and a reduced amount of sediment transported. Because about one- third of the sediment transported was removed continu- ously from the flume system, the input to the flume was reduced continuously also, and the cycle of change and adjustment in the variables was repeated. As in run 17b, equilibrium conditions could not be established. However, when the extraction of sediment was discon- tinued after 3.7 hours of operation, equilibrium was established almost immediately. The variation with time of the several variables in run 19 is shown graph- ically in figure 16. The data shown for the sediment- transport rate during nonequilibrium conditions of the system are the rates of extracting sediment, whereas the data shown for the equilibrium conditions of the sys- tem are the total sediment-transport rates. During the period of extracting sediment, the water-surface slope decreased 22 percent, the sediment-transport rate de- creased 39 percent, and the depth of flow increased 7.9 percent with respect to the equilibrium values of these variables that existed at the time the extraction of sediment was begun. The mean sand-bed elevation de- creased 0.79 cm during run 19. It is interesting to speculate on the final condition of the system if the extraction of sediment had been con- tinued. Rathbun and Guy (1967) found that the mean velocity for cessation of motion on a ripple bed for the sediment used in this study was about 10.4 cm per sec. For the water discharge used in run 19 (22.3 1 per sec D22 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS °° I I I I I I I En"! 1-————Equilibrium———-—-| OLULLJ _ _ all- (00)” 222 figs ’Twn. *— ZZD UJ‘Z 258 D(Lu goal; 5:: " 3 5 mg: 2*5 I I I I I I I 5:: U, E 23.0— —4 r — '- mmI— 225— — —— — I 0800 1000 1200 0900 1100 1300 0900 1100 1300 1500 1200 1400 1600 7-25—66 7—26-66 7-29-66 8—3—66 TIME, IN HOURS FIGURE 17 .—Response of the feed system to an increase in the tail-water depth, run 20. cause a uniform sediment was used. When 03 and Q are constant, the proportionality of Lane (1955) predicts that the sediment-transport rate and the water-surface slope are directly related. A comparison of the direct proportionality of Q3 and S with the results of runs 12—23 is: 1. In run 14b, S increased when Q, was increased by increasing the sediment-feed rate; and in run 16, 8 decreased when Q, was decreased by decreasing the sediment-feed rate. 2. In runs 121), 13, 20, and 23, Q, was constant, and the flame slope or tail-water depth was changed to cause nonequilibrium hydraulic and sediment- transport conditions. S initially deviated from its equilibrium value but returned after the reestab- lishment of equilibrium conditions to its equilib- rium value that existed prior to the change. 3. In runs 15 and 22, Q, was decreased by changes to the sand-bed slope and tail-water depth, and S de- creased in both runs. In runs 18 and 21, Q8 was increased by changes to the sand-bed slope, and tail-waiter depth and 8 increased in both runs. 4. In run 17b, Q,, and 6' increased continuously as sedi- ment was added to the recirculation system. In run 19, Q, and 6' decreased continuously as sedi— ment was extracted from the recirculation system. In the operation of both feed and recirculation sys- tems, the depth of flow and the water-surface slope can be changed by adjustments of the flume slope, or the tailgate at the downstream end of the flume, or of both. These adjustments, however, do not exclude changes in the depth of flow and the water-surface slope resulting from changing hydraulic and sediment- transport conditions in the flume. Runs 12—23 showed that changes in the depth of flow and the water-surface slope can occur with no adjustment to the tailgate (runs 14b, 15, 16, 17b, 18, 19) and with no adjustment to the tailgate or the flume slope (runs 14b, 16, 17b, 19). Depth adjustments can occur only in flume systems that operate with a constant-head tailbox. If the flume system is closed with respect to the quantity of water, then depth adjustments cannot occur. The experimental data were used to determine if, as suggested by Maddock (1968), the relation between D26 SEDIMIENT TRANSPORT IN ALLUVIAL CHANNELS I———————Equilibrium 60 l— 50 — mm: Lu (gt/)2 40 — 2 gain: fig: 30 :281 y. . age 2&8 2° ‘ 8““ menu: 10 _ _ 0 Lu UK mun: 2 Wm 03000 T . 0m w ' : 00 oo : _ o _ m D _22. __ _ _ 53525 22.0 on 0 0 O ‘0 “:82 21.5 — — — — — — ur'g 21.0 I I I I I-z <_ 3 leJ 0—5 00 O o o 0 0 4% I _ __ :TO— _ - 35 4.00 ‘03—0—5'0 0 E2; 00 O o DEE 350 | | l I O . 7-50 I I I 700 — ° — — o — .3 000 o o o O _ 0 C _ _ 6.64 <«: 6.50 — U 0 —~ — o — — oo — 'ES 0 3x «35 6.00 — — —- — — —— 50 I-d _ O _ _ _ _ g 5.50 O _ 5.00 — — — — — — —4'84 Recirculationg—l _ :_Recur _ l——Recirculation—-l 450 I I I I . 1200 1400 1600 1700 1300 1500 0700 0800 1000 1200 8-5-66 8-10-66 8-15-66 TIME, IN HOURS FIGURE. 18.—Response of the recirculation system to a decrease in the tail-water depth, run 21. mean velocity V, and the unit water discharge-slope product, 98', for the feed system significantly differs from this relation for the recirculation system. Recall equations 8 and 9 (p. D5). Because q=VD, the 96' product differs from stream power, yVDS, only by the presence of the constant 'y in the stream power relation. Equations 8 and 9 were put in the general form V=a (98)”. (11) If logarithms are taken, the result is loge V=loge a+b loge (98). (12) Least squares procedures were used in applying the experimental data to equation 12 to determine the values of the constants b and loge a. Six different combinations of the data were used and the‘results are summarized in table 4. The first three entries are the results of using the experimental data from runs 1—11, in which the equilibrium conditions for the feed and recirculation systems were compared. The first entry is for the overall mean values of V and q8 for runs 1—11, in which the mean values of these variables for each part of the run (recirculation, fwd, and recirculation) were weighted in accordance with the number of observations of each variable in each part. For the recirculation rims (entry 2), the mean values were weighted in proportion to the number of observations made for each of the two recirculation parts of the run. In the last three entries, the mean values of V and 98 for the equilibrium con— ditions obtained in runs 12-23 were included with the RESPONSE OF CHANNEL TO CHANGES IN HYDRAULIC AND SEDIMENT-TRANSPORT VARIABLES D27 6° l l I l 50 — 53.7 40 — 3O _ 20— RATE, IN GRAMS PER 10— T l I I l———Equi|ibriumfi-’ 29.0 ‘- 0 3.0 I I 2.5 2.0 1.5 —- 22.2 629 o O 0 WATER DISCHARGE, SEDIMENT-TRANSPORT IN LITERS PER NNMNN PI "1 1.0 I I 5.00 I I I 4.50 * do 0 o 4.00 — 4.06 IN CENTIMETERS SECOND PER METER SECOND PER METER DEPTH 0F FLOW, 7.00 I I 6.00 — 0 5.50— o 69 o 5.00 — GD WATER-8U RFACE SLOPE X 10 3 4.50 _ Recirculation r—IRecirculaltion———l—>I I‘— Recirculation—1 4.00 I I I 0900 l. 100 1300 1500 8— 15-66 TIM 1700 0800 1000 1 200 1400 1 600 8— 16—66 E, IN HOURS FIGURE Ill—Response of the recirculation system to an increase in the tail-water depth, run 22. mean values from runs 1—11. For the “overall” entry (entry 4), the mean equilibrium values for each of the runs 1—23 were used, regardless of whether the method of operation was feed or recirculation. Only data for feed-system runs were used in entry 6 and only data for recirculation-system runs were used in entry 5. TABLE 4.—-Summary of the least squares values of loge a and b Entry Runs Included log. a b 1 ______ Overall, 1—11 1 __________ 1. 852d:0. 171 0. 43:l:0. 04 2 ______ Recirculation, 1—11 ______ 1. 84110. 154 . 44:1:0. 03 3 ______ Feed, 1—11 ______________ 1. 8603: 0. 210 . 43:|:0. 05 4 ______ Overall, 1—23 1 __________ 1. 9422!:0. 145 . 42:|:0. 03 5 ______ Recirculation, 1—23- _ _ -_ _ . 1. 885i 0. 120 . 43:1: 0. 03 6 ______ Feed, 1—23 ______________ 1. 915:1:0. 192 . 42:|:0. 04 I Overall implies mean values based on all runs, regardless of whether the system of operation was teed or recirculation. Runs 1—11 and 12—23 were considered separately as well as together because runs 12—23 covered only a part of the range of hydraulic and sediment—transport condi- tions covered by runs 1—11. The possibility existed that the combination of all the experimental data might be biased toward the range of conditions covered by runs 12—23 because of the large number of runs in this range. The results presented in table 4, however, show no sig- nificant differences between the V versus 98 relation for runs 1—11 and for runs 12—23. The limits shown in table 4 for the b and logea values are based on the 95 percent confidence level of signifi- cance. The 6 or slope values range from 0.42 to 0.44, and no significant difi'erences exist among the six values of b. The 6 values are not significantly different from 0.40, except the value for entry 2 (runs 1—11). This 6 value is D28 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 60 l a 75.2 I | | | | Ecru: — " — BEE k—Equilibrium—H g: s — Egg; .— _ _— I:00. H 220 m-z E58 “ — O : 16.000 — ,- —————--——— 200 Z / O o . // O z 0 . 0.4 g 8 0. 12,000 — // . 0 L 150 8 1 ° 0 O 5 J o O a in 8000 I— . —I 100 E 1 é /o .s s ,s o o .N l— _ 50 Z 4000 If .N 8 u) 0 Lu P .08 . g o I I I | I I l I I I I .s 0 3 0 4 8 12 16 20 24 28 32 36 40 44 48 52 u. TIME, IN HOURS grains at station 3 resulting from addition at station 1. Size range is 0.15—0.18 m. 7 Lu Lu I I I I I I 039. Q Q 20 7, a, I I I I I _ — I / F E EXPLANATION EXPLANATION / g 318 — X — / Z (I) Station 2rat '23 to 25 hours after _ '_‘0'52 / _ 2 beginning experiment I . J cz) o 16 _ I A — Range of time for sample COIIeCtIOnI 086 Station 3 at 20 to 22 hours after _ and particle diameter, in millimeters ’ __ ‘2 g beginning experiment I E 2 _ O / a: a: 14 Station 3 at 27 to 29 hours after — / 0 (5 x beginning experiment —— —— l— l- .__ // 2 E 12 __ Plot of the function, _ / 8 U RAT|O=1+32 e—4 75 DIAMETER U) (I) —— _ — / — L” 3 Plot of the function. a: / o O 10 —- RATIO=1+11 e 75.65 DIAMETER _ / / “- “- 8 __ / O O — x — s s 710.52 I: I: 6 — < < / E E A T // T E E 4 \ £0.38 g g 0 \8 — ”.630 — 8 g \\ A H025 2 — 2 \\ “6 18 . i ‘ I I I l l I I I | g A ‘——~—— 0 100 200 300 400 500 600 700 800 900 1000 L; o l I | I | | I I I TIME. IN MINUTES, FOR FIRST ARRIVAL 810 METERS cc 0 0-1 02 0-3 0‘4 0>5 0.6 0-7 0'8 0.9 1-0 DOWNSTREAM FROM POINT OF SAND INTRODUCTION MEDIAN DIAMETER OF SIZE FRACTIONS, IN MILLIMETERS FIGURE 11.—Re1ation of traveitime to grain size fior fluorescent FIGURE 12.—Latera1 mixing of fluorescent sand as related to sand in Clear Creek. grain size. E10 the point of tracer introduction. The closest cross sec— tion would be intended for study of the coarser sizes and the farthest cross section for the finest sizes. The period of sampling would be approximately the same at all cross sections. ESTIMATION OF SEDIMENT DISCHARGE Uniform mixing of tracer particles and constant sedi- ment discharge are required if an accurate calculation of sediment discharge is to be made using tracer techniques. Also, the concentration of fluorescent particles at the sampling point must reach a constant value. None of these requirements were met perfectly in this study, and the lateral mixing of tracers was poor in the finer grain sizes. Nevertheless, calculations based on available data are enlightening. Although tracer concentrations tended to 'be high on the north side of the stream and low on the south side, an average of the two gave concentrations close to those found for samples collected at the midpoint (figs. 6—10). Therefore, the midpoint concentrations may closely ap- proximate those which would be found with uniform mixing. Because water discharge decreased 11 percent during the first 28 hours of the experiment, it is probable that sand discharge decreased also. The suspended—sediment concentrations mentioned previously suggest this, but the concentration curve of fluorescent particles (fig. 9) for the 0.18—0.25-mm size range indicates in that size range the sand discharge was for the most part constant. - If the sand discharge had decreased gradually during the experiment, the degree of tracer dilution would have been reduced and tracer concentration slowly increased. For purposes of calculation it has been assumed (1) that the tracer concentrations found at the midpoint at station 3 are the same as those that would be found with uniform mixing and (2) that the error due to changing sediment discharge is small compared to other possible errors in the experiment. The remaining requirement, that is, that the concentration of tracer particles at the sampling point reach a constant value, was apparently achieved for some size fraction and not for others. The apparent “plateau” or constant concentrations are shown by dashed lines in figures 6—10 and are used in calculating the sediment discharge in the various size ranges. The results of such calculations are given in table 2 and also in figure 13 as a cumulative curve. The sediment discharge in each size fractiOn is meas- ured independently in the fluorescent-tracer method, so the fact that a smooth curve results from combining the discharge data for several individual fractions suggests that there is at least internal consistency between the discharge estimates. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS The sediment discharge calculated from depth-inte- grated samples is compared with that estimated by fluo- rescent-tracer measurements in table 2 and figure 13. Although the depth-integrating method measures only suspended load Whereas the fluorescent method measures total load in the tracer size range, a comparison was made between them because no accepted reference method was available for this type of stream. In the finer grain sizes one would expect the depth- integrating and fluorescent methods to agree, but in the coarser sizes which move near the bed, poorer agreement would be expected, and such is the case. TABLE 2.—Comparz'son of sediment discharge in Clear Creek calculated from depth-integrated samples and fluorescent-sand measurements Sediment Discharge (metric tons per day) Size range From depth- From “dilution” (millimeter) integrated . of fluorescent Ratio BIA samples (A) sand (B) 0. 15—0. 18 _____ 1. 9 2. 5 1. 3 . 18- . 25 _____ 7. 9 10. 0 1. 3 .25~.30 _____ 3.5 6.3 18 . 30- . 38 _____ 4. 2 8. 8 2 1 .38—.52 _____ 5.9 13.7 2 3 The use of a flow-through trap to collect stream sand in transport inevitably resulted in a tendency to con- centrate more heavy minerals than light ones. This tendency is most evident in the finest size particles caught in the trap. In one set of samples, minerals heav- 01 O I l l | l l w 0 | I l CUMULATIVE SEDIMENT DISCHARGE, IN METRIC TONS PER DAY 0 0 0.1 0.2 0.3 0.4 0.5 0.6 GRAIN DIAMETER, IN MILLIMETERS FIGURE 13.——Sediment discharge in «relation to grain size as determined by depth-integrated sampling and the fluorescent— tracer method. FLUORESCENT SAND AS A TRACER 0F FLUVIAL SEDIIVIENT ier than bromoform (sp gr=2.9) were found to com- prise 10.2 and 7.7 percent of the 0.15—0.18—mm and 0.18— 0.25—mm size ranges, respectively. If it is assumed that no more than about 1 percent heavy minerals would be present in an unsorted sample of any size fraction of stream sand in Clear Creek, based on antestimate by Pettijohn (1957, p. 129) of heavy minerals in rocks, the revised estimate of sediment discharge from fluores- cent-sand measurements would be 2.2 metric tons (2.4 tons) per day for the 0.15—0.18-mm size range and 9.4 metric tons (10.3 tons) per day for the 0.18—0.25—mm size range. This brings the estimates of sediment dis-I charge for the 0.15—0.18—mm size fraction by the two methods to within about 15 percent of each other. The possible errors in the two methods of measuring sedi- ment discharge as used here may be greater than 15 percent; therefore, one method can be said to provide an approximate check on the other for this particular size range. EXPERIMENT WITH BATCH ADDITION The method of continuous addition used in this ex— periment requires that sediment discharge remain con- stant long enough for the fluorescent material to mix thoroughly in the stream cr0$ section and also attain a constant concentration at some downstream sampling point. If the stream is narrow and turbulent enough for rapid lateral mixing (vertical mixing is assumed to be very rapid), these requirements may be met in a reason- alble time and distance. However, in many streams these requirements probably will not be met, and constant E11 concentrations at the sampling site will not be achieved before the sediment discharge changes significantly. One possible way to reduce the effects of varying sedi- ment discharge is to add one color of fluorescent sand (color A) at a constant known rate and also a series of different colors (colors B, C, D, E, etc.) of the same size in batches at perhaps 6—12-hour intervals. When batch material of color B is dumped into the stream, it will label the sand passing the introduction point at time T and, when half of that batch (or perhaps the peak concentration, as a rough approximation) has passed the sampling point downstream, the dilution fac- tor of color A would then yield an estimate of the sedi- ment discharge at time T at the point of tracer intro- duction (assuming thorough lateral mixing). A series of such time points should permit the calculation of sedi— ment discharge at intermediate times by interpolation using concentrations of color A. If the amount of mate- rial in the batches were known and the concentration of color A remained constant for a suitable length of time, the sediment discharge could also be calculated from the area under the time-versus-concentration curve for colors B, C. D, etc. This multiple-color technique would be most applicable under circumstances where longi- tudinal dispersion was minimal. To determine the character of the time-concentration curve resulting from batch addition to Clear Creek, an unmeasured amount of blue fluorescent sand of nomi- nal diameter 0.30—0.52 m was introduced 4 hours and 16 hours after continuous introduction of the red, green, and yellow sand was started. Figure 14 shows the re- sulting concentration-versus-time curves. 60° I I I I I | W‘ \ \ \\ o/ \o / \ \ 500 - 400 — 300 — 200 — FLUORESCENT GRAINS IN 100 GRAMS 100 — | l l | l l EX P LA N AT I O N Size range, in millimeters I 038-052 0 0.30-0.38 0 025—030, ~ TIME. IN HOURS FIGURE 14.—Variation in concentration of 0.25 to 0.52-mm blue fluorescent sand at station 3 afiter batch addition at station 1. E12 Although the size fraction used was supposed to have had grains less than 0.30 mm removed, some still re- mained owing to incomplete sieving. Thus, the 0.25— 0.30-mm material undoubtedly had a size distribution skewed far toward 0.30 mm with a median diameter of perhaps 0.29 mm. Table 3 summarizes the relation of grain size to peak- ing time after introduction. The data suggest that there may be an inverse correlation between the square of grain diameter and the time for the peak concentration to move downstream to the sampling point. TABLE 3.—Time to reach peak concentration of blue grains at station 3 as related to grain'diameter Median Median Time for concentration Size traction diameter diameter curve to peak (min) Ratio (mm) (mm) squared B/C (1111112) Range Average (A) (B) (C) 0.25-0.30- _ _ _ 0. 29 0. 084 150—160 155 0. 54 .30— .38- _ _ _ . 34 . 116 240—270 255 . 46 .38— .52- _ __ . 45 . 202 330—480 405 . 50 ESTIMATION OF SEDIMENT IN ACTIVE STORAGE WITHIN A BEACH The shape of the concentration-versus-time curve (fig. 9, for example) can be helpful in estimating the amount of sediment in active storage within the study reach. (Active storage refers to the sediment within the study reach which is moving on the bed or in suspen- sion.) When a constant concentration has been achieved at the sampling station for a particular size fraction, one can assume that, for the size fraction, the concentra- tion of fluorescent sand in sediment moving on the bed is the same as that in suspension. If this is so, and one extends a horizontal line from the constant concentra- tion back to zero time, an area the shape of an inverted trapezoid or distorted triangle will be enclosed to the left of the rising concentration curve. This area is a measure of the amount of fluorescent sand that went into active storage in the study reach before a plateau concentra- tion was achieved. Knowing the amount of fluorescent sand in active storage and its concentration there, one can compute the amount of nonfluorescent sand in active storage. For a gravel-bed stream it is apparent that a lot of sand cannot be in active storage unless the stream is very turbulent and suspended—sand concentrations are very high. Clear Creek is moderately turbulent but has a low concentration of suspended sand; therefore, one would expect relatively small amounts of sand in active storage there. The calculated sand in active storage in a '1/2-mile reach of Clear Creek is given in table 4. The amounts are rather small. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS In a sand-bed stream, on the other hand, the quantity of sand moving in dunes on the bed may be very large, and this technique should be helpful in estimating the amount of sand in active storage in such streams. If one can calculate the quantity of sand in active storage in a reach and knows the area of the reach, then the average depth of moving sand can be estimated (assuming that all the sand is moving on the bed). The average thickness for various grain sizes was found to be less than 1 grain diameter in Clear Creek (table 4). In other words, if all the moving sand grains were rolling along the bed, only a fraction of the bed would be covered with sand. In fact, there was relatively little sand on the bed of Clear Creek; material on the bed was composed mainly of particles larger than sand. One assumption implicit in the above discussion is that no significant amount of tracer material is lost by “permanen ” deposition on the bed. If this is not so, the estimate of sediment in active storage will be too high. In any case, this estimate of sediment in active storage will be only a gross approximation unless (1) the length of reach required for complete lateral dispersion is small compared with the length of reach above the sampling point in which lateral dispersion is complete, or (2) the sediment discharge per unit width is virtually uniform across the stream and an average tracer concentration across the sampling section is used. The fact that complete lateral mixing did not occur within the study reach on Clear Creek means that the calculated figures are somewhat in error. TABLE 4.——Sediment in active storage in Clear Creek Sand in active storage Maximum depth oi ‘ and movin on the Size range (millimeters) (metric tons) sbed (millingieters) 0.15—0.18 ________________ 0. 3 0. 01 .18- .25 ________________ 1 4 . 07 .25— .30 ________________ 1 5 . 07 .30— .38 ________________ 2 5 . 11 .38— .52 ________________ 4 6 .21 OTHER POSSIBLE USES FOR FLUORESCENT SOLIDS IN STREAM STUDIES The effects of specific gravity on sediment transport can be evaluated by coating particles of different specific gravities with various colored paints and determining their relative speed of transport. Of course, the sieve size and shape would have to be held as nearly constant as possible for the particles of various specific gravities. An attempt to do this was made in the present study, but the heavy particles used were magnetic grains re- moved by electromagnet from Clear Creek sand, and they ranged from a few percent to 100 percent magnetite or high-iron ilmenite. The remainder of these multi- FLUORESCENT SAND AS A TRACER 0F FLUVIAL SEDIMENT granular magnetic particles were commonly composed of quartz or feldspar, thus giving a wide range of actual specific gravities. The results, therefore, were quite un- satisfactory. Shape effects can also be evaluated using an approach similar to that proposed for determining the effects of specific gravity. Yet another potential use of fluorescent sand is that of determining the depth of scour in a stream bed dur- ing a rise. If fluorescent sand equal in size to the median diameter of the bed material were added con-tinously at a point upstream from the area of interest, the sedi- ment in transit would be labeled with fluorescent par- ticles. As discharge decreased the labeled sediment would be deposited on the bed. After the flow had sub- sided, one could t-ake cores of the bed sediment and determine the maximum depth of scour by examining the cores under ultraviolet light. In addition, if one added a series of colors in sequence during the time of decreasing discharge, different colored layers of sand would result showing the approximate time dur- ing whic- “permanent” deposition on the bed occurred. CONCLUSIONS An experiment conducted in Clear Creek at Golden, 0010., showed that the maximum speed of transport of fluorescent sand-sized particles added steadily to the stream correlated inversely with the square of the grain diameter under conditions where sand was being trans- ported by turbulent water above a gravel bed.. There is a suggestion that the modal speed of transport of sand added to the stream in batches may show a similar rela- tion to grain size. Lateral mixing improved with increas- ing grain size. Although complete lateral mixing of fluorescent particles did not occur, an estimate of sediment discharge by the fluorescent-tracer method for medium to fine sand showed reasonable agreement with sediment discharge calculated from depth-integrated samples after the differences inherent in the two methods were taken into consideration. The results of this study suggest that much more effort could be profit-ably devoted to the use of fluorescent tracers in studies of sediment movement in the fluvial environment. REFERENCES CITED Aybulatov, N., Boldyrev, V., and Griesseier, H., 1961, Das studium der sedimentbewegung in flussen und meeren mit hilfe von lu‘mineszierenden farbstofien und radioactiven isotopen: Petermann’s Geog. Mitt. 1. 105, no. 3, p. 177—186; no. 4, p. 254—263. E13 Bruun, P., 1965, Quantitative tracing of littoral drift, in Fed. Inter-Agency Sedimentation Conf., 1963, U.S. Dept. Agr. Misc. Pub. 970, p. 756—765. Clayton, C. G., and Smith, D. B., 1963, A comparison of radio- isotope methods for river flow measurements, in Radio- isotopes in Hydrology: Vienna, Internat. Atomic Energy Agency, p. 1-24. Cummins, R. S., J r., and Ingram, L. F., 1965, Use of radioisotopes in sediment transport studies, in Fed. Inter-Agency Sedi- mentation Conf., 1963: U.S. Dept. Agriculture Misc. Pub. 970, p. 578—592. DeVries, M., 1966, Applications of luminophores in sand trans- port studies: Delft Hydraulic Lab., Delft, The Netherlands. Pub. 39. Glazov, N. V., and Glazov, A. N., 1959, New Instruments and methods of engineering geology: New York, Consultants Bureau, 91 p. Hubbell, D. W., and Sayre, W. W., 1964, Sand transport studies with radioactive tracers: Jour. Hydraulics Div. Am. Soc. Civil Engineers, v. 90, no. HY3, p. 39—68. Ingle, J. C., J r., 1966, The movement of beach sand: New York, Elsevier Pub. 00., 221 p. Kidson, C., and Carr, A. P., 1962, Marking beach materials for tracing experiments: Jour. Hydraulics Div. Am. Soc. Civil Engineers, v. 88, N0. HY4, pt. 1, p. 43—60. Krone, R. B., Einstein H. A., Kaufman, W. J., and Orlob, G. T., 1960, Methods for tracing estuarial sediment trans- port processes: California Hydraul. Eng. Lab. and Sanita- tion Eng. Research Lab., 57 p. Lean, G. H., and Crickmore, M. J., 1963, Methods for measur- ing sand transport using radioactive tracers, in Radio- isotopes in Hydrology: Vienna, Internat Atomic Energy Agency, p. 111—131. 1966, Dilution methods of measuring transport of sand from a point source: J our. Geophys. Research, v. 71, No. 24, p. 5843—5855. Pettijohn, F. J., 1957, Sedimentary Rocks: New York, Harper Bros, 718 p. Russell, R. C. H., 1961, The use of fluorescent tracers for the measurement of littoral drift: Coastal Eng. Conf., 7th, The Hague, Netherlands, August 1960, Proc., p. 418—444. Teleki, P. G., 1965, A summary of the production and scanning of fluorescent tracers, in Fed. Inter-Agency Sedimentation Conf. 1963: U.S. Dept. Agriculture Misc. Pub. 970, p. 765— 768. 1966, Flourescent sand tracers: Jour. ‘Sed. Petrology, v. 36, no. 2, p. 468-485. U.S. Inter-Agency Committee on Water Resources, 1952, The design of improved types of suspended sediment samplers: Washington Govt. Printing Oflice, Rept. 6. 1963, Determination of fluvial sediment discharge: .Washington Govt. Printing Oflice, Rept 14. ‘ Yasso, W. E., 1962, Fluorescent coatings on coarse sediments: An integrated system: U.S. Navy, Office of Naval Research, Geography Br., Project NR 388—057, Tech. Rept. 1, 29 7p. (Columbia Univ. Dept. Geology). 1965, Fluorescent tracer particle determination of ,the size velocity relation for foreshore sediment transport, Sandy Hook, New Jersey: Jour. Sed. Petrology, v. 35, no. 4, p. 989-993. Zenkovitch, V. P., 1958, Emploi des luminophores pour l’étude du mouvement des alluvions sablonneuses: Inf. Comité Cent. Océanographie Etude des Cotes, Bull. 10, p. 243—253. Q 75 7 DAY E 3%: v.562-F Statistical Properties of Dune Profiles GEOLOGICAL SURVEYVP’ROFESSIONAL PAPER 562—F Docuwmsfisméwm” [APR ,1 18/1 lelmn - - ,~»--r;~_~zw r35 muwmm 03.3.0- Statistical Properties of Dune Profiles By CARL F. NORDIN, JR. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS GEOLOGICAL SURVEY PROFESSIONAL PAPER 562—F UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1971 UNITED STATES DEPARTMENT OF THE INTERIOR GEOLOGICAL SURVEY William T. Pecora, Director Library of Congress catalog-card No. 77-609557 For sale by the Superintendent of Documents, US. Government Printing Office Washington, DC. 20402 — Price 50 cents (paper cover) CONTENTS Page Page Abstract .......................................................................... F1 Data and analysis—Continued Introduction .............................................. l Stationarity and equilibrium flow ............................. F18 Background ............ 1 The Markov model for dune profiles ......................... 20 Purpose and scope ...................................................... 3 Dimensionless spectra ........................................... 2] Acknowledgments ....................................................... 3 Other properties of the spectra ................................ 27 Some properties of a Gaussian process ................................. 4 Cross correlation and cross-spectral analysis... 32 Zero and h-level crossings ............................................ 4 Prediction ................................................... 35 Wave heights and amplitudes ........................................ 5 Summary and conclusions. 37 Theory of time series analysis ....................................... 6 Discussion of results .................................................... 37 Data and analysis .............................................................. 3 Conclusions ............................................................... 38 Basic data ................................................................. 8 Recommendations for future studies ............................... 39 Zero and h-level crossing analyses.... 10 References ...................................................................... 39 Distribution 0f wave heights and amplitudes .................... 15 Planning of data requirements ............................................. 4-0 Spectral analysis ......................................................... 13 ILLUSTRATIONS Page FIGURE 1. Sketch of idealized dune shape ........................................................................................................................... Fl 2. Definition sketch of bed profile ........................................................................................................................... 2 3—37. Graphs showing— 3. Ratio of the expected number of h-level crossings to the expected number of zero crossings, E{Nh}/E{Nu}. as a function of h ................................................................................................................................. 5 4. Cumulative probability distribution functions for dimensionless maxima, 7], as a function of 8 ........................... 6 5. Distributions of bed elevations .......................................................................................................... 10 6. Comparison of the expected length or duration between zero crossings for a Gaussian process, E{lo}, with the observed values, lo ......................................................................................................................... 11 7 Observed values of Nn/No as a function of h ................................................................................ 12 8. Average values of Nh/Na as a function of h ............................................................ 12 9 Observed-values of the ratio lg/l; plotted against h ................................................ 12 10. Observed distributions of 1,7 for run 1 ...................................................... 13 11. Observed distributions of I; for runs 1, 2, and 3 ........................................................................................ 14 12. Observed values of the coefficient of variation, Cr. for the distributions of 1,“,( plotted as functions of h .................. 14 13. Comparison of observed If,“ distributions with the theoretical class frequencies from a gamma distribution ............ 14- 14-. Percent of particles in the bed above the level It ................... 15 15. Distribution of positive and negative a values for run 1 ............................................................................... 16 16. Distribution of positive and negative (1 values for run 2 ............................................................................... 16 17. Distribution of positive and negative (1 values for run 3 ............................................................................... 17 18. Approximate exponential distribution of positive a values for run 55 .............................................................. 17 19. Distribution of wave heights, H, for run 55 ................................................................................................ 17 20. Relation between twice the average maximum ordinate between zero crossings, 2a +, and 1:1 .............................. 18 21. Relation between mean values of the distances between successive zero upcrossings of y and the mean dune length. L ................................................................................................................................................ 18 22. Relation between average of maximum ordinates between zero crossing, 6+. and standard deviation of bed ele- vation, 0-,, ..................................................................................................................................... 18 23. Comparison of means and standard deviations for eight short segments of the record of run 3, Atrisco Lateral and for eight longitudinal profiles during equilibrium flow in the 13-foot Hume, runs 8 through 15 ......................... 19 24. Spectra for indicated flume records ......................................................................................................... 20 25. Relation of Co, C I, and C2 to unit water discharge ...................................................................................... 20 26. Comparison of estimated and observed average distance in feet between zero crossings ...... 21 27. Spectra of the processes, y=y(x) ...................................................................................................... 22 28. Spectra of the processes, y=y(t) ..................................... 23 29. Comparison of ripple and dune spectra, 2-foot flume ................................................................................... 24- Ill IV CONTENTS FIGURE 3-37. Graphs Showing—Continued Page 30. Dimensionless spectra for the process y=y(x) .................................................................................... F25 31. Dimensionless spectra for the process y=y(t) .......................................................................................... 26 32. Relation of maximum value of C'(x) to mean velocity and to E' .................................................................... 27 33. Dimensionless spectrum based on similitude criteria ..................................................... 28 34. Spectra of longitudinal profiles, y= y(x), showing effect of channel size and bed configuration ........................... 29 35. Autocovariance function and spectrum of longitudinal profile, y= y(x), for run 3, Atrisco Lateral ....................... 30 36. Relation between average distance or time between successive zero upcrossings and the mean wavelength or period of spectra from equation 8 ............................................................................................................... 31 37. Relation of wave celerity, C, to wave number, 6, for various wave—number components of a single record, How condi- tions constant, and for average wave numbers from the spectral moments of records obtained under different flow conditions ..................................................................................................................................... 32 38. Cross correlograms for run 8 with runs 9 through 15... 34 39. Graphs showing distance from the origin of the maximum cross correlation as a function of time and change in maximum corre‘ ’ lation with time .................................................................................................. 34 4-0. Graphs showing coherence, 3’2, and gain functions, A, for runs 8 and 9 and for runs 9 and 15 .......................................... 35 4-1. Correlograms and spectra of y=y(x) for run 16, 2 feet left of centerline; for run 17, centerline; and for run 18, 2 feet right of centerline ...................................... 35 4-2. Cross correlograms ........................................................................................................................................... 36 43. Coherence diagrams .......................................................................................................................................... 36 44-. Graphs showing relation of standard deviation of bed profiles, (Ty, to mean flow depth, D, and relation of standard deviation of bed profiles, (Ty, to unit water discharge, Q ............................................................................................................ 37 TABLES Page TABLE 1. Summary of basic data ........................................................................ F9 2 Statistical properties of raw data .............................................................................................................................. 11 3 Miscellaneous properties from the zero-crossing and spectral analysis ............................................................................. 16 4- Summary of flow characteristics for dimensionless spectra . 27 5. Comparison of wave celerities .................................................................................................................................. 31 6 Summary of wave properties ..................................................................... 33 7 Average values of observed variables ........................................................................................................................ 37 SYMBOLS Symbol Definition Units Symbol Definition Units A (w) ...... Gain function ....................................................... 0 . Acceleration due to gravity ........................... Ft per see2 a ............ Dune amplitude, the maximum ordinate of y between A fixed leved of the bed, measured in units of standard zero crossings ................................................... 0 deviation of y from the mean bed level... 0 c ............ Wave celerity ..................................................... Fpm H ........... Dune or wave height, from crest to trough .............. Ft 0(a)) ...... Cospectrum ......................................................... 0 H(cu) ...... Frequency response function ................................... 0 D ........... Mean flow depth... .. Ft 1,, .......... Duration or length of the upward excursion of the E ........... Expected value ..................................................... 0 process y above the fixed level It ........................... or ft F ........... Froude number ..................................................... 0 L ........... Dune length, from trough to trough... Ft . . Frequency number ......................... Cycles per unit time In" .......... The n‘" moment of the spectrum .............................. 0 f ........... Dimensionless frequency ........................................ 0 Number of zero crossings ....................................... 0 0,“,(w) ..... Spectral density function ..... . (Cycles per unit time)" . Number of h-level crossings .................................... 0 Gyz(w) ..... Cross spectrum ........................ (Cycles per unit time)‘1 Probability distribution function ............................... 0 C(x) ........ Spectral density function for Proability density function ......... . 0 the process y=y(x) ........... (Cycles per unit distance)“ Water discharge per foot of width ............................ Cfs C(t) ......... Spectral density function for Quadrature spectrum ............................................. 0 the process y=y(t) ................ (Cycles per unit time)’1 3.... A time or distance lag .................................... Min or ft C’ .......... Dimensionless spectra ........................................ 0 S ............ Water-surface slope ............................................... 0 CONTENTS V Definition Units . Time.......... .. Min Wave period ........................................................ Min V ........... Mean flow velocity ................................................ Fps x ............ Distance along channel in flow direction .................... Ft Bed elevation, measured from y=0 .......................... Ft . Height of local maximum of y(t).... .. Ft Coherence function ............................................... 0 A parameter ........................................................ 0 . Wave number ......................................... Cycles per ft ........... Dimensionless wave number 0 Symbol Definition Units 1;... . A dimensionless wave height ................................... 0 0(w) ....... Phase angle ......................................................... 0 p. ........... Mean number of upcrossings per unit time ............ (Min)—l p,,,,(s) ..... Autocorrelation function ......................................... 0 pyz(s) ..... Cross-correlation function ....................................... 0 0"]; .......... Variance of the process y ........ . Sq ft (15,”,(3) ..... Covariance function .............................................. 0 (bugs) ...... Cross-covariance function ....................................... 0 w ........... Angular frequency, w=277f. ........... Radians per unit time SEDIMENT TRANSPORT IN ALLUVIAL GHANNELS STATISTICAL PROPERTIES OF DUNE PROFILES BY CARL F. NORDIN, JR. ABSTRACT Properties of sand waves formed by subcritical unidirectional water currents are investigated by statistical analyses of records of streambed profiles. Records of bed elevation y as a function of distance x along the channel, y=y(x), and time records at a fixed point of the channel, y=y(t), were collected in three laboratory flumes that were 8 inches, 2 feet, and 8 feet wide and in a straight alluvial channel that was 55 feet wide. All bed material was fine sand. The continuous analog records were converted to discrete data points and were analyzed by digital computer. The analyses show that both types of records, y(x) and y(t), can be approximately represented as stationary Gaussian processes. When the data are standardized and the lengths or distances are expressed as ratios of the mean duration between zero crossings of y, the statistical properties of all the flume data are similar, with no distinguishing char- acteristics that can be attributed to size of flume or to whether the bed forms were ripples or dunes. The field data, however, reflect the in- fluence of large alternate bars that were not present in the flumes. The Gaussian assumption, together with the spectral properties of the records as expressed by a dimensionless parameter, 8, permits predict- ing the distributions of maximum and minimum values of y between successive zeros of y. These distributions represent the probability distributions of the depth of local scour and fill due to the formation and migration of sand waves, and the parameters that specify the distribu- tions relate approximately to flow velocity and depth. Observed values of the number of zero and h-level crossings, the mean duration between zero crossings, and the mean duration of up- ward excursions of the process y(t) above the fixed level h compared reasonably ‘well with theoretical values for the Gaussian model. The distribution of the duration of upward excursions is the conditional prob- ability distribution of the rest period of a particle, given that it is de- posited on the downstream face of a ripple or dune at the level h. Observed distributions of these durations can be approximated by a gamma distribution with parameters that relate to h, where h is meas- ured in units of standard deviation from the mean bed level. These distributions and other probability distributions that enter into stochastic models of sediment transport can be determined either from the theo- retical model or empirically from the observed data. The results of the study show that, even though the bed elevation deviates somewhat from the postulated normal distribution, reasonable estimates of many properties of the bed profiles can be derived from fairly simple statistical models. INTRODUCTION BACKGROUND A distinguishing characteristic of sand waves formed by unidirectional subcritical water currents is their tendency to form “en echelon” with gently sloping up- stream faces and more steeply sloping downstream faces that meet the horizontal at approximately the natural repose angle of the sand. These features migrate slowly in the mean flow direction as material is eroded from their upstream faces and deposited on their downstream faces. Generally, these features are described as simple tri- angular forms, in profile, somewhat as sketched in figure 1, with a mean length from crest to crest or trough to FIGURE 1. —Idealized dune shape. trough, I2, a mean height from crest to trough, 1:1, and a constant angle of downstream face, B. If the waves are long-crested, or two-dimensional, their geometric prop- erties then are considered completely specified by E, H, B. The ratio of mean length to mean height, Elf—I, called the ripple index, is a measure of the wave steepness. In reality, the simple waveforms of figure I rarely exist. Long-crested sand waves occur apparently only under rather restricted flow conditions which will not 'be con- sidered here. In the general case of flow in a wide channel with a bed of fine sand, the ripples and dunes that form are three-dimensional and highly irregular in size, shape, and spacing. The three-dimensional properties of these features are completely described by a contour map of the bed, and with modern sounding, navigation, and computing equip- ment, large areas of a streambed can be mapped with ease and dispatch. However, the expense involved in obtaining detailed contour maps is generally prohibitive, and more generally, one has available only profiles of the streambed, obtained either by sounding along the channel from a boat or by sounding at some fixed point in the flow and recording changes in the bed elevation as the dunes and other bed features migrate past the sounding point. F1 F2 Although the profiles give only a two-dimensional picture of the streambed, they still provide a great amount of useful information. From longitudinal records, one can determine directly the distributions of lengths and heights associated with a particular ensemble of waveforms. From time records, the average wave period is easily found, which, together with mean wave height, provides a very good estimate of the bed load transport (Simons and others, 1965). The distribution of troughs and crests indi- cates the amount of local scour and fill associated with the migrating sand waves; this information may be im- portant in such practical problems as designing and main- taining navigation channels or estimating the depth to which a structure such as a pipeline or siphon should be buried beneath the mean bed level to minimize the probability of local scour exposing the structure to the current. From a comparison of the properties of different streambed profiles, it may be possible to establish whether or not there are any essential differences, other than scale, between ripples and dunes, and whether or not there are statistical properties of the dune profiles other than scale that can be attributed to the size of the channel. Both questions have important implications in modeling alluvial channel processes. Perhaps the potentially most useful information to be derived from streambed profiles is information that relates to stochastic models of sediment transport. For example, in their two-dimensional stochastic model for the trans- port and dispersion of bed-material sediment particles, Sayre and Conover (1967) require the probability that a sediment particle will be deposited at a given level in the bed and the conditional probability for the length of time a particle will remain buried in the bed (that is, that it will experience a rest period of a certain duration), given that it is deposited at a particular level. These probabilities, together with some other distributions of interest, are easily found from the bed profiles. To be more specific, consider the short segment of profile sketched in figure 2. Assume a straight uniform channel with equilibrium flow conditions, as defined by Simons and Richardson (1966, p. J3). Ify is the bed eleva- h—level crossingsV h /_____H “:4“— A 6+ / \f/ xorf \U p crossings K \ . Zero crossmgs Wavelength or wave period FIGURE 2.-—Definition sketch of bed profile. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS tion, measured from the mean bed level so that 37:0, and x is distance along the channel in the direction of flow, the bed profile then can be represented in the form y=y(x, t), xeX, teT. At any given position x=xo along the channel, one may record the change with time of bed elevation y to produce the record, y=y(l). Similarly, at any given instant of time, t=to, one can sound along the channel to obtain a record of the bed profile, y=y(x). In reality, of course, it is impossible to obtain instantane- ously a longitudinal profile, but practically the time re- quired to obtain a profile is small compared with the time required for a dune to shift appreciably downstream, so that the assumption 3/: y(x) is quite reasonable. For either y=y(x) or y=y(t), the bed elevation y, measured about the mean bed level, is a random variable that depends on a parameter (t or x) defined on an arbi- trary parameter set (T or X, respectively). By definition, then y=y(x, t) is a stochastic process (Cramer, 1964, p. 137). In all cases, 3/ is a continuous function; obviously, there can be no discontinuities in the sand bed of a stream. Intuitively, one also would expect that, if the mean prop- erties of the flow, of the sediment, and of the sediment transport do not change with time or with distance along the channel, then y will represent a stochastic process which meets the requirements both of stationarity and of ergodicity. Consider next, in figure 2, some simple definitions that will be used later. The points where the processes y(x) or y(t) cross the zero axis are zero crossings, and the average distance between successive upcrossings (values of y going from negative to positive) is an average wavelength or wave period, somewhat analogous to I: shown in figure 1. The maximum ordinate between zero crossings, in absolute values, is defined as the amplitude, a, and is roughly comparable to one-half of the wave height of figure 1. Crossings of the level h are defined in a similar manner. Note that the average duration of the upward excursion of the process y(t) above the fixed level II is the average rest period experienced by a particle after it is deposited on the downstream faces of the sand waves at the level It. The probability that a particle will be deposited at the level II also can be determined from the bed profiles for at least some simple postulated depositional patterns. If a particle is equally likely to be deposited at any place on the bed, the distribution is simply the frequency distribution of the 3/ values. If deposition occurs only on the downstream faces of the ripples or dunes, the distribu- tion can be determined from the distribution ofy values where the process y(x) has a negative slope or y(£) has a positive slope. If nothing is known of the previous history of a particle, that is, if it is equally likely to be STATISTICAL PROPERTIES OF DUNE PROFILES found any place in the bed above the lowest point of particle motion, then the probability that it will be found at the level It can be determined approximately as the ratio of the area bounded by the fixed level It and the up- ward excursions of the process y(x) above h to the total area of the bed profile above the minimum 3/ value. Many properties of the processes y(x) and y(t) that are of interest can be determined empirically if suitable records of streambed profiles are available. Usually, though, it is difficult to obtain both types of records. In the laboratory, where flows can be controlled, it is possible to obtain long records of y(t) , but longitudinal profiles of the process y(x) are limited by the effective length of the flume. On the other hand, in field studies, it may be possible to obtain suitable longitudinal profiles, but the sand waves generally move so slowly that satisfactory samples of the process y(t) cannot be obtained under constant flow conditions. It has not been established that the statistical properties of the processes y(x) and y(t) are comparable, although some similarities have been noted (Nordin and Algert, 1966). Thus, it is extremely important to determine in what respects the two types of records are similar and to develop methods of correlating the properties of the two types of records. Ultimately, of course, one will wish to predict something about the streambed profiles, given only information on the characteristics of the flow and the bed sediment. In order to do this, it is necessary first to determine if there are any consistent or recognizable patterns in the proper- ties of interest, and then to attempt to relate these properties to flow and sediment parameters. There is little theoretical or empirical basis upon which to postulate the statistical properties of y(x) or y(t). However, during the course of preliminary studies of the bed profiles, several facts emerged that led to the ap- proach adopted for this investigation. First, it was noted that the y values were distributed about their mean values approximately as normal distributions, which was to be expected as most natural processes that develop under the influence of many random factors exhibit approxi- mate Gaussian distributions. Second, many of the prop- erties of a Gaussian process with known covariance functions, particularly the mean values of duration be- tween zero and h-level crossings and the maximum between zero crossings, are well established from previous work on the statistical properties of random noise (Rice, 1954) and on ocean waves (Longuet-Higgins, 1958, 1962, 1963). Finally, it has been shown that properties of the covariance function near the origin relate to a simple flow parameter, at least for a limited range of flow condi- tions (Nordin and Algert, 1966), so that in considering the prediction problem, the assumption of a known covariance function may be rather simple to satisfy. 405-448 0 - 71 — 2 F3 Therefore, the approach adopted for this study was to compare the observed properties of the bed profiles with the theoretical properties of a Gaussian process of known covariance function. In the following section, the scope and specific objectives of the study are given in more detail. PURPOSE AND SCOPE In broad terms, this study was designed to investigate the statistical properties of streambed profiles. Data were collected in both laboratory and field investigations, and attention was always restricted to equilibrium flow over a bed of fine sand in a straight uniform channel with either ripple or dune bed configuration. The classification of bed configurations as either ripples or dunes is according to Simons and Richardson (1966, p. J5—J7). Details of the hydraulic and sediment data are given in a later section. Specifically, we are interested in the mean values and the distributions of the durations between zero and h-level crossings, of the durations of upward excursions of the process y(t) above the fixed level It, and of the positive and negative maximums of y(x) or y(t) between zero crossings. In addition, it is of interest to consider whether or not the statistical properties of y(x) and y(t) are similar, whether or not there are any significant differ- ences other than scale in the statistical properties of ripple and dune profiles, and whether or not or to what extent the statistical properties of dune profiles depend on the scale of the flow system. V Particular attention is paid to the spectral representa- tions of the process y because the distributions of the amplitudes a for a Gaussian process depend to a large extent on the properties of the spectra (Cartwright and Longuet-Higgins, 1956). Some applications of cross corre- lation and of cross-spectral analysis are examined briefly. As indicated above, the approach used in this study is to compare the observed properties of the bed profiles to the theoretical properties of a Gaussian process of known covariance function. Similarities and differences between the observed and the theoretical processes are noted, and some of the statistical parameters that describe the observed processes are related empirically to proper- ties of the flow. In the following section, a review of the properties of a Gaussian process is given, and some of the mathematical relations for spectral analysis are listed. Then the data is described and the results of the analysis are presented. Finally, the paper discusses the implication of the results, summarizes the conclusions drawn, and lists some recom- mendations for future research along these same lines. ACKNOWLEDGMENTS This study was a part of the US. Geological Survey Water Resources Division research program on me- F4 chanics of flow and sediment transport in alluvial chan- nels. This report was prepared in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Civil Engineering from Colorado State University, Fort Collins, Colo. Dr. V. M. Yevjevich, Colorado State University, assisted in the initial planning of this work, and Mrs. Lois Niemann did the programing and computing. The writer expresses his appreciation for the counsel and encouragement of his major professor, Dr. D. B. Simons, and of his committee members, Dr. E. V. Richardson, Dr. E. J. Plate, Dr. M. M. Siddiqui and Dr. Scott Creely. Special thanks are due to J. K. Culbertson, R. E. Rathbun, and H. P. Guy, US. Geological Survey, and Tsung Yang, Colorado State University, for permitting use of their unpublished data, and to W. W. Sayre and Ignacio Rodriguez-[turbe for many useful suggestions and stimulating discussions. SOME PROPERTIES OF A GAUSSIAN PROCESS ZERO AND h-LEVEL CROSSINGS Suppose that y(t) is a real stationary Gaussian random function of the continuous parameter t, 0 "(0) ]"2 E N =— — - 10 The expected number of h-level crossings is 1 ‘ _¢n(0) 11/2 :— — 2/ — - MM} 77 e h 2[ ¢<0> ] (11) The ratio of the average number of h-level crossings to the average number of zero crossings from equations 10 and 11 is E{Nn}/E{No}=e"'2/2' (12) The expected duration of an upward excursion above the level II is given by Cramer and Leadbetter (I967): E{lf.}=;r‘ pr{y(0) > h} (13) STATISTICAL PROPERTIES OF DUNE PROFILES where p. is the mean number of upcrossings per unit time and pr denotes probability. The mean number of upcross- ings is one-half of the mean number of crossings per unit time, so that, combining equations 10 and 13, the ratio of expected duration of upward excursions above the level it to expected duration of upward excursions above the zero level is Efltl/E{13}=2 perO) > ’1} 6"2/2- (14) An interesting alternative to Rice’s approach is given by Tick and Shaman (1966) for a straight line interpola- tion of an underlying continuous Gaussian process deter- mined by sampling the underlying process at equispaced intervals. Again, it is assumed that y(t) is a stationary Gaussian process with continuous parameter t,—00< t< 00, and with zero mean and covariance function ¢yy(s), and possessing a spectral density function ny(w) de- fined by equation 3. Assume that (MO) =1 and that y(t) is sampled discretely at the time points . . . —2At, —At, 0, At, 2At, . . .. The sampled process also is Gaussian with covariance sequence ¢(nAt), n=0, :1, i2, . . .. Connecting successively the observed ordinates of the sampled sequence with straight line segments yields the interpolation process mentioned above. The expected number of zero crossings in a record of length kAt is found to be E{N0} = k[-;-—% arcsin ¢(At)]. (15) To determine the expected number of h-level crossings, choose two adjacent values, y(nAt) and y({n+1}At), and denote them by Y1 and Y2. The joint distribution of Y] and Y2 is bivariate normal with correlation (MAI). Then, the expected number ofh-level crossing is E{Nh}=k[pr(Y1>h, Y2< h) +pr(Y1 < h, Y2 > h)] =2/.-[pr(Y1 >11, Y2 >—oo) —pr(Yl >h, Y2 >h)]. (16) From equations 15 and 16, the value of the ratio of the expected number of h—level to the expected number of zero crossings is seen to depend on the covariance func- tion at one lag, ¢(At). Values were computed for ¢(At)=0.7 and 0.9, and the curve for ¢(At)=0.7 is plotted in figure 3 along with equation 12 for the con- tinuous process. There is so little difference in the two curves for values of ¢(At) greater than 0.7 that the simpler expression of equation 12 is to be preferred. Although the probability distribution of the 1 values cannot be precisely determined in the general case, F5 _ -2 -1 0 1 2 /7 FIGURE 3. —Ratio of the expected number of h-level crossings to the expected number of zero crossings, E{N,,}/E{No} , as a function of h. Longuet-Higgins (1962, 1963) gives some approximations for upper and lower bounds of p(lo) , with particular at- tention to certain ideal forms of the spectra of y(t), and Cramer and Leadbetter (1967) give equations for the moments of the distribution functions of the duration of upward excursions above the level h. From a practical point of view, the mean values of l; are of most interest, particularly the mean in an interval hz—hl, which is the mean rest period of a particle deposited on the down- stream face of a sand wave between the elevations 111 and kg, and which can be determined easily by integrating equation 13 between appropriate limits. WAVE HEIGHTS AND AMPLITUDES The wave height H was defined as the difference in elevation between a crest (maximum) and the following trough (minimum) in figure 1. The statistical distribution ofH generally is not known, but where y(t) has a narrow spectrum, it has been established that H/2 is distributed according to a Rayleigh distribution (see Cartwright and Longuet-Higgins, 1956): H _(H p(H/2) :W e ‘f/(mofl/z (17) 2 where mg, the variance of y(t), is determined by equation 5 or equation 7. If the process y has unit variance, the equation simplifies to p(H/2) =He“"/2’” (18) F6 and the cumulative probability distribution of H/2 is given by [NH/ZS §)=1—-ee§2. (19) Although the probability distribution ofH is not estab- lished, the statistical distribution of the local maxima of y(t) is known. If y(t) is a strictly stationary process possessing a continuous sample derivative y’(t), a local maximum or crest is said to occur at t=to if y’(t) has a downcrossing of zero at t (Cramer and Leadbetter, 1967, p. 242). Define oz as the difference in height between the crest and the mean level of y(t). Then, for the Gaussian process considered here, the probability distribution of (1 depends only on (m0)‘/2 and on a parameter 8 that represents the relative width of the frequency spectrum, ”107714 — m2 2 52 2 (20) m0m4 where 0 < 8 < 1. For 8—) 0, the spectrum becomes infinitely narrow and the dimensionless maxima, n, tend to a Rayleigh distribu- tion: 12(7)) =ne~77 (21) where 7) > 0, and PM) = 0» where 1; < 0. where 1) is defined by the relation 7): a/(m0)1/2. (22) When 8 approaches its maxima value of l, the distribution of 1) is Gaussian, 1)(n)=W2e—"2/2,—oo°° T —r/2 The cross spectrum is defined as the Fourier transform of the cross-covariance function GM...) =%f ¢yz(s)e‘i‘”sds=c(w) +iq(w) (29) where co represents the angular frequency, 6(a)) is the cospectrum, a measure of the in-phase covariance, and q(w) is the quadrature spectrum, a measure of the out-of- phase covariance. The cospectrum measures the contribu- tions of oscillations at the lag zero between two time series. The quadrature spectrum measures the contribu- tion of the different harmonics t0 the total cross covari- ance between the series when all the harmonics of the series y(t) are delayed by a quarter period but the series z(t) remains unchanged. The real quantity defined as coherence, y§z(w), is a direct measure of the square of the correlation of the amplitudes of frequency w of the processes y(t) and z(t), or 6320») +q§z(w) cameo») ’0‘“) g 1’ 732“") = (30) where Gy(w) and Gz(w) represent the spectra of y(t) and z(t), respectively. Even if the amplitudes are fully correlated, it is possible that the corresponding frequency components will have different phases. The phase lag at each frequency is given by q(w) C(w) 0(a)) =arctan (31) where 0(a)) is called the phase function. F8 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS Another quantity sometimes useful in cross-spectral analysis is the frequency-response function, H (to), calcu- lated from the relation H(w)=%:%=A(w)eiW (32) The quantity A (w) is the gain function or amplitude gain of the system and measures the ratio of the amplitude of the frequency components of the series y(t) and z(t) at each frequency a). The cross covariance measures the dependence be- tween two time series at the given lag, s, and for this study, it was applied to investigate the three—dimensional properties of the sand waves, their mean rate of shifting, and the time or distance required for the waves effectively to lose their identity. The cross-spectral functions, equa- tions 29-32, were used in conjunction with the cross covariance. The above theory is presented for a continuous process with the: parameter t representing time. The frequency f= w/27T is then given in cycles per unit time. The param- eter t is simply a member of an arbitrarily specified parameter set, and it can be any quantity that permits the set of y or z values to be ordered linearly. If time t is replaced by distance x, the frequency f is replaced by wave number 6 and the wave period T: l/f is replaced by wavelength L = 1/6. DATA AND ANALYSIS BASIC DATA Profiles from four different channels were selected for these analyses. Table 1 gives a summary of the records. Three of the channels were recirculating laboratory flumes located at the Research Center Hydraulics Laboratory, Colorado State University, Fort Collins, Colo. The other channel was Atrisco Lateral near Bernalillo, N. Mex., a conveyance channel with a sand bed and with banks stabilized by clay and vegetation. The dimensions of the flumes were: 0.67 foot wide by 30 feet long, 2 feet wide by 60 feet long, and 8 feet wide by 200 feet long. Atrisco Lateral was approximately 55 feet wide, and the profiles were obtained about midway in a straight reach 12,000 feet long. The median diameters of bed material and flow parameters are shown in table 1. Fifty-four records representing six different flow condi- tions were selected for analysis. Runs 1, 2, and 3 were data collected from Atrisco Lateral on three different days, but with similar flows. Records 4 through 19 and 20 through 39 are from the 8-foot flume for two different flow conditions, and like the field data for the first three runs, the bed configuration was dunes. The records for runs 40-43 are for a ripple bed in the 2-foot flume, and runs 44-47 are for identical flow conditions. Runs 48-51 are for a dune-bed flow in the 2-foot flume, and runs 52-54 are for a ripple bed in the 0.67-foot flume, corre- sponding to the experiments reported by Rathbun and Guy (1967). Run 54 subsequently was discarded because of suspected errors in the basic data, so analysis even- tually was carried out on 53 profiles from the six different flow conditions. Profiles of the bed elevations were obtained with the sonic depth sounder described by Karaki, Gray, and Collins (1961) except for the smallest flume where the profiles were traced on a stripchart from the plastic side- walls of the flume. All data were digitized with an analog- to-digital converter at the intervals shown in table 1. The flume data, runs 4 through 54, were standardized with zero mean and unit variance after removing a straight line trend to account for the possibility that the sand bed in the Hume was not parallel to the instrument carriage rails supporting the sonic sounder. At first, the trend was not removed from the Atrisco Lateral data because the sounder was mounted on a boat at a constant depth below the water surface. However, initial analyses showed some long-term trends in the data, so that parts of records from run 2 were selected for trend removal. These shorter records from Atrisco Lateral are shown as runs 55 through 57 in table 1 and are discussed in detail in a later section. Only longitudinal profiles were available for Atrisco Lateral and the smallest flume; for the 2- and 8-foot—wide flumes, time records y=y(t) were available along with the longitudinal profiles. All the computations described in this and subsequent sections were accomplished on the CDC 6400 computer at Colorado State University. For the discrete data used in this study, the values in equations 25 through 32 were approximated by the esti- mates presented by Granger and Hatanaka (1964), using the Blackman and Tukey spectral estimates with a Hanning window (Blackman and Tukey, 1958, p. 34). Formulas for the digital calculations of the covariance functions and spectra and some guidelines for estimating the length of record required for the various calculations are given in the appendix. A detailed discussion of the calculations and an excellent review of spectral theory are given in the above references and in a recent book by Bendat and Piersol (1966). Rodriguez-Iturbe (1967) investi- gated the application of cross-spectral analysis to hydro- logic data and gave a thorough discussion of the computa- tional procedures for discrete data. The procedures used in this study are identical to those listed by him (Rodriguez- Iturbe, 1967, p. 5-7). STATISTICAL PROPERTIES OF DUNE PROFILES F9 TABLE 1.—Summary of basic data [Transverse station: CL, centerline; L and R. left and right third points of the channel; 2, 4. and 6, stations from the left wall of the 8—1"! flume. Lag interval: given in minutes for runs 4,19,33, 40, 44. and 48] Median Channel Time or Trans— No. of Lag Mean Mean Water diam Bed and run Date Time station verse data interval depth velocity Slope temperature of bed configura- station points (ft or min) (ft) (fps) (° C) material tion (mm) Atrisco Lateral: 1966 Run 1 ....... June 23 ......... 0—4000 CL 12.924 0.333 2.20 2.16 0.00055 19 0.23 Dunes. 2 ....... June 22 ......... 0—4000 CL 13,116 .333 2,30 2.11 .00055 20 .23 Do. 3 ....... June 21 ......... 1000—4000 CL 9,864 .333 2.29 2.08 .00058 20 .23 Do. 8-ft flume: Run 4 ....... Mar. 15 ......... 936 min CL 936 1.00 5 ....... Mar. 17 1115 60—180 2 924 .130 6 ........... do ..... 1115 180—60 4 924 .130 7... ....d0 ..... 1115 60—180 6 912 .132 8... ....do ..... 1255 60—120 4 432 .139 9.... ....do ..... 1300 60—120 4 444 .135 10 ......... do ..... 1305 60—120 4 432 .139 11 ......... do ..... 1310 60—120 4 432 .139 2.80 2.09 .00063 20 .24 Do. 12 ......... do ..... 1315 60—120 4 444 .135 13 ......... do ..... 1320 60—120 4 444 . 135 14 ......... do ..... 1325 60—120 4 456 .131 15 ......... do ..... 1330 60—120 4 444 .135 16 ......... do ..... 1530 60—180 2 876 .137 17 ......... do ..... 1536 60— 180 4 900 .133 18 ......... do ..... 1540 60—180 6 900 .137 19 ......... do .............. 888 min CL 888 1.0 20 ...... July 12 1732 60-180 4 468 .256 21 ......... do ..... 2114 60—180 4 736 .163 22 ......... do ..... 0930 60—180 4 984 .122 23 ......... do ..... 0924 60—180 4 720 .167 24 ......... do ..... 0935 60—180 4 876 .137 25 ......... do ..... 0946 60—180 4 612 .196 26 ......... do ..... 0950 60— 180 4 480 .250 2.36 2 .01 .00056 24 .24 Do. 27 ......... do ..... 0953 60— 180 4 528 .228 28 ......... do ..... 1113 60—180 4 480 .250 29 ......... do ..... 1308 60— 180 4 468 .256 30 ......... do ..... 1328 60—170 4 792 .152 31 ......... do ..... 1329 170—60 4 969 .158 32 ......... do ..... 1727 60—180 4 852 .141 33 ......... do ..... 1735 505 min 4 672 .750 34 ...... July 13 0907 60— 180 4 864 .139 . 00053 35 ......... do ..... 0912 60— 180 4 480 .250 .00053 36 ......... do ..... 1012 60— 180 4 864 .134 . 00053 37 ......... do ..... 1016 60—180 4 480 .250 2.36 2.01 .00053 25 .24 Do. 38 ...... July 14 0810 60—180 4 1,188 .101 .00045 39 ......... do ..... 1435 60— 180 4 1,176 .102 .00045 2 ft Hume I 967 Run 40 ...... Feb. 23 ......... 395 min CL 395 1.0 41 ...... Feb. 21 1110 5—55 CL 668 .075 1 .518 1.10 .00088 20 .35 Ripples. 42 ...... Feb. 22 2350 5—55 L 667 .075 43 ...... Feb. 23 1412 5—55 R 766 .070 l 44 ...... Mar. 23 ......... 532 min CL 532 1.0 45 ...... Mar. 21 1720 5—55 CL 640 .078 .522 1.07 .00088 20 .35 Do. 46 ...... Mar. 22 0908 5—55 CL 696 .072 } 47 ......... do ..... 2156 5—55 L 640 .078 48 ...... Apr. 12 1640 1160 min CL 776 1.50 49 ...... Apr. 11 1400 5-55 CL 416 .120 .521 1.62 .00212 20 .35 Dunes. 50 ...... Apr. 12 1403 5-55 L 407 . 123 - 51 ......... do ..... 1536 5—55 L 393 .127 J 0.67-ft flume: 1 965 Run 52 ...... Nov. 30 1000 0-7.2 L 306 .0208 .174 .508 .00148 20 .30 Ripples. 53 ......... do ..... 1000 9— 16 L 348 .0208 . 174 .508 . 00148 20 .30 Do. 54 ...... Dec. 1 1000 0—7.2 L 318 .0208 .174 .508 .00148 20 .30 Do. Atrisco Lateral: I 966 Run 55 ...... June 22 ......... 0—2000 CL 6,000 .333 2.30 2.11 .00055 20 .23 Dunes. .. C L 600 .333 2.30 2.1] . 00055 20 .23 Do. CL 600 .333 2.30 2.11 .00055 20 .23 Do. F10 ZERO AND h-LEVEL CROSSING ANALYSES In this section, mean values of the durations between zero and h-level crossings, the mean durations of upward excursions above the level It, and some of the probability distributions of interest in the two-dimensional stochastic model of particle movement (Sayre and Conover, 1967) will be considered. First, it is noted that the bed elevation 3/, measured from the mean bed level follows approximately a Gauss- ian distribution (fig. 5). Intuitively, an approximate normal distribution is expected, because physical phe- nomena governed by the complex interaction of many factors often exhibit such a distribution. Logically, the distribution can be only approximate; in a finite flow 8—inch flume 8—foot flume BED ELEVATION,y. (DIMENSIONLESS) 1llllltlllll SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS depth, the variation of the bed elevation about the mean can never assume infinite values. In addition, the pre- ferred orientation of the dune forms, with the characteris- tic steeply sloping downstream faces, suggests a pattern more regular than normal distribution. Figure 5 shows examples of the distributions from each of the four chan- nels, and although the sets of values plot around the straight line of a normal distribution, each shows some departures from normality. The cumulative distribution curves of figure 5 tend to smooth out irregularities of the data and are not really a good indication of the normality or lack of normality of the data. A better criterion, perhaps, is to compare the skewness of the data with the skewness of a normal dis- 2—foot flume Atrisco Lateral —2 99 98 95 90 50 10 5 2 1 9998 95 90 50 10 5 2 1 PERCENTAGE EXCEEDING y FIGURE 5.—Distributions of bed elevations. STATISTICAL PROPERTIES OF DUNE PROFILES tribution, which is zero. Table 2 lists the properties of the raw data and shows that the skewness varied from— 0.3 to about 1.7, with a preponderance of values on the posi- tive side. Both the skewness and kurtosis show a con- siderable range values with no recognizable pattern. TABLE 2.—Statistica[ properties of raw data Run Variance Standard Skewness Excess of deviation kurtosis 6.70X10‘2 2.59X10‘l 6.38X10‘l l.07X10° 7.63X10‘2 2.76X10—l 5 09X10“ 9.47X10‘l 7.28X10'2 2.70X10‘1 2 77X10‘l 3.35X10—l 4.00 X 10‘2 2.00 X 10‘1 1 71X 10° 9.91 X 10" 2.09><10‘2 1.44X10‘l 4.04X10‘1 —8.12X10‘3 1.58X10‘2 1.26X10’1 4.92X10‘I 6.45X10‘2 1.77X10‘2 1.33X10‘1 1.48X10’l —2.87X10‘l 2.62 X 10‘2 1.62 X 10‘1 6.06 X 10’2 —2.03 X 10—1 1.90X10‘2 1.38X10‘1 2.59X10‘l —5.62X10‘l 3.12X10‘2 1.77X10‘l 5.70X10‘l 3.35X10‘1 3.59X10‘2 1.89X10‘l 4.12X10‘1 —3.15X10—l 3.38X10‘2 1.84X10‘l 3.38X10'1 —2.58X10‘l 2.96X10‘2 1.72X10‘l 520X10‘1 —1.49X10‘l 3.80 X 10‘2 1.95 X 10‘1 6 07 X 10‘1 —3.23 X 10‘1 3.83 X 10‘2 1.96 X 10'1 5 57 X 10‘1 —4.36 X 10‘1 3.22 X 10‘2 1.79 X 10‘1 8 66 X 10‘1 2.32 X 10° 17 ....... 4.68X10‘2 2.16X10—l 165X10‘l —-5.84X10'l 18 ....... 3.37X10‘2 1.84X10‘1 2 06X 10‘1 —l.53X10‘l 19 ....... 1.14X10'3 l.07><10‘1 129X10‘1 —1.67X10‘l 20 ........ 2.16X10‘2 1.47X10‘1 4.50X10'l 5.03X10‘l 21 ....... 1.23XIO‘2 1.11 XIO’l 2.28X10‘l 4.46X10‘1 22 ....... 1.94X10‘2 1.39><10‘l 3.17X10‘1 -2.21X10’l 23 ....... 1.88 X 10‘2 1.37 X 10‘1 147 X 10'1 —2.2() X 10‘1 24 ....... 1.96X10‘2 1.40X10“ 509X10‘l —8.21X10‘2 25 ....... 2.61X10‘2 1.62X10‘l 8.33X10‘l 8.11X10“ 26 ....... 2.77X10‘2 1.67X10‘l 6.97X10‘l 4.20X10‘l 27 ....... 2.98 X 10‘2 1.73 X 10‘1 6.91 X 10‘1 4.41 X 10‘l 28 ....... 1.76X10‘2 1.33X10'l 4.06X10‘l 7.06X10‘l 29 ....... 1.44X10‘2 1.20X10‘l 5.37X10‘l 1.66X10° 30 ....... 1.07 X 10“2 1.03 X 10‘1 9.84 X 10‘2 8.41 X 10‘3 31 ....... 1.17X10'2 1.08X10‘l —9.77X10‘2 5.49X10‘l 32 ....... 2.11 X 10‘2 1.45 X 10" 8.07 X 10“ 1.55 X 10° 33 ....... 1.45X10—2 1.20X10’1 1.75X10‘l 2.57X10’l 34 ....... 1.22X10‘2 1.10X10‘1 2.04X10“ —1.79X10‘1 35 ....... 1.23X10‘2 1.11X10“ 1.16X10° 9.00X100 36 ....... 1.03 X 10‘2 1.01 X 10‘1 1.60 X 10‘1 2.91 X 10‘1 37 ....... 1.04X10’2 1.02><10‘l —2.71X10'2 —4.17X10‘2 38 ....... 1.25X10’2 1.12X10’l 7.66X10‘l 1.12X10° 39 ....... 8.52 X 10'3 9.23 X 10‘2 1.03 X 10° 1.71 X 10° 40 ....... 1.29 X 10‘3 3.6OX10‘2 6.78 X 10‘1 4.76 X 10" 41 ....... 1.91 X 10’3 4.37 X 10'2 2.81 X 10’1 1.98 X 10‘1 42 ....... 2.25X10‘3 4.74X10’2 —l.85X10‘l —7.54X10‘3 43 ....... 2.09 X 10’3 4.57 X 10‘2 3.33 X 10“ -4.25 X 10‘1 44 ....... 1.20X10‘3 3.46X10‘2’ —2.29X10‘l —4.87X10‘l 45 ....... 1.64X10—8 4.04X10‘2 7.92X10—2 —5.28X10‘l 46 ....... 1.50X10‘3 3.87X10‘2 2.15X10‘1 —4.16X10“ 47 ....... 1.79X10‘3 4.23X10‘2 2.40X10‘l —1.78X10‘l 48 ....... 5.62X10‘3 7.50X10’2 9.27X10‘l 6.70X10‘1 49 ....... 5.48X10‘3 7.39X10’2 1.03X10° 1.64X10° 50 ....... 5.54X10‘3 7.44-X10’2 3.60X10“ 2.68X10° 51 ....... 3.23X10‘3 5.68X10’2 1.46X10—l —8.08><10‘l 52 ....... 2.16X10‘3 4.64X10‘2 4.44X10‘1 —4.99X10“l 53 ....... 1.19X10‘3 3.44X10‘2 2.84X10‘l ~4.33X10" 55 ....... 8.09 X 10‘2 2.84 X 10‘I 5.41X10’l 3.83 X 10° 56 ....... 8.72X10’2 2.96X10'l 1.16X10° 2.49X100 57 ....... 3.95 X 10’2 1.99 X 10‘1 4.81 X 10‘2 —5.73 X 10‘2 NOTE—Run 54 not used. Even though the distributions of the data depart from normality, the relation of equation 10 provides a good estimate of the mean duration or the mean distance between zero crossings, lo, as shown in figure 6. Although 405-448 0 — 71 - 3 F11 so (0 Lu ’— D E 2 K O .— uJ Lu L E \°10 5 5 10 50 w (0) V2 [{ lo}=1 - . IN FEET OR MINUTES _¢//(0) FIGURE 6,—Comparison of the expected length or duration between zero crossings for a Gaussian process. E{ lo}, with the observed values, 10. there is considerable scatter, the data group around the line of perfect agreement. N0 consistent trends in the scatter could be attributed to flume size or type of bed form, so that most of the scatter is assumed to be due to the shortness of the records of the flume data. The ratio of the expected number of h-level crossings t0 the expected number of zero crossings was given for both the continuous process and the discrete approximation to the continuous process in figure 3. Because the two curves are so similar, the simpler expression of equation 12 will be used. Observed values of the ratio Nh/No are plotted in figure 7, along with the curve representing equation 12. Values for 13 profiles were plotted. Six of the profiles, runs 4, 19, 33, 40, 44 and 48, are of the process y=y(t), and seven of the profiles, runs 16, 32, 41, 45, 53 and 56, are of the process y: y(x) . For positive values of h, the points scatter symmetrically about the curve of equation 12, but for negative values of It, most of the points fall above the curve for values of h from 0 to —1 and below the curve for values of h from —1 to —2. Figure 7 shows clearly that there are more crossings below the mean bed elevation than above, which would be expected from consideration of flow conditions over a dune. Below the mean bed elevation, the reverse flow in the trough and the flow impinging on the back of the dune result in lower velocities which promote the growth of small—scale features. Above the mean bed elevation, the converging flow up the back of the dune results in a F12 ii.” N FIGURE 7.—Observed values of Nh/No as a function of h. higher-than-average velocity and shear stress near the bed, and small-scale features cannot form. Figure 8 shows the average of all observations, with the points connected by dashed lines to give an indication of the shape of the distribution of Nil/No values and with averages of y(t) and y(x) differentiated. The figure indicates that records of both y(t) and y(x) yield values of Nh/No that agree very well with the theoretical curve for h > 0, but that deviate appreciably from the curve of equation 12 for h $ 0, with the values from the process y: y(t) showing the greatest deviation. Figure 8 suggests that there may be some slight differences in the properties of y(x) and y(t). However, distributions of the raw data and the spectral analyses of the processes, discussed in a later section, indicate that there are no appreciable D Average of 13 0 Average ofyU) A Average ofJ/(x) —1 0 1 2 /7 FIGURE 8.—Average values of Nn/No as a function of h. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS differences, so that the greater deviation of the values for the process y=y(t) probably is fortuitous. No consistent differences in the deviations of the values from the curve in figure 7 could be attributed either to flume size or to bed forms, where both ripples and dunes are represented. The mean duration of an upward excursion of the process y(t) above the level h, E{l;t} , was given by equa- tion 13, and equation 14 is the ratio of mean duration of upward excursions at the level h to mean duration of up- ward excursions at the zero level. Equation 14 is plotted in figure 9 along with observed values of the ratio [jg/lg. Again, as in figure 7, there is systematic deviation from the curve for values of h from 0 to -1, and there is considerable scatter at the higher values of h. However, this is not too disturbing because the number of upward excursions that are observed in the relatively short flume records probably is too small to get reliable average values of 1;. The average rest period of a particle deposited between the levels h; and hz can be computed from equation 14 or estimated graphically from figure 9. Theoretically, there are no limitations to equation 14; it is applicable between any two levels of the bed, —°° < h < + 00. The ratio l;/lg approaches zero as h assumes large positive values and approaches an infinite value as h assumes large nega- tive values. From a practical point of view, these extremes l l I l I I _ a —4 50 _ Run 4 O ._ . Run 19 .. D _ Run 33 _ . A Equation 14 Run 40 R O 10 _ un 44 _ _— I q : 0 Run 48 : s :o - ~ V _ _4 Lu (.9 < >— _ t: m > < _ 1.0 : | l l l 0.2 -2 —1 0 h FIGURE 9.—Observed values of the ratio [if/lot plotted against h. STATISTICAL PROPERTIES OF DUNE PROFILES rarely would be of interest. The major transport of bed material occurs in the activity shifting part of the bed, and it is unlikely that one would need to consider anything beyond two standard deviations of the mean bed level to account for the bulk of the sediment movement. Within these limits, a reasonable estimate of an average rest period can be determined from figure 9 or equation 14-. Equation 13 gives the mean rest period, 1;, of a particle deposited on the downstream face of a dune at the level h. We are interested in not only the mean value but also the distribution of 1,7, the conditional probability distribu- tion of rest periods, given that a particle is deposited at the level h. As indicated previously, there is no theoretical basis for predicting a distribution of the 1; values, and, unfortunately, the records of y(t) were not long enough to establish the rest period distributions. However, it may be useful to establish some of the properties of the distributions for 1; values of the process y(x), even though these values do not represent rest periods, because if the statistical properties of y(x) and y(t) are similar, the distribution of crossings and other features of interest should be the same. (For Gaussian processes with zero means, similar covariance functions insure similarity of all other properties.) For this purpose, the Atrisco Lateral records were selected because they were the longest available. Figure 10, a bar graph of l; distributions for run 1, shows that shapes of the distributions vary with h and suggests that at the level h=0 the lengths of upward excursions follow an exponential distribution. Figure 11 shows as solid lines exponential distributions with the same means as observed mean values of l; for runs 1, 2 and 3. The plotted points represent the observed values. Obviously, the exponential distribution is only a rough approximation. W. W. Sayre (oral commun., 1967) suggested that per- haps a gamma distribution would serve as a model for the distribution of 1;; values over any practical range of bed elevations that are of interest. To investigate this possibility, consider the gamma distribution with param— eters b > 0, A > 0, pH) 3—35 (ma—Item, (33) where x > 0, and DU) =0, where x < 0. When b= 1, this is the negative exponential distribution shown in figure 11, with A=1/lo. The variance of the F13 PERCENTAGE IN CLASS /h+ FIGURE 10.—Observed distributions of [,7 for run 1. gamma distribution is MM, and its coeificient of variation Cu, the standard deviation divided by the mean, is l/Vh. Figure 12 shows observed values of CE for the distri- butions of If, values plotted as functions of h. The trend line sketched through the plotted points is positioned with C1): 1 at h = 0, corresponding to the exponential distribu- tion of figure 11. Thus, the postulated gamma distributions of the lengths or durations of positive excursions above the level h can be determined directly from figures 12 and 9, with A and b computed from the following equations: b=1/C,2, A: (1/C%)avg- (34) (35) Figure 13 shows bar graphs of the observed [,7 dis- tributions for run 1, with points plotted at the midpoint of each class interval representing the frequency for that class from a gamma distribution with parameters given by equations 34- and 35. The observed mean value of It, F14 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 1.0 — O ._ 0 PM ’- . x /\I \0 hp! ,_ Q 0.1 '- F I l 1 l 0 10 20 FIGURE ll.—Observed distributions of 10* for runs 1, 2, and 3. Solid lines are exponential distributions with the same mean values as the observed means. The lengths are in multiples of the lag interval, 0.333 feet. I l I l I 50 -—1 was used to compute )t for h = 0, and all other parameters 40 4) T [7:12 A were determined from figures 9 and 12. The results of ' 0 this example certainly are encouraging but not conclusive. 30 " L ’_ __ ‘ It should be noted that the data from one time record, 20 _, l .. run 19, are plotted in figure 12. These data deviate more 0 g from the trend line of the C, values than do the data from 10 ' I Q _ . . . L. .. the longitudmal profiles, but the number of crossmgs o .L I 7511‘ l 1 I observed in the time records was too small to provide reliable statistical estimates of the distribution of the m 50 _ ' ' ‘ ' ' _ [,1 values. Thus, the approach outlined above appears to g be equally applicable to records of y(x) or y(l) , but confi- : 40 h [7:0 ' T 30 0 Lu - .--w - A ‘2 “6" A Run 1, yzy (x) E 20 " L6”. ‘ (‘E E] Run 2, yzy (X) g 10 L01 _ 0 Run 3, y=y(X) g F LQ”U""b'-— . Run 19’ yzy 0) 0 __—L_—l———.—L—m-—J——— I I I I I 50 - - 40 — /7 : — 1.2 .. U 0 O I I —2 —1 o 1 2 /.+ A FIGURE 13.—Comparison of observed 1,: distributions with the FIGURE 12.—0bserved values of the coefficient 0f variation, Cm for theoretical class frequencies from a gamma distribution. The the distributions of 1,,+ plotted as functions of h. plotted points are from the theoretical distribution. STATISTICAL PROPERTIES OF DUNE PROFILES dence levels for estimating the distributions of rest periods cannot be established until longer records of the process y=y(t) become available. One other distribution of interest that will be con- sidered in this section is the probability that a particle is residing in the bed at the level h. This is not the same as the probability that a particle is deposited at the level h, for deposition occurs on the downstream faces and in the troughs of the sand waves; this latter probability no doubt depends on flow conditions. The distributions derived empirically by investigating the area bounded by the curve y=y(£) or y=y(x) above a level h give the percent of particles found in the bed above the level h and represent the probability of finding a particle at the level h if nothing is known of its previous history. Figure 14 shows the com- puted values for y(x) and y(t) records from the 2-ft flume, with a smooth curve drawn by eye to indicate the trend of the distributions. An approximate equation for P(h), the probability that a particle is residing in the bed above the level h, is given by P(h):1_e—0.157(h+1.75). (36) Equation 36 is a good approximation in the range 0.1 < P < 0.9, but it is not applicable for extreme values of h. y=y (f) 0 Run 40, ripples — 0 Run 44, ripples - 0 Run 48, dunes - ‘2 I I I I I T ‘I I I y=y (X) 0 Run 41, ripples —I 0 Run 45, ripples —‘ 0 Run 48, dunes — I | l l I I I o 50 PERCENTAGE OF PARTICLES ABOVE THE LEVEL II 100 FIGURE I4.—Percentage of particles in the bed above the level h. F15 DISTRIBUTION OF WAVE HEIGHTS AND AMPLITUDES The absolute maximum value ofy between zero cross- ings was defined in figure 2 as the wave amplitude, a, and it was noted that the distribution of positive amplitudes, a+, represented the probability distribution of local deposition and that the distribution of negative values, a—, represented the probability distribution of local depth of scour associated with the formation and migra- tion of sand waves. If the processes y(x) and y(t) were symmetric about their mean values, the distribution of positive and negative (1 values would be identical, and for a Gaussian process, it was postulated that the distribu- tions of a values would approximate the distribution of crest heights, 1), shown in figure 4. All of the records analyzed exhibited relatively broad spectra, with values of 82 from equation 20 varying from 0.83 to 0.99 (see table 3) and with most of the values greater than 0.9. Figures 15 through 17 show distributions of positive and negative (1 values for runs 1 through 3. The solid curves on the figures represent the Gaussian distribution from figure 4 of crest heights for a process with a broad-band spectrum (82:1.0). Two points of interest should be noted: (1) the distributions are not symmetric, and (2) the negative values, a—, follow more closely the normal distribution than do the positive values. The positive amplitudes, a+, followed approximately an exponential distribution, as shown in figure 18. In this figure, P (a) is the cumulative probability distribution of a, and for this form of plotting, a Rayleigh distribution (eq 21) would have a slope of two and an exponential distribution, a slope of one. Clearly, except for very small values of a, the slope is one, indicating an approximate exponential distribution. As discussed previously, there is no basis for extimating the probability distribution of wave heights, H, the trough- to-crest height, and there is no reason to expect simi- larities in the distribution of H and a values. Figure 19 shows the distribution of wave heights to approach the Rayleigh distribution, rather than the exponential distribu- tion. The same data were used to prepare figures 18 and 19, but in figure 19 the raw data were not standardized and the wave heights are given in feet rather than in units of standard deviations. Even though the distributions are different, the mean values of a+ and H relate reasonably well (fig. 20) as do the mean values of distances between successive up- crossings of y and mean dune lengths, L, (trough-to- trough distance) (fig. 21). Note, however, that values of 2a and of the distance between successive upcrossings are not strictly comparable to H and L because entire waveforms occur above or below the mean bed level, and their lengths and heights are not reflected in the average F16 TABLE 3.—Miscellaneous properties from the zero-crossing and spectral analysis [Type of profile is y(x) except type for runs 4. 19. 33. 40, 44, and 48, which is y(t)] Length: L0 is the average distance in feet, or time in minutes for runs 4, 19, 33, 40, 44. and 48. between successive upcrossings of y=0. Amplitude: d+ is the average of maximum y values between successive zeros. in: From eq 5. 32: From eq 20. l/miz Mean wavelength in feet, or wave period in minutes for runs 4. 19. 33, 40. 44-. and 48. from spectra, eq 8. Length Amplitude Run a + ((1-4) 62 1/ml L; C.. (F!) C,. 1 ......... 8.96 0.577 0.277 0.850 2 ......... 9.22 .589 .287 .913 3 ......... 7.79 .560 .302 .782 4 ......... 57.3 .504 .386 1.46 5 ......... 4.97 .599 .164 .868 6 ......... 4.94 .681 .158 .886 7 ......... 5.37 .618 .156 .673 8 ......... 5.24 .631 .180 .712 9 ......... 6.13 .379 .225 .573 10 ....... 5.78 .511 .221 .687 11 ....... 6.59 .596 .223 .684 12 ....... 3.39 .877 .119 1.21 . . 13 ....... 6.39 .481 .243 .690 . . 14 ....... 4.74 .789 .192 1.02 . . 15 ....... 7.38 .186 .306 .467 . . 16 ....... 6.21 .512 .256 1.09 . . . 17 ....... 8.45 .384 .274 .747 .216 .983 7.59 18 ....... 6.96 .358 .226 .555 .184 .979 6.48 19 ....... 29.3 .591 .099 .885 .107 .974 42.5 20 ....... 4.68 .448 .169 .800 .147 .931 5.35 21 ....... 4.34 .648 .138 .834 .111 .946 4.01 22 ....... 4.21 .575 .189 .648 .139 .974 4.47 23 ....... 4.19 .623 . 167 .708 .137 .946 4.07 24 ....... 5.04 .416 .190 .705 .140 .966 4.43 25 ....... 5.61 .412 .201 .843 .162 .952 5.15 26 ....... 5.62 .598 .212 .836 .167 .938 5.85 27 ....... 5.79 .530 .227 .702 .173 .944 5.68 28 ....... 3.70 .635 .137 .928 .133 .909 4.72 29 ....... 4.04 .706 .144 1.00 .120 .876 3.48 30 ....... 3.98 .620 .091 .899 .103 .968 5.37 31 ....... 5.69 .576 .129 .716 .108 .966 5.86 32 ....... 4.78 .644 .157 .853 .145 .970 5.44 33 ....... 16.6 .317 .103 .815 .120 .961 26.8 34 ....... 4.67 .662 .132 .732 .110 .965 4.95 35 ....... 5.78 .453 .179 1.06 .111 .830 3.02 36 ....... 3.20 .709 .093 .836 .101 .961 4.31 37 ....... 4.12 .756 .106 .755 .102 .923 5.25 38 ....... 4.20 .552 .072 1.01 .112 .983 6.21 39 ....... 2.79 .757 .088 1.23 .0923 .962 3.32 40 ....... 14.3 .989 .0237 1.16 .0360 .958 29.7 41 ....... .968 .635 .0432 .857 .0437 .886 1.36 42 ....... 1.16 .666 .0483 .666 .0474 .895 1.61 43 ....... 1.36 .542 .0512 .680 .04-57 .921 1.75 44 ....... 27.4 .630 .0279 .963 .0346 .970 38.8 45 ....... 1.14 .546 .0493 .619 .0404 .874 1.33 46 ....... 1.01 .515 .0430 .652 .0387 .881 1.24 47 ....... 1.13 .679 .0431 .820 .0423 .904 1.58 48 ....... 25.5 .562 .0885 .817 .0750 .927 32.4 49 ....... 2.56 .472 .0952 .901 .0739 .948 3.00 50 ....... 2.77 .610 .0734 1.03 .0744 .927 2.37 51 ....... 3.16 .665 .0653 .687 .0568 .956 3.56 52 ....... .636 .534 .0384 .920 .0464 .980 1.08 53 ....... .782 .460 .0416 .449 0344 .964 .81 distance or average of maximum ordinates between zero crossings. An interesting correlation was found to exist between the average of maximum ordinates between zero cross- ings and the standard deviation of the bed elevation SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 100 l (8—) o O C O 0 o 0 ° 0 O 0 Normal . \ distribution . o (.94.) ”JP 0 0 El 9 o 'D ~3—v 0 r—SO— ° 0 - Z 0 8 o 5 - ° 9. o 8 Runl O O 1 C 0 1 2 FIGURE 15.—Distribution of positive and negative (1 values for run 1. 100 . (a—) o . t \ o o 0 O O O t-M ‘Q 0 VI Norma' o \(H) _ distribution ° 0 m o 0 ca 0 1250- o — é 0 Lu 0 O Q. 0 8 Run2 a O C | o 1 2 /7 FIGURE 16.—Distribution of positive and negative 0 values for run 2. (fig. 22). For the smaller features, a direct linear relation applies, with the standard deviation of the bed elevation approximately equal to the average amplitude of the sand waves. This is precisely the relation predicted for the mean value of local maxima given by equation 23 and STATISTICAL PROPERTIES OF DUNE PROFILES 100 l o 1 O I (a—) ' c 0 o O 0 Normal o 0 distribution A ' c’\\(a+) Q 0 0 Vi ° _ o o I“ O .2, o I— 50— ' ‘ z O 8 o I: III 8 n. 9 ° Run 3 . O o O . O O I 0 1 2 FIGURE 17.—Distribution of positive and negative (1 values for run 3. shown in figure 4 as the curve corresponding to 82= 1.0. The relation of figure 22, then, supports the assumption that the distribution of a values should be similar to the distribution of the local maxima. The deviation from the line of agreement at the larger a values might be at- tributed to the fact that some of the details of the record 1.0 h I I I I T I I I I l I I .1 ’3 T Q __‘, 0.1 : —_ (D " _ O '- -I -' Exponential _ distribution _ 0.01 I I 1 l I I I I l I I l 0.1 1.0 5.0 FIGURE 18,—Approximate exponential distribution of positive a values for run 55. F17 5-0 l 1 I I r r ‘I I I >- .— 1.0— I. I _ H “is _ K Exponential (D O - — _l - -l 0.1 -- .- - -l l I I 1 1 l 1 IL 0.1 1.0 H, IN FEET FIGURE I9.—Distribution of wave heights, H, for run 55. are lost in digitizing the continuous trace of bed elevation. The larger dunes are not more regular than the smaller features; in fact, the reverse is true. If the bed profile is represented as a succession of identical triangles, similar to the idealized dune form of figure 1, with ripple index, Z/FI, of 15 and tan B=0.6, the relation of mean amplitude to standard deviation of y is given by a=0.64- 01,. If this condition were to hold for the larger dunes represented in figure 22, the plotted points would fall to the left of the line of agreement. Summarizing, the average amplitude a is approximately equal to the standard deviation of the bed elevation, and the distributions of a values predicted by the relations in figure 4 appear to give reasonable agreement with the observed distributions. However, the bed profile is not symmetric about its mean level, and the distribution of negative values a— agrees more closely with the predicted normal distribution than do the positive values (1+. For the positive values, an exponential distribution can be shown to apply (fig. 18). F18 1~°_r111r1 1 I 111111_ ,_ _. I“ ‘I .— LU '_ —I 1.1.1 LL z ' . ‘ IA- __ 0 $ .’~o .. 'i 0’0 ' g . . O m — O _ o I o/ o “J 0.0 o i o 3 LLI w . o g 0.1— _. :1 : s - - < o. — _ o _ I— . u— 0.04 1 1 1 1 1 l 1 1 1 1 1 1 1 1 0.04 0.1 1.0 TWICE THE AVERAGE MAXIMUM ORDINATE BETWEEN ZERO CROSSINGS, IN FEET FIGURE 20.—Relation between twice the average maximum ordinate between zero crossings, 2a +, and H. 10° 1 1 I I 1 I 1 I— _ LU I.” LA. E _ If. I _ _ 5 z 0 Lu d o g o . o 1.0— __ >— . - 0'4 1 1 19 1 I 1 1 1 1 1 1 1 1 0.4 1.0 10.0 AVERAGE DISTANCE, IN FEET, BETWEEN SUCCESSIVE UP-CROSSINGS FIGURE 21.—Relation between mean values of the distances between successive zero upcrossings of y and the mean dune length, L. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 1.0 I )— IAJ L“ L E 5% Z 9 I; o c 0 .0 o o a /. o". .1 “1 /'é .0 D O 1.11 _ 0'. ' ° _ “30.1 00., B o/~ S / " I E .0 '1 . 0 E .0 ° 0 D K < D Z < )— (I) 0.01 l 0.01 0.1 1.0 AVERAGE OF MAXIMUM ORDINATES BETWEEN ZERO CROSSINGS (5+), IN FEET FIGURE 22.—Relation between average of maximum ordinates between zero crossings, 6+, and standard deviation of bed elevation, cry. SPECTRAL ANALYSIS In the previous discussion, the autocovariance func— tions or the spectral density functions for the processes y(x) and y(t) were assumed known. These functions were required to predict the number of zero and h-level crossings for the model Gaussian process, and for the experimental data the functions were known because they were computed. In the following sections, the prop- erties of the covariance functions and spectra will be considered in somewhat more detail. STATIONARITY AND EQUILIBRIUM FLOW A critical assumption in spectral analysis is that the processes under consideration are stationary, at least to the second order. At the initiation of this study, it seemed intuitively obvious that stationarity of the processes y(t) and y(x) would be a direct consequence of equilibrium flow conditions. If the mean characteristics of the flow, the sediment, and the transport do not change with time or with distance along the channel, then surely the statis- tical properties of records of the bed profile should be invariant with respect to shifts in the origin of the records. For the longer field records, it can be demonstrated that the assumption of weak stationarity is justified. Figure 23A shows mean values and standard deviations for eight short segments from the record of run 3 plotted with their respective 90 perCent significance levels. The standard STATISTICAL PROPERTIES OF DUNE PROFILES 1‘5 I 4 1 I I I I ——_.___ Mean _._ ._ __.__0__1____ _ 1.4'- . O 1.3 I l 1 I l l 1 p— m Lu u. 0'4 I I 1 I I I I Standard deviation ()3. ——.———.—_————— J '— ____.___.___ _2_ L 0.2 L L I I I I 0 l 2 3 4 5 6 7 8 A F19 1-5 I I I I I I T Mean 1 _______._______. c 1 4 1.5 —I—+—Y—1——r—r—-fi-—' 0.20 , I I I I 1 I Standard deviation 0 i — — — —-——.—’—_ — —— 0.18- i .. C 0.16- . ' 014 I ‘ l I I I J 0 1 2 3 4 5 6 7 8 FIGURE 23.—Comparisons of means and standard deviations, in feet: A, for eight short segments of the record of run 3, Atrisco Lateral; B, for eight longitudinal profiles during equilibrium flow in the 8-foot flume, runs 8 through 15. The solid line represents the average value and the dashed lines indicate a 90-percent significance level. deviations do not vary significantly. The rather large variations in the mean values resulted from large alternate bars and a meandering thalweg that existed in the channel and that introduced apparent trends in the short segments of the record. The bed profiles were obtained by sounding from a boat with the water surface as a datum, and the depth of flow varied somewhat systematically along the channels. However, when the bed elevations were meas- ured from the mean bed level established by a linear trend line through short segments of the reach, the assumption of second-order stationarity for these short segments of record was satisfactory. For longer segments of the record, on the order of 40 to 50 times the mean channel width, no significant differences were noted in the means and variances. The flume records presented a somewhat different problem. It was assumed that, for equilibrium fiow condi- tions, any two records of the bed profile would show approximately the same statistical properties. However, this was not found to be true. Figure 233 shows that the standard deviations for runs 8 through 15, all of which were taken during apparent equilibrium flow conditions over an identical reach of the flume (see table 1), vary significantly. Two factors appear responsible for the large variations in the flume records. First, the flume records for y(x) are short relative to the number of dunes that are observed, and the short records introduce inherently large variations in the statistics from one observation to the next. Second, the concept of equilibrium flow implies a time-averaged stability that may not necessarily apply to any single observation. Simons and Richardson (1966, p. J3) indicate that equilibrium flow obtains when the time-averaged water-surface slope and bed slope are parallel and con- stant and the time-averaged sediment discharge is constant. Rathbun and Guy (1967, p. 111) have shown that extremely large variations in sediment transport rates are to be expected in recirculating fiumes, and probably these variations are reflected in changes in the properties of the bed profiles from one observation to the next. Despite the rather large variations in the flume records due to the fact that equilibrium flow conditions do not prevail over short time intervals, the spectral properties of the individual records are remarkably similar for a given flow condition, provided the data are standardized to zero mean and unit variance. Figure 24 shows the spectral ordinates for runs 8, 10, 12 and 14 as points plotted against a dimensionless wave number, 6/6max, where emax is the maximum wave number for which the computations were carried out; the solid line represents an average curve for the spectra and the dashed lines represent a 90-percent confidence band based on the procedure given by Blackman and Tukey (1958, p. 21—23). Only two of the 80 points fall outside the confidence band; the general shapes of the spectra are therefore quite reproducible from one observation to the next. The ap- proximation used in this study, therefore, was to treat each individual record as if it were weakly stationary. The moments of the spectra for the individual records could then be used to estimate the number of zero cross- ings by equation 10 to compare with observed values. However, in attempting to relate the statistical properties, especially the variance, of the bed profiles to flow param- eters, it will be found convenient to work with average values over a consistent set of flow conditions. F20 WAVELENGTH. IN FEET 03 5.4 2.8 1.8 1.35 1.08 ._ _ _\ T T I I ’ \\ .I \ A 10.0 —— — _ Average curve _ - //\ \\ -I _ 0 Run 8 d / 7 0 Run 10 4 F A Run 12 _+ A Run 14 g _ —( t Z I) _ .. m 90-percent confidence band Lu 0. m \ m _l U 5 1.0 _ E _ I; ,- 5 r I. r 0.1 g I I \ + l 0 2.0 6/6,“, FIGURE 24-. —Spectra for indicated flume records. THE MARKOV MODEL FOR DUNE PROFILES A major question with regard to spectral analysis is whether or not the properties of the covariance functions or the spectra can be predicted from only the charac- teristics of the flow and the sediment. Some work already has been accomplished along these lines. Algert (1965) observed that the general shapes of the autocorrelation functions and of the spectra for the process 3/: y(x) were similar to that of a second-order Markov process, and he developed a model for the spectra based on previous work of Siddiqui (1962). Nordin and Algert (1966) pre- sented virtually the same development, based on Algert’s 1965 study, but added some observations on the process y=y(t). Ashida and Tanaka (1967) noted that a second- order Markov process fits the observed spectra only for dunes and postulated a higher-order linear regressive scheme for other bed forms but did not develop a model or apply the higher order scheme to any of their data. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS In the studies by Algert (1965) and Nordin and Algert (1966), the parameters upon which the model of the spectra is based are the values of the covariance function at zero, one, and two lag intervals, and these values were shown to relate roughly to the flow parameter, unit discharge (fig. 25). We can use figure 25 and equation 15 to predict the average length between zero crossings of the process y(x) by noting that the spacing of the discrete data points used by Nordin and Algert (1966) in figure 25 was approximately given by Ax = 40y: 4C01/2. (37) Here Ax is equivalent to Al in equation 15,C1/C0 is ¢(At) , and Ci is (Ty d)(iAt) . Substituting these relations in equa- tion 15 and reading values of Co and C1 from figure 25 for values of unit discharge given in table 1, the average distances between zero crossings were computed and are compared with observed values in figure 26. For the dune bed configuration, the observed values of lo fall between plus and minus 4-0 percent of the expected value, E{lo}. For the ripple bed configuration, the variations are con- siderably greater, probably because the size of ripples is more dependent on grain size than flow conditions, so that figure 25 perhaps is not applicable. In view of the 2-5 I I I I I 2.0 '- .4 . 3(Co)'/2 1.5 — A 3 (CQVZ -* I 3 (02)” 1.0 3(00)”, 3(C,)V2, AND 3(CZ)VZ IN FEET 0.5 .1 A o I l I I 1 o 2 4 6 8 10 12 UNIT DISCHARGE IN CUBIC FEET PER SECOND PER FOOT FIGURE 25.—Relation of C0. C1. and C: to unit water discharge (from Nordin and Algert, 1966). STATISTICAL PROPERTIES OF DUNE PROFILES 10 I I I I l I I I I _ / - _ / O E ‘ «of ° 0/‘/_ z DQQ/ F15 — f/ / __ \° / / 2: - / . / A960 _ o / x 4 v / _ o _ / Ripples / / - _ Dunes - 0 I I I I I I l l J 0 5 10 /o, IN FEET FIGURE 26.—Comparison of estimated and observed average distance in feet between zero crossings. gross assumptions that went into estimating E{lo}, the results of figure 26 are considered quite good. There are a number of problems involved in using the second-order Markov model and the relations of figure 25 for predictive purposes. Both the model and the relations of figure 25 are strongly dependent on the lag interval at which the continuous records are digitized. In addition, spectral analyses by the writer and by D. R. Dawdy and N. C. Matalas (personal commun., 1966) have shown that the Markov model does not apply for many of the dune profiles examined. Finally, Plate (1967) has raised some serious questions with regard to the lack of physical basis of this model. It is desirable, therefore, to consider an alternative approach to describe the properties of the spectra and to relate their properties to characteristics of the flow. DIMENSIONLESS SPECTRA Autocovariance functions and spectra were computed for all the data listed in table 1. Figure 27 shows spectra for the process y=y(x) for runs 17, 32, 43, 46 and 49. Spectra of the process y=y(t) for identical flow condi- tions, runs 19, 33, 40, 44 and 48, are shown in figure 28. The data include dune flows in the 8-ft flume and both ripples and dunes in the 2-ft flume. The abscissa in both figures is dimensionless, with each value of frequency or wave number divided by the maximum value. All the spectra are remarkably similar in general shape, and there is little in the two figures to differentiate the processes F21 y(t) and y(x); this fact suggests that the statistical prop- erties of the two types of records are similar. Figure 29 shows a comparison of spectra for ripples and dunes for the 2-ft Hume, with a 90-percent confidence band estimated according to the method given by Black- man and Tukey (1958). Here, as in figures 27 and 28, the similarity in the spectra is apparent. For both ripples and dunes, the major part of the variance is contributed by the longer wavelength components, greater than 2 feet. Both spectra show peaks at about 0.3 cycle per foot and again at about 0.8 cycle per foot. Both show additional peaks in the range from 2 to 4 cycles per foot, but within the confidence limits the peaks on the dune spectra in this range probably are not significant, whereas those for the ripples are. The rather wide band of the confidence limits leaves open to question the significance of most of the peaks at the lower wave numbers, but there is no question as to the general shape of the spectra. The similarity of shape of the spectra in figures 27 and 28 suggests that a model incorporating flow parameters might be developed from dimensional considerations. For a first approximation, consider the major part of the spectra, that part which contributes all but a small per- cent of the variance, to be a function (III) of only four variables: C(t)=¢(f, g, D, V) C(x)=dl(€,g, 0. V) (38) (39) where D is mean flow depth, V is mean flow velocity, g is the acceleration due to gravity, and other symbols are as defined previously. Dimensionless spectra 0’ are then given in terms of a dimensionless frequency f ' or wave number 6’ and the square of the Froude number, F, as follows: G’(t)=w’(f’,F2) (40) G’(x) =¢’ (6’, F2) (41) where G’ (t) =Gg/V. (42) f ' =fV/g. (43) G'(x) =Gg/V‘l. (44) e' =eV2/g, and (45) F2: V2/gD. (46) Neither fluid nor sediment properties enter into equa- tions 38 and 39 on the assumption that water temperature and particle size for the data analyzed were approximately F22 G(x), IN (CYCLES PER UNIT LAG)—l SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 100.0 10.0 1.0 .0 ._. 0.01 0.001 a Run 17 Dune bed formation I Run 32 Dune bed formation A Run 43 Ripple bed formation a Run 46 Ripple bed formation 0 Run 49 Dune bed formation 1 I l | l L 1 l I 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 E/Cmax FIGURE 27.—Spectra of the process y=y(x). 1.0 GU), IN (CYCLES PER UNIT LAG)-l STATISTICAL PROPERTIES OF DUNE PROFILES 100-0 | I I I I I I I I 0 Run 19 Dune bed formation 0 I Run 33 Dune bed formation 0 Run 40 10-0 Ripple bed formation _ A Run 44 Ripple bed formation I Run 48 Dune bed formation 1.0 — 0.1 — 0.01 — l I l | L J l I 1 0.001 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 RELATIVE FREQUENCY f/fmax FIGURE 28.—Spectra of the process y=y(/). F23 F24 20.0 ‘ 10.0 . I" o G(x). IN (CYCLES PER FOOT)-l .0 ._. 0.01 0002 J_ I l I I I 0 ... N w 4:. GI 01 \l SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS l I I 0 1 2 3 4 WAVE NUMBER, IN CYCLES PER FOOT FIGURE 29,—Comparison of ripple (left) and dune (right) spectra, 2-foot flume. constant. Then, the sediment transport rate and the bed forms are primarily functions of velocity and depth (Colby, 1964, Nordin and others, 1965). The mean flow depth enters equations 40 and 41 only through the Froude number. It is assumed that the equilibrium height of the bed configurations depends on flow depth, and it was shown in the previous section that the mean height of the bed irregularities and the variance of the process y(x) are closely related. Thus, because all the records were previously standardized in terms of the variance, the Froude number should be a parameter of only minor importance in the spectra, and for the first approximation, 0’ should be a function only of the dimensionless fre— quency or wave number. Figure 30 shows the relation between C' and e’ for the same data given in figure 27. For values of dimensionless wave numbers greater than 0.03, all data follow the relation 0’ =0.0001(e’)—3-2. (47) For lower wave numbers, each set of data follows a separate curve without a consistent pattern. It does not appear possible to collapse the family of curves into a single curve on the basis of Froude number. The dashed curve on the figure is intended only to show the general trend of the data, which seems always to show a maximum for values of 6' less than 0.025. The dimensionless spectra for the process y=y(l) are shown in figure 31, where the general relation for dimensionless frequencies less than 0.001 is given by C’=0.000015(f’)-2-1. (48) In figure 31 as in figure 30. there is considerable scat- ter; each set of data defines a general trend which tends to parallel equation 48. Again, it was not possible to sort the curves in terms of the third parameter, Froude num- ber, which fact supports the assumption that depth should be a variable of minor importance in this analysis. Equation 47 by no means characterizes the entire spectrum, but if the maximum values of C’ and the di- mensionless wave numbers at which they occur were either constant or functions of the flow and sediment, the spectra would be reasonably well described. Table 4 summarizes pertinent data for such an analysis for the process y=y(x). The maximum spectral ordinate re- lates roughly to flow velocity, as shown in figure 32 (upper). The same weak relation appears to hold between the maximum C'(x) and the dimensionless wave number, 6', at which the maximum occurs, as shown in figure 32 (lower). No apparent relation was found between values of 6' corresponding to maximum values of (}’(x) and any of the flow or sediment characteristics, but it simply STATISTICAL PROPERTIES OF DUNE PROFILES F25 3° ITIIII| I lllllll' 10r— C] 1.0 l— G’ (X) Ru: 17 - Froude number=0.220 Rug 32 Froude number=0.230 A Run 43 Froude number: 0.270 CI 0.1 — Run 46 — Froude number:0.262 Ru: 49 - Froude number=0.396 l I | |1|l 0'3 0.01 FIGURE 30.—Dimensionless spectra for the process y= y(x). may be that there was an insufficient number of observa- wave period, T: l/f, or to the third power of the wave tions to establish any trends. length, L=1/e. The wave celerity c is defined as L/T=f/€, From equations 47 and 4-8, the spectral density func- so that from the equations for the dimensionless spectra, tion C is approximately proportional to the square of the we can conclude that wave celerity is directly proportional F26 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 100,000 | I l r I I [ I 10,000 -- 6’ (f) 1000 T7 0 — Run 19 Froude number:0.220 0 Run 33 " Froude number=0.230 A Run 40 Froude number: 0.270 D Run 44 Froude number=0.262 Run 48 Froude number:0.396 \ 100 lllJLlL 0.00001 FIGURE 3].—Dimensionless spectra for the process )'=y(!). to 61/2. Thus, for constant flow conditions, the small waves move faster than the large waves. This conclusion is supported by Simons, Richardson, and Albertson (1961), who state, “Smaller dunes with their higher velocities overtake the larger dunes.” One arrives at the same conclusion by considering a simple model for sediment transport based on continuity principles, such as the one given by Simons, Richardson, and Nordin (1965), which states that, for ripples or dunes, the transport rate of bedload, qb, is directly proportional STATISTICAL PROPERTIES OF DUNE PROFILES TABLE 4.—Summary offlow characteristics for dimensionless spectra Mean Mean Median 5' Run velocity depth particle F Maximum for (fps) (ft) di:imet)er ' maximum 53 ....... 0.593 0.174 0.30 0.246 29.0 0.0086 46 ....... 1.07 .522 .35 .262 15.5 .012 43 ....... 1.10 .518 .35 .270 22.8 .004 49 ....... 1.62 .521 .35 .396 17.8 .023 32 ....... 2.01 2.36 .24 .230 17.3 .015 17 ....... 2.09 2.80 .24 .220 21.8 .009 to wave height, H, and wave celerity, 0. Suppose that the bed forms are dunes with ripples superposed, and that the dune movement is due entirely to the ripples over- taking the dune crest and depositing material on its downstream face. Then, continuity requires that qb~c1H1~czH2, which states simply that the larger features move at a smaller velocity. Note, however, that equations 47 and 48 say nothing about how the mean wave celerity might vary with vary- ing flow conditions. This matter is considered in the next 50 l l 1 T r l l v 3 r . — CD 2 . 3 O E _ _ >< . < o E O 10 l 1 J 1 L l 4 | 0.4 1.0 4.0 V. IN FEET PER SECOND 50 I l I I i I I I 3 b — o 1 E D ' . g _ _ >< ( a o 2 0 10 1 I l LELl. | 0.004 0.01 0.04 6' CORRESPONDING TO MAXIMUM GU) FIGURE 32.—Relation of maximum value of G’(x) to mean velocity and to e’. F27 section in connection with mean frequencies and wave numbers of the spectra computed from equation 8. Equations 47 and 48 describe only the high frequency or high wave number parts of the spectra. The generality of the results are supported by Hino’s (1968) study of sand wave spectra, in which he showed from dimensional considerations that the wave-number spectra at high wave numbers should follow the wave number, 6, to the minus third power and that the frequency spectra should vary as the minus second power of the frequency. In considering sand wave properties in relation to channel roughness, however, it is the low frequency part of the spectrum that is important, and the dimen- sionless spectra of figure 30 do not reduce the low fre— quency part to a single relation. Engelund (1969) derived a universal dimensionless wave-number spectrum from similitude criteria that is of the form ZgDS C(x): ‘11 o-eV2 V2 o- ZgDS (49) where e is wave number in cycles per foot, C(x) is in (cycles per foot)‘1, d; is an arbitrary function, S is the water-surface slope, and the quantity (2gDS)/V2 is the friction factor. Engelund computed the relation of equation 49 for selected data from this report and plotted the results to define the general shape of the function as shown in figure 33. The results are encouraging, but additional data for greater flow depths probably need to be collected before it will be possible to determine whether or not the relation of figure 33 is superior to the relation of figure 30. OTHER PROPERTIES OF THE SPECTRA The probability distributions of the y values, the char- acteristics of the zero and h-level crossings, and the con- sistent shapes of the dimensionless spectra all point to some remarkable similarities of the bed profiles, irrespec- tive of the size of the channel or of whether the bed forms were ripples or dunes. Indeed, the analysis to this point has been directed primarily toward exposing such simi- larities, and the procedures for standardizing the raw data to zero mean and unit variance and for nondimensional- izing the spectra really are nothing more than procedures for applying appropriate scale factors to the data to facil- itate comparison. Quite often, however, one is more interested in the differences than in the similarities of the bed profiles, and if this is the case, it is more appro- priate to compare the spectra of the records directly in terms of the actual frequency or wave number compo- F28 0.1 0.01 0.001 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS Run 17 Run 32 Run 56 Run 3 Oxlo 0.1 1.0 (IE V2 2905 FIGURE 33.—Dimensi0nless spectrum based on similitude criteria (modified from Engelund. 1969). 10.0 STATISTICAL PROPERTIES OF DUNE PROFILES nents. Figure 34 is an example of such a comparison. Spectra of longitudinal profiles, y=y(x), from each of the four channels, are plotted against wave numbers in cycles per foot. The one-sided spectra were computed from the standardized data, so that the area under each curve is equal to 0.5. The standard deviation, 01,, for each record is shown in the figure. The effects of channel size on the distribution of the variance over the various wave number components is obvious. Several features of figure 34 are particularly interest- ing. First, note that the flow conditions for run 56 and run 24 are quite similar (table 1), yet there are appreciable differences in the spectra of the dune profiles. Run 56 is a ZOO-ft reach of Atrisco Lateral, and the major dif- ferences in fluid and flow characteristics between the field data and fiume data are given below. In the field the velocity is about 5 percent higher and the temperature is lower by 4°C. In addition, a fine sediment load was associated with the field data that was not present in the /—Atrisco Lateral run 56, dunes a}, = 0.296 N I l 8-foot flume run 24, dunes 0’] =0.140 2-foot flume run 49. dunes a] =0.0739 G(x), IN (CYCLES PER FOOT)"1 2-foot flume run 46, ripples 0) =0-0387 8-inch flume - run 53.ripp|es _’ {‘~‘~\(\ay =0.0344 \D-o—Ck m—o.“—I. awn—fig E~*\‘: I 2 3 1 e, CYCLES PER FOOT l I L I L a: 10 2 1 0.5 WAVELENGTH, lN FEET FIGURE 34.—Spectra of longitudinal profiles. _\‘=y(,r), showing effect of channel size and bed configuration. F29 flume. For Atrisco Lateral, the observed sediment con— centration from suspended sediment samples was 1440 mg/l (milligrams per liter) of which 220 mg/l were in the sand sizes, greater than 0.062 mm. For the flume data, the sediment concentration was 164 mg/l, all of which was sand. It is rather surprising that the dune profiles would be so markedly different with only the minor differences in mean flow properties. However, the effects of channel width, of the 4°C difference in temperature, of the 1,200 mg/l fine suspended sediment, and of the minor velocity variations are all undefined. Their combined effect on the bed forms, though, is ap- preciable, and comparison of the spectra indicates that, even if the mean velocity, depth, and slope are similar in the laboratory and the field, there may exist important differences in bed forms. A second point of interest concerns the comparison of run 46 and run 49. Here, the difference in the distri- bution of variance is due strictly to bed configuration and not to channel size. The only difference in the flows for these two runs is the increase in velocity, slope, and sedi- ment transport rate associated with the dune bed con- figuration; all other factors—depth, width, water temperature, and particle size of bed meaterial—were constant. For the dune bed configuration, values of the standard deviation of the bed elevation, the mean wave amplitude, and the mean length between zero crossings are approximately double the values observed for the ripples. Surprisingly, the flow resistance as measured by the dimensionless Chezy coefficient is very similar for these two runs. Finally, a third interesting feature of figure 34 is the indication that, for all the dune records, the variance is distributed generally over components of wavelength greater than 2 feet, whereas for the ripple bed configura- tion, the variance is distributed fairly uniformly over a greater range of wave numbers. The higher wave-number, or shorter wavelength, components contribute an appre- ciable part to the total variance of the profiles of the ripple bed configurations, but their contribution to the variance of the dune profiles is almost negligible. The question of whether the transition from ripples to dunes is gradual or abrupt cannot be answered from these data, but if additional experimentation were to show the transition to be abrupt, then the distribution of variance over the wave-number components would serve as a reliable criterion for distinguishing between ripples and dunes. Spectral analyses of the longer records from Atrisco Lateral also are of particular interest because they permit better definition of the spectra at the lower wave numbers. F30 An example of these analyses is shown for run 3 in figure 35. In part A, the autocovariance function shows an ap— parent cyclic trend with a wavelength approximating the maximum lag of 600 or 200 feet. Inspection of cross sec- tions of the channel every 50 feet along the length of the reach revealed the existence of a meandering thalweg and of alternate bars spaced approximately three to five times the channel width through the entire 4,000-ft reach. The trend in the autocovariance function (fig. 35A) is almost certainly due to the presence of these alternate bars. The spectra for these longer records show the gen- erally decreasing values of C(x) with increasing wave SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS numbers (fig. 353) and are very similar in shape to the spectra shown in figures 27 and 28, but afford much greater detail at the lower wave numbers. Figure 35C shows the spectrum for wave numbers less than 0.1, corresponding to wavelengths of 10 feet or greater, with the wavelengths of the spectral peaks noted. The chi- square test with 20 degrees of freedom to establish a 90vpercent confidence band on the spectral estimates indicates that the average ordinate should fall between 1.85 C(x) and 0.66 C(x). The peak at 200 feet may or may not be related to the meandering thalweg, but there is clearly a significant peak in the spectrum at wave num- 1.0 0.8 _ m g a S. 0.6 a: 3‘ o _ O .4 0 ,9 D 0.2 — —I < 0 i A . IL k L. AW 1 I IV' V V W w ' 50 100 150 200 250 300 350 400 450 500 550 600 —0.2 LAG A I I l l I i 12 ’ ‘ T 42 I I 1 l I I I 7 I a < _l l: ‘ 36 — Z I) E 30 — o. u) '3 O ' 24 _ > 8 Z _ 18 _ 3 40 feet C) — 12— 20f t lllfeet 25 feet ee 13 feet ‘ l \ / | 6 ._ l l l I l l 1 I l 0.6 0 0.02 0.04 0.06 0.08 0.1 WAVE NUMBER (6), IN CYCLES PER FOOT B C FIGURE 35,—Autocovariance function (,4) and spectrum (B and (I) of longitudinal profile. _y=y(.r), for run 3. Atrisco Lateral. C is an expanded version of part ofB to show greater detail for thr- low wave numbers. STATISTICAL PROPERTIES OF DUNE PROFILES bers less than 0.01. All other peaks shown on the spectrum of figure 35C are considered significant with the exception of the one at 13 feet, but the wavelengths at which these significant peaks occur were not found to correlate with any recognizable features of the bed profile. There is, of course, no reason to suspect that these peaks in the spec- trum should relate to the lengths of the physical waves on which the analysis is being performed, although it has been observed that for dune records there sometimes is a correlation between the wavelength corresponding to the peak in the spectra and the average dune length (Nordin and Algert, 1966; Ashida and Tanaka, 1967). As a final consideration of the properties of the spectra, it might be worthwhile to explore further the relation between the characteristics of the spectra and the physi- cal characteristics of sand waves. It was previously shown (fig. 22) that a correlation exists between the average amplitude, a, and the standard deviation of the bed ele- vation, (Ty, which is related to the spectrum of y through equation 5. The reciprocal of the mean frequency or wave number from equation 8 is the mean period or wavelength of the spectrum, and this value relates reasonably well to the mean period or wavelength defined from the zero- crossing analysis, as shown in figure 36. Thus, it is pos- sible to relate empirically the spectral properties and the observed properties of the sand waves. Ashida and Tanaka (1967) used spectral analyses for determining the propagation velocity of sand waves by plotting the wavelength of the maximum spectral ordinate 100 r I l r I III L|J _ Z a) P _ 3 U l- ' ‘5’ _ o (I) . "‘ z o g . .09 . 0 NE 9 . ' Ea I—g _ o I _ n: o 08 '0. “JD 0 o :2: O o . o o I- L o - Q o 0 I In . . 0 < 0.5 . E > o < 10 l L i i 4 l l 1 10 100 MEAN WAVELENGTH OR WAVE PERIOD OF SPECTRA FIGURE 36.—Relation between average distance or time between suc- cessive zero up crossings and the mean wavelength or wave period of spectra from equation 8. Dimensions are in units of lag intervals. F31 for the process y(x) against the wave period for the maximum spectral ordinate of the process y(t). For the records analyzed in this study, some of the corresponding records of y(x) and y(t) possessed maximum ordinate values of their spectra at the origin; therefore, this method could not be used. In addition, no consistent relations were found between the peaks in the spectra and the average wavelengths or periods of the ripples and dunes. Consequently, the procedure used by Ashida and Tanaka (1967) is not recommended. However, from the relation in figure 36, it should be possible to determine the mean wave celerity either from the mean length and period found in the zero-crossing analysis or from the mean wave number or frequency of the spectra by using equa- tion 8. Table 5, which shows a comparison of mean wave celerities computed by these two methods, indicates that values of 6 obtained by the two methods are comparable. TABLE 5,—Comparison of wave celerities Run From zero crossing From equation 8 _ B .d y(x) y”) L T 6: UT 1. =1/E T: l/f c=f7 E configfiration (ft) (min) (fpm) (ft) (min) (fpm) E ...... 19... 8.45 29.3 0.233 7.62 42.5 0.179 Dunes. 32 ...... 33... 4.78 16.6 .288 5.45 26.8 .204 D0. 43 ...... 4-0. .. 1.36 14.3 .0952 1.75 29.7 .0590 Ripples. 46 ...... 44-. .. 1.01 27.4 .0368 1.24 38.8 .0320 D0. 2.56 25.5 .100 3.00 32.4 .0926 Duties. 4-9 ...... 48... The data in table 5 also give an indication of how the mean wave celerity varies with mean wave number for different flow conditions. In the previous section, it was established that for a constant flow condition, the wave celerity of the different wave—number components varied directly as the square root of the wave numbers. This relation is shown schematically in figure 37A. In figure 373, the mean wave celerities computed from equation 8 are plotted against mean wave number from the spectral moments. Here we see that, with increasing flow velocity, the average wave celerity varies inversely with wave number or directly with wavelength. This implies that the mean wave celerity is independent of frequency; or on the average, for these data it took just as long for a ripple to move past a given point as it did for a dune. The importance of the relations in figure 37 is in the fact that these relations permit determining the properties of the process, y(t), from the properties of only the longi- tudinal profiles, y(x). If the spectral properties of y(x) are known, then the spectral properties of y(t) can be determined from the relation in figure 37A and equations 47 and 48. If the mean wave number for the process y(x) is known, then the mean frequency or wave period of y(t) can be established by the relation in figure 37B, F32 § E LIJ d c z 51/2 0 '$‘ < 3 WAVE NUMBER (£://L) A 0-3 r I I I I I I I I K “J O. '— m .- UJ LL 120 Z c _ .7, A: N l0 2 V to 8 t 5 '; “ 0.1 - E a _ g d 5 E U ' > a ' 5 < __ LL 3 w _ o < I m _ > < 0.03 I I I I I l P 1 I 0.1 1.0 AVERAGE WAVE NUMBER(F). IN CYCLES PER FOOT 8 ¢ FIGURE 37.—Relation of wave celerity, C, to wave numer, e. A, for various wave-number components of a single record, flow conditions constant. B. for average wave numbers from the spectral moments of records obtained under different flow conditions. and the mean particle rest period at any level it and the conditional probability distributions for the rest periods at any level It can be determined directly from the relations in figure 12 and equations 14- and 33. Note, however, that the relation in figure 37B is no doubt a consequence of the sediment transport rates associated with the particular flow conditions examined here, and it is not known if the relation is generally applicable for greater flow depths. O’Loughlin and Squarer (1967) and Squarer (1968) have urged that the standard deviation of the bed eleva- tion and some characteristic wave length from the spec- trum of the bed profiles be used to describe the geometric properties of sand waves, rather than simply the mean lengths and heights. Because no consistent terminology for describing bed configurations or methods for com- SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS puting average wavelengths and wave heights exists in the literature, it is very difficult to evaluate the results of different investigators. Certainly, then, it is desirable to develop some standard and rigorous method for de- scribing the properties of the bed profiles that will permit comparison of different studies, and perhaps the standard deviation of the bed elevation and the reciprocal of the mean wave number of the spectrum from equation 8 would serve that purpose. In addition, it might be useful to specify the value of 8 (eq. 20), which generally may be interpreted as a measure of the root-mean-square width of the variance spectrum (Cartwright and Longuet- Higgins, 1956, p. 216). Values of these parameters and of othermeasures of wavelengths and heights are given in tables 6 and 3. CROSS CORRELATION AND CROSS-SPECTRAL ANALYSIS Several interesting properties of the sand waves can be investigated using the techniques of cross correlation and cross—spectral analysis. Cross correlation is the simpler to use and admits to direct physical interpre- tations. Figure 38 shows the cross correlograms for cor- relations of run 8 with each of the runs 9 through 15. The profiles are all for the same reach of flume (see table 1) and were obtained 5 minutes apart. If the distance of the peak of the correlogram from the origin is plotted against time (fig. 39A), the slope of the trend line, 7 feet per hour, may be taken as the mean speed of movement of the dunes. An independent check on this figure is provided by the zero—crossing analysis, where the mean dune length for runs 8 through 15 is 5.7 feet and the mean period of runs 4 and 19 is 0.72 hours; these data give a dune velocity of about 8 feet per hour. The general trend for the attenuation of the peak value of the correlation with time (fig. 398) gives an indication of the rate of change in shape of the dune profiles. The dune profiles are assumed to be uncorrelated when the maximum value of the correlation function is 0.3 or less. The value of 0.3 is chosen because cross correlation of any two profiles taken at random from a group collected dur- ing approximate equilibrium flow conditions shows a maximum correlation generally less than 0.3. Then, extrapolating figure 393, it is inferred that the profile virtually loses its identity in about 90 minutes, or in about the same time for the average-size dune to migrate twice its own length. From figure 38, it is seen that the maximum value of the cross-correlation function for runs 8 through 15 is approximately the same as the maximum value for runs STATISTICAL PROPERTIES OF DUNE PROFILES F33 TABLE 6. —Summary of wave properties [Average length is troughAto-trough distance; height is difference in elevation. crest to trough] Wave characteristics Height in feet Ripple index Run Average Average Coefficient Coefficient Coefficient length. in wave period. of Average of Average of feet in minutes variation variation variation 6.06 0.533 0.370 0.643 22.8 0.857 6.14 .535 .368 .655 22.7 .815 5.28 .535 .408 .597 17.2 .764 4 .................................... .763 .214 1.43 163. .786 5.07 .658 .225 .571 25.7 .678 3.73 .700 .184 .377 21.6 .733 4.24 .604 .201 .388 22.2 .575 5.16 .408 .341 .514 22.3 .870 4.66 .553 .269 .535 21.7 .772 3.89 .742 .268 .509 17.5 1.05 5.13 .524 .305 .482 20.5 .722 3.89 .757 .251 .477 18.8 .916 6.44 .340 .384 .468 19.4 .590 4.49 .812 .264 .616 21.7 .979 6.18 .462 .364 .483 18.3 .513 5.06 .575 .315 .915 23.7 .739 4.84 .779 .265 .547 25.0 1.23 4.54 .698 .297 .483 17.8 .821 ..................... .664 .149 .229 175. .674 4.31 .475 .261 .473 18.6 .429 3.55 .502 .221 .506 18.4 .671 3.49 .564 .265 .476 16.2 .826 3.67 .574 .257 .524 16.0 .584 4.40 .471 .296 .578 19.2 .770 4.31 .595 .316 .484 15.8 .627 4.34 .532 .300 .546 19.0 .897 4.89 .................. .489 .367 .506 16.5 .668 4.55 .................. .515 .276 .538 18.7 .536 4.77 .................. .528 .253 .494 23.9 .704 3 85 .................. .649 .165 .347 25.6 .727 4 12 .................. .754 .161 .450 27.5 .868 4 72 .................. .445 .260 .506 21.3 .577 ........................... 16.3 .941 .133 .216 127. .929 4.36 .................. .521 .200 .411 27.4 .735 4.59 .................. .562 .255 .645 25.5 .783 3.27 .................. .538 .173 .381 21.6 .647 4.64 .................. .428 .204 .446 26.7 .576 4.28 .................. .510 .175 .380 26.5 .559 3.78 .................. .545 .185 .457 21.6 .549 ........................ 30 2 .426 .0783 .277 399. .426 1 20 .................. .484 .0922 .328 14.7 .648 1 15 .................. .568 .0902 .288 13.4 .579 1 24 .................. .606 .0913 .307 14.3 .679 ............................. 40 4 .744 .0750 .353 577. .802 1 24 .................. .534 .0856 .268 14.9 .545 1 34 .................. .542 .0827 .216 15.9 .422 1 28 .................. .518 .0874 .318 15.7 .583 ........................... 17 7 .514 .111 .491 183. .574 2 73 .................. .408 .167 .454 18.7 .642 2 75 .................. .424 .149 .482 24.4 .836 3 15 .................. .630 .114 .369 27.4 .589 . 498 .................. .353 .0609 .752 13.7 1.08 440 .................. .485 .0520 .752 14.3 .697 8 and 9. Even though the maximum cross correlations are about the same. it is assumed that the distributions of variance over the wave-number components should be appreciably different for the two series of runs because the waves change shape somewhat as they shift down- stream. In other words. the general shapes of the cross correlograms are not the same even though their maxi— mums are equal. Plots of the coherence function, 3,2, F34 0.6 Runs 8 and 9 0.4 I /—l\l 1/02 \_/ o ' ‘ v -0.2 Runs 8 and 10 0.6 r/ 1 0‘4 - \ /.2 _ L I I I 0 _0_2 I— —0.4 c Runs 8 and 11 0'“ \l . 0.4 - Runs 8 and 13 0'4 \ 0.2- I I I I I \J/ —0.2 - —0.4 0.5 Runs 8 and 14 0.4 '- 0.3 - 0.2 - 0.1 k l I l I l l 0.6 Runs 8 and 15 0.4 - : /\ O. 0.2 _ l 4 1 l I —40 -30 — 0 —10\§/ 10 20 30 40 L -0.2 l LAG FIGURE 38.—Cross correlograms for run 8 with runs 9 through 15. and the gain function, A, in figure 40 support this assump- tion. The general decrease in both coherence and gain from the cross-spectral analysis of runs 8 and 15, as opposed to the values for runs 8 and 9, shows that the SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS wave-number components of the two records 8 and 15 are virtually uncorrelated. The cross correlation and cross—spectral analysis also proved useful in investigating the three-dimensional properties of the dunes. Run 17 was a profile y(x) taken down the centerline of the 8-ft fiume. Runs 16 and 18 were profiles taken 2 feet on either side of the centerline. The correlograms and the spectra for the individual profiles (fig. 4-1) do not suggest any appreciable differ- ences in the profiles. A major part of the variance in all profiles is contributed by the shorter wave-number com- ponents corresponding to wavelengths generally greater than 4 feet. The cross correlogram for runs 16 and 17(fig. 42) shows that the two profiles, taken 2 feet apart along the same reach of flume, are practically uncorrelated, indicating that the sand waves certainly are not long crested. How- ever, the cross correlogram for runs 17 and 18 (fig. 4-2) 6 I l l E Lu 4— . a LL 3 o LIJ o z < I— ‘2 o 2" . _ o C I I | MAXIMUM CORRELATION O L I 1 0 10 20 30 40 TIMEIN MINUTES 5 FIGURE 39. —A . Distance from the origin of the maximum cross correla- tion as a function of time. B. Change in maximum correlation with time. STATISTICAL PROPERTIES OF DUNE PROFILES F35 I I l l 0.8 T I I 0.6 _ _ ‘t 0.4 _ 0.2 — _ O0 0 l E ii) WAVE NUMBER (6), IN CYCLES PER FOOT FIGURE 40.—Colierence. W. and gain functions, A. for (left) runs 8 and 9. (right) runs 9 and 15. O 10 20 30 40 50 60 0 10 20 N O 1 J ,_. U1 V 1 01 u t v 0 0.5 1.0 O G (X),|N (CYCLES PER UNIT LAG)-1 8 0.5 1.0 O 0.5 1.0 A FIGURE 4l.—Correlograms and spectra of y:y(x). A. Run 16. 2 feet left of centerline. B. Run 17. centerline. C. Run 18. 2 feet DIMENSIONLESS WAVE NUMBER (E/emfl) 8 right of centerline. C shows a somewhat better correlation, suggesting that the dunes along the centerline of the flume extend to or at least influence the dunes along the right side of the Hume. The coherence diagrams for the spectral analyses of the two sets of data (fig. 43) show the same effect; values of the coherence function 3/2 for runs 17 and 18 are approxi- mately twice those for runs 16 and 17. PREDICTION In previous sections, the problem of predicting the properties of the bed profile from only the characteristics of the flow and the sediment was considered briefly in terms ofthe Markov model and the dimensionless spectra. Neither of these approaches was found to be completely satisfactory. At this point, some additional aspects of predicting the properties of the bed profiles will be considered. Under the assumption that the bed profiles can be ap- proximated by a random Gaussian process, only three factors are needed to predict the mean values of durations between zero and h-level crossings and the distribution of maximum and minimum 3/ values between zero crossings. These factors are the variance of the bed profile, 0'5, the second derivative of the covariance function at the origin, F36 Runs 16 and 17 0.3 > 0.1 / O -0.1 Runs 17 and 18 0.5 —60 —5‘0 —40 —30 —’20 —10 0 10 20 \30 \/ 40 50 0 —O.2 LAG FIGURE 42. —Cross correlograms. 0.3 I 0.2 - 0.]- Runs 16 and 17 72 0.4 I 0.3 - 0.2 — 0.1- Runs 17 and 18 0 0.5 DIMENSIONLESS WAVE NUMBER (E/emax) FIGURE 43.—Colierence diagrams. 1.0 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS ¢"(0) , and the parameter 82. The parameter (1)”(0) enters only in calculations of the mean duration between zero crossings, so that it could be replaced by E{lo}. Values of 62 approached unity, and therefore as a first ap- proximation it can be considered equal to one, and the prediction problem reduces to determining try and "(0) 01' E{ 10} . Definition of the dimensionless spectra in terms of flow parameters would permit determination of ¢"(0) and E{ lo}, and this approach is favored by the writer. Some simple alternatives are to relate lo directly to flow param- eters or to find a relation between 10 and the standard devi- ation of the bed profile; such a relation would be analogous to the ripple index commonly used in geologic literature. In either event, it would still be necessary to determine (Ty, because the dimensionless spectra are based on the standardized data. As we might expect, the standard deviation of the bed elevation, O'y, relates roughly to flow depth (fig. 44A) or to the unit water discharge (fig. 448). Data for these figures are summarized in table 7 and include average values from this study and values reported by Nordin and Algert (1966). It was not possible to reduce the scatter in these relations by consideration of other hydraulic or fluid vari- ables. The point falling farthest to the left in the figures may be unrepresentative, because the bed profiles (runs 52 and 53) were collected after cessation of sediment motion and probably represent residual features from higher velocity flow. (See Rathbun and Guy, 1967, for details of this experiment.) All things considered, the scatter of the points in figure 44 is neither unexpected nor discouraging. The data rep- resent observations from five different flumes and two field channels. Two of the flumes used a sand feed system and three were of the recirculating type. In all the experi- ments except those performed by Algert (1965) in the 0.4-foot flume, information on the bed configurations was a consideration peripheral to the main objectives of the study. A number of unknown factors may contribute to the scatter in the data, such as flume entrance and exit characteristics, operating procedures in the experiment, imposed fine-sediment load (in the field case), and particle- size distribution of the bed material. The one other property of the bed profiles that is of most interest is the probability distribution of the dura- tions of upward excursions of the process y(t) above the fixed level h, which is the conditional probability distribu- tion of the rest period of a particle, given that it is de- posited on the downstream face of a dune at the level it. The gamma distribution with parameters that relate to h, as shown in figures 12 and 13, is an attractive possibility. However, before this approach can be recommended, it is STATISTICAL PROPERTIES OF DUNE PROFILES F37 1.0 l o I I. 0 3 L E g; I 0.. i :' LL 2 o O O 0 n. o o B o an0.1 — _ _ _ LL. 3 ° ' 9 a . o o D . o D o I: a < D Z < t— u) 0.01 l l 0.1 1.0 10.0 0.1 1.0 10.0 MEAN DEPTH (D), IN FEET A UNIT DISCHARGE(Q). IN CUBIC FEET PER SECOND PER FOOT 8 FIGURE 44. —.4. Relation of standard deviation of bed profiles. a”. to mean How depth, D. B, Relation of standard deviation of bed profile. 0'”. to unit water discharge. 0. necessary to verify both the gamma distribution and the relation of figure 12 with additional observations of the process y=y(t). In summary, the problem of predicting the properties of interest of the bed profiles is still not solved, but the re- sults of this study have suggested several promising ap- proaches. Some crude empirical relations, such as those of figures 12, 13, 26, 37 and 44, permit approximations to to be made of most of the properties of interest, but the need for both refined theoretical models and additional experimental data is obvious. SUMMARY AND CONCLUSIONS DISCUSSION OF RESULTS The application of statistical techniques to analyze the properties of sand waves is a relatively recent under- taking, and therefore it is perhaps difficult to evaluate objectively some of the ramifications of this investiga- tion. Nonetheless, three implications of the results seem to the writer to be of particular importance and to merit further discussion. TABLE 7.—Average values of observed variables Channel V D W S T 5.. (7,, Avg (1 + 1.. Remarks (fps) (ft (It) (°C) (mm) (It) (fit 1ft) Atrisco ...................... 2.16 2.20 55 0.00057 19 0.23 0.259 0.277 4.48 Dunes. Atrisco ...................... 2.11 2.30 55 .00055 20 .23 .276 .287 4.61 D0. Atrisco ...................... 2.08 2.29 55 .00058 20 .23 .270 .302 3.90 D0. 8-ft Hume .................. 2.09 2.80 8 .00063 20 .24 .169 .214 2.95 Dunes; recirculating system. 8-ft flume .................. 2.01 2.36 8 .00056 24 .24 .127 .146 2.28 D0. 2-ft flume .................. 1.62 .521 2 .00212 20 .25 .0700 .0806 1.42 Do. 2-ft flume .................. 1.10 .513 2 .00088 20 .35 .0432 .0416 .58 Ripples; recirculating system. 2-ft Hume .................. 1.07 .522 2 .00088 20 .35 .0390 .0408 .54 o. 0.67-ft Hume ............... .80 .197 .67 .00148 20 .30 .0404 .0400 .36 Ripples; sand feed system. Bernardo* .................. 3.62 2.60 70 .00058 8.34 .23 .647 ........................... Dunes. Bernardo* .................. 2.48 4.15 70 .00058 8.34 .23 .745 ............. Do. 8-ft Hume* ................. 2.11 1.05 8 .00134 16.7 .28 .175 ............. Dunes; recirculating system. 8-11 fiume* ................. 1.91 .670 8 .00136 17.8 .28 .115 ................... D0. 0.4-ft flume* ............... 1.81 .580 .4 .0044 18.4 .34 .0478 ........................... Sand feed system. 0.4-ft Hume* ............... 1.78 .485 .4 .0038 15.6 .34 .0330 ........................... D0. 0.4-ft fiume* ............... 1.74 .400 .4 .0037 17.8 .34 .0270 ........................... Do. *Data are from Nordin and Algert (1966). F38 The first important conclusion drawn from these in- vestigations is that the properties of the profiles obtained in the laboratory flumes are all very similar, regardless of the size of the flume or of whether the bed configura- tions are ripples or dunes, provided that scale effects are properly taken into consideration. The scale effects seem to be completely accounted for by standardizing the raw data to zero mean and unit variance and by ex— pressing the length of h-level crossings as a ratio of the mean length between zero crossings, or by forming dimen- sionless parameters in terms of the flow properties, as in the case of the spectra. This means that certain simple properties, such as the average values of the conditional probability-density functions of rest periods, can be modeled in a ripple bed configuration or in a very small flow system, and the results can be extrapolated to dune configurations of much larger flow systems. Similarity of the properties of the ripple and dune profiles does not imply that there are no differences in these features but only implies that their general shape and method of movement are similar, as noted by Taylor and Brooks (1961). In fact, the comparisons of distribu- tions of variance over the wave-number components shown in figure 34 support very strongly the notion that there are appreciable differences. The major differences between ripples and dunes are described in detail by Simons and Richardson (1966) and need not be con- sidered here. In addition, there were important differences between the flume and field data for dune bed configurations. The longer records from Atrisco Lateral reflected the influence of a meandering thalweg and of accompanying large alternate bars that generally were not present in the flumes. Simons and Richardson (1966) have noted that alternate bars do form in flumes, but for the flume data analyzed here, the width-to-depth ratio was not great enough to permit the bars to develop significantly. A second important implication arises in the develop- ments leading to figures 30 through 33 of the dimension- less spectra. These figures show that the spectral representations of the processes can be determined as unique functions of the flow, fluid, and sediment prop- erties. It was fortunate for these studies that the water temperatures and sediment sizes varied over rather narrow ranges, because this permitted expressing the dimensionless spectra in extremely simple form. On the other hand, because of this limited range of conditions, it was not possible to define adequately the shapes of the spectra. Nevertheless, the results are encouraging, so far as they were carried, and they point the way to future experimental studies that will permit a better definition of the spectra. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS However, the most important result by far is the demon- stration in figures 6—9 and 15-17 that the properties of the profiles can be estimated by theoretical considera- tions of fairly simple models. Certainly, the assumption that the processes y(x) and y(t) are Gaussian is a crude approximation, but the results obtained using this model are reasonable and consistent. In one important aspect, this study was unsuccessful. It was not possible to relate uniquely the statistical properties of the bed profiles to the characteristics of the flow. However, some simple empirical relations were considered that will permit predicting approximately many of the properties of interest. The most important relations in this regard are shown in figure 44, which gives 0'y as a function of either depth or unit water dis- charge, and figure 25, from Nordin and Algert (1966, p. 109), which shows values of the correlation function at zero, one, and two lag intervals as functions of unit water discharge. These values, along with the length of profile record, permit calculations of most of the factors consid- ered in the zero and h-level crossing analysis and the approximations of [3/13, as given by equations 15 and 16. However, the relations of figure 25 apply only if the lag interval is selected so that it bears a constant ratio to the standard deviation, cry. CONCLUSIONS In this study statistical properties of streambed pro- files from four different size channels are compared by the techniques of time-series analyses and by a considera- tion of the mean values and distributions of zero and h- level crossings, the durations of upward excursions of the records y(x) and y(t) above a fixed level h, and the distribution of maximum y values between successive zero crossings. The principal conclusions drawn from the study are the following: 1. No appreciable differences in the statistical properties of the profiles from the flumes could be attributed to flume size or to whether the bed forms were ripples or dunes, provided that the raw data were standardized to zero mean and unit variance and that the length scales were expressed as ratios of the mean length between zero crossings. In addition, only minor differences were noted between the properties of the longitudinal profiles, y=y(x), and the properties of the profiles, y=y(t), obtained by sounding continuously in time at a fixed point. Longer records of both types, particularly the time records, are required to establish if the differences are real or apparent. 2. Spectra of the longer records from Atrisco Lateral appeared to reflect the influences of a meandering STATISTICAL PROPERTIES OF DUNE PROFILES thalweg and large alternate bars that were not present in the flume data. 3. By dimensional analyses, forms of dimensionless spectra were derived which describe reasonably well the observed forms in the higher frequency and wave number regions. From the equations of the dimensionless spectra, it was established that, for constant flow conditions, the celerities of the individual wavelength components vary directly as the square root of the wave numbers. 4-. From the mean spectral moments, it was shown that the mean wave celerity varied inversely as the mean wave number for the different flow conditions con- sidered. This relation, together with the relation for celerity of wave-number components under con- stant flow conditions, permits determining the prop- erties of the process, y(t), from the properties of the longitudinal profiles, y(x). 5. The techniques of cross-spectral analysis were found useful for defining the mean rate of shifting of ripples and dunes and investigating their three- dimensional properties. 6. Values of the bed elevation follow an approximate Gaussian distribution. For a Gaussian process of known covariance function, the expected number of zero or h-level crossings, the expected length between crossings, and the mean duration of upward excursions of the process y(t) above the fixed level h can be computed. The comparison of observed and computed values shows good agreement for positive values of h and indicates systematic deviations for values of h below the mean bed elevation. The mean duration of upward excurions of the process y(t) is the mean rest period of a particle at the level h. 7. The distributions of the distances between zero cross- ings, l”, are approximately exponential. Values of the durations of upward excursions of y above the level h follow a gamma distribution with parameters that relate to h, as shown in figures 10 through 13. 8. The distributions of maximum values of 3/ between zero crossings represent the distributions of scour and fill associated with the formation and migration of sand waves. The sand waves are not symmetric about the mean bed elevation. The positive maxi- mums, a+, are distributed exponentially and the negative maximums, a—, are distributed according to a Gaussian distribution. Both distributions are functions of the standard deviation of the bed elevation, o-y, which relates approximately to mean flow depth or unit water discharge (fig. 44-). 9. Finally, the results of this study show that some of the distributions entering the two-dimensional model of sediment transport (Sayre and Conover, 1967) and F39 most properties of the dune profiles that are of inter- est can be determined from theoretical considera- tions of fairly simple models. RECOMMENDATIONS FOR FUTURE STUDIES The results of this study suggest a number of areas for future investigations. Four, in particular, appear especially promising. These are: 1. Studies should be undertaken to include fluid and sedi- ment properties in the dimensionless spectra and to determine more accurately the dimensionless wave numbers at which the peak spectral ordinates occur. 2. An investigation should be made of the possibility of incorporating the distribution of wave height and wavelength and the relation of wave celerity to wave- length components (fig. 37) into a continuity-type bedload transport relation based on size and rate of shifting of the sand waves. 3. Experiments should be designed to obtain longer rec- ords of y=y(t) so that the probability distributions of particle rest periods (the durations of upward ex- cursions) can be adequately defined. 4. Models other than the simple Gaussian model should be investigated as possible representations of the processes y(x) and y(t) to see if more accurate pre— dictions of the properties of the bed profiles can be obtained theoretically. In addition, it should be possi- ble to investigate some models by simulation tech- niques. One such possibility would be a process of the form y(t) =Ip cos (Ay-l- 0), where p, A, and 0 are all random variables of some specified distribution. In addition to the above studies, it is necessary to ob- tain reliable field records of bed profiles to permit extend- ing these studies to a greater range of flow COnditions. Records of the- process y=y(t) are especially lacking, and many existing longitudinal profiles suffer from inade- quate horizontal control. As noted in the section “Data and analysis,” reliable relations between the statistical properties of the pro- files and the characteristics of the flow still remain to be developed. Empirical relations exist, but they are far from satisfactory for predictive purposes. Finally, detailed descriptions of bed profiles are of value only if they lead ultimately to a better understand ing of sediment transport processes. It is hoped that the results of this study and of future studies along the lines outlined above will contribute to such an understanding. REFERENCES Algert. J. H., 1965, A statistical study of bed forms in alluvial channels: Colorado State Univ. Rept. CER65JHA26, 31 p., Fort Collins, Colo. Ashida, Kazuo, and Tanaka, S., 1967, A statistical study of sand waves: Internat. Assoc. Hydraulic Research Cong, thh, Fort Collins, Colo., Sept. 11—14, 1967, Proc., v. 2, p. 103—110. F40 Bendat, J. S., and Piersol. A. (2.. 1966. Measurement and analysis of random data: New York. John Wiley & Sons. Inc., 390 p. Blackman, R. B.. and Tukey. .l. W.. 1958. The measurement of power spectra: New York, Dover. 190 p. Cartwright, D. E.. and Longuet-Higgins, M. S.. 1956. The statistical distribution of the maxima of a random function: Royal Soc. [London] Proc.. ser. A. v. 237, p. 212—232. Colby, B. R.. 1964, Discharge of sands and mean-velocity relationships in sand-bed streams: U.S. Ceol. Survey Prof. Paper 462-A. 47 p. Cramer. Harald. 1964. Model building with the aid of stochastic proc- esses: Technometrics. v. 6, no. 2. p. 133—159. Cramer, Harald and Leadbetter. M. R.. 1967. Stationary and related stochastic processes: New York. John Wiley & Sons. Inc.. 348 p. Engelund. F. A., 1969. On the possibility of formulating a universal spectrum for dunes: Basic Research l’rog. Rept. 18, p. 1-4. Hy- draulic Laboratory, Technical University of Denmark. Copenhagen. (Iranger, C. W. J.. and Hatanaka. Michio. 1964. Spectral analysis of economic time series: Princeton. N.J., Princeton Univ. Press. 299 p. Hino. Mikio. 1968. Equilibrium-range spectra of sand waves formed by flowing water: Jour. Fluid Mech., v. 34, pt. 3. p. 565-573. Karaki, S. 5., Gray, E. E.. and Collins, Jack. 1961. Dual channel stream monitor: Am. Soc. Civil Engineers Proc.. v. 87. no. HY6. p. 1-16. Longuet-Higgins. M. 5., 1958. On the intervals between successive zeros of a random function: Royal Soc. [London] Proc.. ser. A. v. 246. p. 99—118. 1962, The distribution of intervals between zeros of a stationary random function: Royal Soc. [London] Philos. Trans. ser. A. v. 254. p. 557—599. 1963. Bounding approximations to the distribution of intervals between zeros of a stationary (laussian process. in Rosenblatt, Murray. ed.. Time series analysis: New York, John Wiley & Sons. p. 63—88. Nordin, C. F.. and Algert. J. H.. 1966. Spectral analysis of sand waves: Am. Soc. Civil Engineers Proc.. v. 92, no. HYS. p. 95-114. Nordin. C. F.. Simons, D. B.. and Richardson. E. V., 1965. Interpreting depositional environments of sedimentary structures: Colorado State Univ. Civil Eng. Rept. CER65CFN-DBS-EVR15. 17 p.. Fort Collins, Colo. 0’l.oughlin. E. M.. and Squarer, David. 1967. Areal variations of bed- form characteristics in meandering streams: Internat. Assoc. Hydraulic Research Cong, 12th. Fort Collins. Colo.. Sept. 11—14. 1967. Proc.. v. 2. p. 118—127. Plate, E. J.. 1967. Discussion of “Spectral analysis of sand waves" by C. F.. Nordin. Jr. and J. H. Algert: Am. Soc. Civil Engineers Proc. v. 93, no. HY4. p. 310—316. Rathbun. R. E., and Guy. H. P., 1967, Measurement of hydraulic and sediment transport variables in a small recirculating Hume: Water Resources Research, v. 3, no. 1. p. 107-122. Rice. S. 0.. 1954. Mathematical analysis of random noise. in Wax. Nel- son. ed., Selected papers on noise and stochastic processes: New York, Dover. p. 133-294. Rodrigues-Iturbe, Ignacio, 1967. The application of cross-spectral analysis to hydrologic time series: Colorado State Univ. Hydrology Paper 24, 46 p.. Fort Collins, Colo. Sayre, W. W.. and Conover. W. J., 1967, General two-dimensional stochastic model for the transport and dispersion of bed-material sediment particles: Internat. Assoc. for Hydraulic Research Cong., 12th. Fort Collins. C010,. Sept. 11—14, 1967. Proc., v. 2. p. 88-95. Siddiqui, M. M.. 1962. Some statistical theory for the analysis of radio propagation data: [U.S.] Natl. Bur. Standards .lour. Research. v. 661), no. 5. p. 571—580. Simons, D. B.. and Richardson, E. V.. 1966. Resistance to flow in allu- vial channels: U.S. (Ieol. Survey Prof. Paper 422-J. 61 p. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS Simons, D. B.. Richardson, E. V.. and Albertson. M. L.. 1961, Flume studies using medium sand (0.45 mm): U.S. (leol. Survey Water. Supply Paper 1498-A, 76 p. Simons, D. 3.. Richardson. E. V., and Nordin. C. 17.. 1965. Bedload equation for ripples and dunes: U.S. (Leol. Survey Prof. Paper 462—H. 9 p. Squarer. David, 1968. Discussion of “Relation between bed forms and friction in streams” by V. A. Vanoni and l.. S. Hwang: Am. Soc. Civil Engineers Proc.. v. 94. no. HYl. p. 327-330. Taylor. R. H.. and Brooks. N. H.. 1961, Discussion of “Resistance to flow in alluvial channels” by D. B. Simmons and E. V. Richardson: Am. Soc. Civil Engineers Proc., v. 87. no. HY]. p. 246-256. Tick. L. J.. and Shaman. Paul. 1966. Sampling rates and appearance of stationary Gaussian Technometrics. v. 8. no. 1. p. 91—106. Yaglom, A. M.. 1962, An introduction to the theory of stationary random functions: Englewood Cliffs, N.J.. Prentice-Hall, Inc.. 235 p. [)I‘OCCSSCSZ PLANNING OF DATA REQUIREMENTS This appendix gives some approximate guidelines for planning the length of records required for the various analyses considered in the text. The statistical basis for determining record length and the computa- tional procedures are given by Bendat and Piersol' and will not be re- peated here. The computer programs used in this study are available from the writer or from Mrs. Lois Niemann. Civil Engineering Depart- ment, Colorado State University. The computational procedures used in this study can be applied to any continuous record of streambed elevation. provided that the record meets the necessary conditions for stationarity. From a practical point of View. this means that. for longitudinal profiles. the channel cross section should not vary appreciably along the channel and that, for either longi- tudinal or time records, the flow and sediment transport rates should be approximately constant during the period of observation. We consider here only flow conditions which occur where well- defined sand waves are know to be present at the streambed. that is. only lower regime flow. The bed configurations for lower regime flow are ripples. dunes. bars. and combinations of these features (Simons and Richardson 2). In the following discussion the computational proced- ures for spectral analysis of a single record first are outlined. Next are given some rough guidelines for determining the length of record and the spacing of observations for converting a continuous record to dis- crete data points for spectral analysis. Finally. the record length and spacing of data points for other types of analysis, such as estimating the mean lengths between zero and h-level crossings. are considered. COMPUTATIONAL PROCEDURES A continuous record of bed profile. y=y(x). of length L,- is converted to discrete data points by sampling the continuous records at intervals Ax=h ft. so that the sampling rate is l/h samples per ft. The entire record is converted to N discrete data points, y;. i=1, 2. . . ., N. We consider the entire sequence of y.- values to have zero mean and unit variance. The covariance function corresponding to equation 2 of the text is computed by the formula 1 .V—s ¢UU(5)=N_SZ}’ny, (1) 1+3 ”:1 for s=0, 1, . . ., m, where m is the maximum number of lags. ‘Bendal. 1.5.. and Piersol. ’\. (L. 1966. Measurement and analysis of random data: New York. John Wiley & Sons. Inc.. p. 278—320. 2Simons, D. B.. and Richardson. E. V.. 1966. Resistance to flow in alluvial channels: I .S. (it-oi. Survey Prof. Paper 422-]. 61 p. STATISTICAL PROPERTIES OF DUNE PROFILES Next, the finite cosine series transform function of the autocovari~ ances is computed from - - 1m 0(5) =E’diU) cos 7 (2) fors=0. 1, 2, . . ., m. In the above, 43(0) =¢,.(0), $(t)=2¢..(i). where i=1, 2, . . ., m—l, and (3) $(m)=¢..,2,000 ____________________________________________________________________________________ 4 4—6. Photographs showing— 4. View downstream of test reach at Blue Creek ________________________________________________ 6 5. View upstream of Blue Creek showing the site at the downstream end of the test reach where particle orientation was studied _______________________________________________________________ 7 6. Weight-mounted Pygmy current meter, standard A-reel, and counting device ___________________ 9 7—9. Graphs showing— 7. Dimensionless average velocity distribution for cross section at cableway _______________________ 10 8. Relation between bed velocity at incipient motion and intermediate particle diameter for the range in specific gravity, 0, and SF found in the test reach at Blue Creek as calculated from equation 3-- _ 11 9- Comparison of measured and calculated bed velocities at 0.6a for test particles __________________ 12 10—12. Graphs showing—— 10. Comparison of previous studies relating bed velocity to particle Size with present study ___________ 13 11. Low-water cross sections, Blue Creek gaging-station reach ____________________________________ 14 12. Thalweg profiles of a reach of Blue Creek extending approximately one-fourth of a mile downstream from the gaging station ______________________________________________________________ 15 13~15. Maps of—' 13. Cable-section reach of Blue Creek, 1966 ____________________________________________________ 16 14. Cable-section reach of Blue Creek, 1967 ____________________________________________________ 17 15. Cable-section reach of Blue Creek, showing change of streambed topography, 1966—67 ____________ 18 TABLES Page TABLE 1. Summary of physical properties of test particles and theoretical threshold velocities ___________________________ G8 2. Distance moved and measured threshold velocities of recovered test particles ________________________________ 11 In SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS FIELD MEASUREMENT OF THE INITIATION OF LARGE BED PARTICLE MOTION IN BLUE CREEK NEAR KLAMATH, CALIFORNIA By E. J. HELLEY ABSTRACT More than two-thirds of the field measurements of bed veloc- ity necessary to initiate motion of coarse natural particles whose size, shape, specific gravity, and orientation angle were known agree within 20 percent of those velocities predicted from theory. The theory is based on balancing turning moments of the fluid forces of drag and lift with the resisting moment of the submerged particle weight. Initial motion seems to depend more on size and shape than on specific gravity or orientation angle. In fact, shape differ- ences almost completely compensate for diflerences in specific gravity ranging from 2.65—3.00 and orientation angles ranging from 0°—25°. Bed velocities necessary to initiate motion of coarse bed mate- rial in Blue Creek are equaled or exceeded about 5 percent of the time. This fact and changes in channel topography and cross-sectional area emphasize the ability of perennial moun- tain streams to transport coarse bed material frequently. INTRODUCTION A particle on a rough streambed begins to move when the force of the column of moving fluid intercepting it generates a moment equal to the oppositely directed moment of the immersed particle weight. This phenom- enon may be viewed as a balance between fluid forces of drag and hydrodynamic lift, which tend to turn a particle, and resisting forces of immersed-particle weight, which tend to keep the particle at rest. When these two opposing forces are just in balance, the fluid is competent to move its bed particles and critical or threshold conditions exist. In this report, mean values of drag and lift are used, but it should be recognized that forces much larger than the mean exist. Determination of critical or threshold conditions of sediment movement has long been a problem for hy— draulic engineers as well as for those geomorphologists interested in fluvial processes. An excellent historical review of measuring threshold conditions for sediment motion is given by Leliavsky (1966), who stated that measurements of this type began as early as 1753. Unfortunately, the problem of measuring and predict- ing these threshold conditions is still largely unsolved. This is especially true with respect to bed materials larger than pebble size. If the problem of measuring threshold conditions of sediment motion is viewed as a balance between the forces of fluid flow and resting particle, then the initi- ation of motion becomes one of the simpler problems involving threshold conditions (Vanoni, 1966) and one which hold promise of solution. This should be partic— ularly true when dealing with coarse bed material, whose physical properties can be measured more accurately than those of sand or finer size particles. Attempts at measuring threshold conditions necessary to initiate motion of very large bed particles in this study are based on the use of “bed velocity” rather than on the depth—slope product (“critical tractive force”). Rubey (1938) in a review of Gilbert’s (1914) flume data showed that “bed velocity” is more significant than the depth- slope product, especially when measuring threshold con- ditions for particles larger than 2.5 mm (millimeters). In addition, the slope of the water surface of most natural streams needed to calculate tractive force is usually difficult to measure accurately—especially at high stages. This is particularly evident in mountain streams, Whose alinement and channel geometry change frequently and irregularly, a change that generates secondary currents and superelevations and gives rise to local and changing slopes. In this report, bed velocity is defined as the velocity measured at some finite distance close to the bed. PURPOSE The primary purpose of this study was to determine bed velocities necessary to initiate motion of very coarse bed material by direct measurement and, thereby, to extend existing size-versus—velocity relations. A second- G1 G2 ary objective was to determine channel changes due to aggradation or degradation in the vicinity of the test reach during the period of study. This was done in an attempt to evaluate the geomorphic significance of threshold conditions of particle motion. The study was made by the US. Geological Survey in cooperation with the California Department of Water Resources. The work was done under the immediate supervision of Loren E. Young, chief of the Menlo Park office of the Water Resourses Division of the Geo- logical Survey. The author wishes to express gratitude to personnel of the US. Geological Survey, especially Gerald LaRue, for assistance in the field and Carl Good- win and Winchell Smith for assistance in the theoretical calculations and computer programming. The manu- script benefited from critical review by Carl Nordin, Everett Richardson, and John Ritter. LOCATION Blue Creek, a small tributary to the Klamath River in northern California (fig. 1), was chosen as the study site for the following reasons. Discharge measurements at the US. Geological Survey gaging station at Blue Creek indicated that runoff from this small, 120-square- mile drainage basin had velocities ranging from less than 2 fps (feet per second) to as much as 13 fps but ‘1 DEL NORTE co. HUMBOLM co. U535. Guln. station Surveyed cmn suction: N o 1 2 MILES l___.l_4 FIGURE 1.——Location map of Blue Creek near Klamath, Calif. SEDIMENT TRANSPORT DI ALLUVIAL CHANNELS that the discharge was not flashy or large enough to be difficult to measure. Observations of the streambed during summer low-flow periods indicated that the bed material consisted of particles averaging about 0.5 foot but as much as 3 feet in median diameter. Shifts in the rating curve during periods of moderate to high discharges showed that the streambed at the gaging- station cableway was changing and, hence, that Blue Creek was actively transporting its coarse particles as bedload. Blue Creek’s drainage basin is underlain by a wide variety of rock types including shale, sandstone, and ultrabasic intrusive rock as well as minor amounts of granite (Irwin, 1960). Weathering characteristics of these rocks make available a wide variety of shapes and differences in mineralogy provide a large range in specific gravity from 2.60—3.10. Thus, the natural set- ting at Blue Creek was ideal for a study of the transport of coarse bed material. The gaging station and cable- way also provided a means by which bed velocities could be measured. PREVIOUS WORK Previous attempts at measuring threshold conditions for sediment motion have been reviewed by Leliavsky (1966) and more recently by Raudkivi (1967). Most of their discussions concern smaller size particles and will not be discussed here. Mavis and Laushey (1949, p. 39) presented critical bed velocity-versus-size curves for particles up to 100 mm (0.3 ft). The coarsest material studied by direct measurement was that of Fahnestock (1963, p. 29), and his is probably the only data on particles greater than 1 foot in diameter. His measurements, however, were made under less than ideal conditions and on material in transport rather than at rest. THEORY The bed velocities necessary to initiate motion of coarse particles can be calculated by balancing turning moments of the fluid forces of drag and lift with the resisting moment of the submerged particle weight. The concept of balancing the turning and resisting moment is not new as shown by Leliavsky (1966, p. 36 and p. 149). Although past workers have considered various aspects of the initiation of motion of bed material, none have considered all the physical characteristics of the particles, their orientation, or a lift force. The general physics of initial grain motion is summarized by Shepard (1963) Who reviewed the work of Shields (1936), White (1940), and Bagnold (1942). Consider, for example, a particle at rest on the streambed as shown in figure 2. The orientation of the three mutually perpendicular axes as shown places the LARGE BED PARTICLE MOTION, BLUE CREEK, CALIFORNIA Y Lift Weight—buoya ncy G3 Drag turning arm 0.1 (x cos 9+(‘V 3/160<2cose-5/4sin e) Lift turning arm 5/4 c059 +N 3/16a2 -sin6) Where a: short axis fi=intermediate axis 7=Iong axis 0=horizontal A /3 FIGURE 2.—Orientation of test particles placed on bed of Blue Creek. long axis, 7, normal to the flow direction. The angle, 0, between the intermediate axis, 6, and the horizontal is designated as the orientation angle. This neglects the bed slope, which is here considered insignificant. The orientation shown in figure 2 is considered typical of the bed material found in the test reach. TURNING MOMENT The moment tending to turn the particle in figure 2 must consist of two parts: first, the drag-force mo- ment of the fluid parallel to the streambed, and second, a hydrodynamic-lift moment acting normal to the streambed (Einstein and El Samni, 1949, Vanoni, 1966, and Egiazarofl’, 1967). DRAG-FORCE MOMENT The drag-force moment, neglecting fluid shear, may be expressed as the product of the average differential fluid pressure in the downsteam direction, the inter- cepted area of the particle, and the drag-force turning arm. Because the shapes of natural particles vary, the area intercepting the flow also varies, so that particles of the same size but of different shape exert a different form resistance to the flow. The Corey shape factor, SF = a/x/fi, (Schultz and others, 1954), quantitative— ly expresses shape and can be related to the familiar drag coefficient, 01,. Because the Reynold’s number in natural mountain streams like Blue Creek is ex- tremely high, the drag coefficient (01)) will be constant for a given shape factor; hence, the drag coefficient can be related to various shape factors. Figure 3 was constructed from the Reynold’s number-versus-drag coefficient curve for various Corey shape factors, SF (U.S. Inter-Agency Committee on Water Resources Project Report No. 12, 1957, p. 20). The drag coef- ficient thus determined is for naturally worn sediments and was determined for free-falling bodies. Where par— ticles are initially at rest on the streambed, not all the area described by the shape factor and drag coefficient exerts a form resistance to the flow. It is apparent that the drag coefficient for free-falling bodies must be modified before application to bodies at rest. An average drag coefficient used in this study is assumed to be 0.750;, and is designated as C’D. Egiazaroff (1967) has shown that the centroid of the drag force is 0.63 particle diameter up from the bottom of the particle. For simplicity this is taken as 0.6a, where a is the short axis of the particle shown in figure 2. As shown in figure 2. the drag-force turning arm is dependent on the location of the pivot point. This point was determined from observations of the orientation of particles deposited on the bed of Blue Creek. The position of this point, as shown in figure 2, may be expressed in terms of the flow direction, X, and lift direction, Y. Assuming that the particle shape is an ellipse in cross section and that the centroid of the drag force is at 0.60:, the X location is on a normal 6 from the intersection of the mutually perpendicular particle axes. In the Y or lift direction the pivot point G4 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 1.0 ‘ 0.8 \\ \\\\< 0.6 g. 3 \ } 65:0.75 CD \\ n K U) 04 \\\\l \ \\ \\~\\ 0.2 \ \ \\\ \‘~\ \ 0 o 0.4 0.8 1.2 1.6 2.0 2.4 ' 2.8 3.2 3.6 4.0 DRAG COEFFICIENT (CD and cg) FIGURE 3.—Relation between shape factor, SF, and drag coefficient CD and 0’]; for high Reynold’s numbers, >2000. CD from US. Inter-Agency Committee on Water Resources Report No. 12 (1957, p. 20). may be located by solving the equation of an ellipse which yields K 2 172: ( M __ (73;) a2 _ 3 2 .7416... The coordinates which describe the location of the pivot in the drag and lift directions are L3 3 2 4 and \/16 a 7 respectively. The drag-turning arm shown in figure 2 is then 0.1a cos 0+(\/% «12 cos (9—2 sin 0) and is here designated as MR D. Using the symbols in figure 2 and expressing the particle shape in cross section as approximating an el- lipse, the drag moment be written as which reduces to (02,) (drag force) (turning arm) , 02 ray (0D) (23 . 62.4) (T (MR0), where v: the bed velocity at 0.6a up from the bed 9: the acceleration due to gravity. It should be noted that the expression is applicable for angles of theta less than about 25°. LIFT-FORCE MOMENT The lift—force moment may be expressed in a manner similar to that of the drag-force moment; however, the lift moment turns about a different turning arm. Actually, very little data are presently available to calculate lift coefficients reliably except for those devel- oped by the experimental work of Einstein and El Samni in 1949 (in Vanoni, 1966). Because the size of the parti- cles used in their experimental work is relatively large (0.225 ft), the Einstein and El Samni lift coefficient, 0.178, is applicable here. The lift force acting normal to the streambed turns about an arm of length 9 i 2- ) 4lcos0+(\/16¢x sma, where B is the intermediate axis, a is the short axis, and 0 is the orientation angle shown in figure 2. This turning arm is here designated as MRL. Again ap— proximating the particle shape as an ellipse in cross section, the lift-force moment may be written LARGE BED PARTICLE MOTION, BLUE CREEK, CALIFORNIA (lift coefficient) (lift force) (turning arm) ()2 1rfi‘y (0.178) (E . 62.4) (T) (MRL). Combining the drag-force and lift-force moments into the turning moment (MRT), we have drag-force moment+lift-force moment MRT=(0;,) (232g . 62.4) (7%) (MRD) 2 +(0.178 é; - 62.4) (7%) (MRI); and simplifying, 2 MRT=;’_9 . 62.4 74’ [0,, ay(MRD)+0.178 137(MRL)]. (1) RESISTING MOMENT The force which resists the turning of the particle consists of the immersed weight. This force may be ex- pressed as the product of the submerged specific gravity, the specific weight of water, and the volume of the par— ticle. Because the force of the immersed weight acts downward normal to the streambed, the turning arm needed to compute the resisting moment is the same as that for the lift-force moment. Approximating the vol— ume with an ellipse rotated about its minor axis to form a prolate spheroid and using the symbols in figure 2 we may write the resisting moment (MRR) as: (submerged specific weight) (volume) (turning arm) 2 MRR=(sp gr—l) (62.4) (31%) ($3) (MEL), where sp gr is the specific gravity of the particle. Rearranging and simplifying: MRR=(sp gr—l) (41.6 m) (::£)2(MRL), (2) which holds for small angles of theta (less than 25°). CONDITIONS FOR MOTION At the instant when motion takes place, the sum of the turning and resisting moments is zero. Moment (turning)=Moment (resisting) @ incipient motion combining equations (1) and (2); MRT=MRR. g; . 62.4 :1” [02 w, (MRD)+0.178/3y (MRL)] 2 =(sp gr—l) (41.6w) 6%?) (M3,). Simplifying and solving for cat 0.6a G5 311%“ (sp gr—1>v31 3 A 34 100.0 FIGURE 9.—Comparison of measured and calculated bed veloc- ities at 0.6a for test particles. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS paring previous work relating bed velocity and par- ticle size (fig. 10). It should be noted that all curves are extrapolations over two log cycles when, in fact, most measurements are actually made over a range of about one log cycle. The direct measurements by Fahnestock (1963) agree fairly well, but the curve of Mavis and Laushey (1949) fitsbetter—especially in the same size range as Fahnestock’s. The major con- sideration in figure 10 is the fact that most differences in relations between velocity for the initition of motion and size result from differences in particle shape, den- sity, and orientation. The envelope curves shown here are representative for the range in physical charac- teristics of particles in many natural streams with coarse beds and, therefore, should be applicable to other areas. CHANNEL CHANGES Channel changes, as shown by aggradation or degradation, were studied at Blue Creek for two purposes. First, it was desired to describe the general channel behavior during the study period. This was necessary to relate the measured bed velocities needed to initiate motion to either an aggrading, degrading, or stable streambed. The second objective was to measure the response of a mountain stream, such as Blue Creek, to the effects of the devastating floods of December 1964. Blue Creek, as many other rivers and streams in northern California, underwent considerable streambed changes during these floods (Hickey, 1967). According to the studies done on Coffee Creek, also in northern California (Stewart and La Marche, 1967), the catastrophic 1964 flooding largely determined the channel morphology and the location and character of the alluvial deposits. The general hydrologic character of the December 1964 flood has been described by Rantz and Moore (1965); they showed that this event has been without precedent back to 1861 in northern California and in adjacent parts of Oregon, Idaho, and Nevada. In fact, geo- morphic and botanical evidence indicate that a flood of the magnitude of the December 1964 flood had occurred only once in the last 400 years (Helley and La Marche, 1968). Fresh landslide scars, bank collapse, and uprooted trees give evidence to the fact that large volumes of colluvium and bank material were supplied to the channel’ of Blue Creek during the 1964 flood. Most of this material was deposited in the lower few miles of Blue Creek because of simul- taneous high stages on the Klamath River. Narrow reaches in the lower course of Blue Creek commonly displayed boulder levees, and Wide reaches contained large volumes of finer grained well-stratified deposits. Inspection of the Blue Creek channel from the gaging LARGE BED PARTICLE MOTION, BLUE CREEK, EXPLANATION x Field measurements from Fahnestock (1963) Hjulstrom (1935) Mavis and Laushey (1949) This study BED VELOCITY, IN FEET PER SECOND 6.01 0.1 CALIFORNIA G13 INTERMEDIATE DIAMETER, IN FEET FIGURE 10.—Comparison of previous studies relating bed velocity to particle size with present study. In the present study, particles are initially at rest. station downstream to its mouth (fig. 1) indicated that during the period of this study there was active erosion of the flood debris stored in the channel. CROSS-SECTION SURVEYS Seven cross sections were surveyed annually for 3 consecutive years (1965—67) at a reach extending about one—quarter of a mile downstream from the gaging sta- tion (fig. 1). Each cross section, spaced about 200 feet apart, was marked by steel reinforcing bars, which made relocation from year to year accurate. A tag line was stretched from each section end, and elevations were measured with a level. Elevations were determined at intervals of 10 feet along each section. Figure 11 shows these seven sections as Viewed downstream. Most noticeable is an increase in cross-section area during the study period which was caused by an increase in depth. As expected, width changed only slightly be- cause most of the side slopes are exposed bedrock of sandstone and shale. The thalweg profile of this reach G14 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 1965 0 100 200 300 FE ET VEflYICAL SCALE FOUR TIMES HORIZONTAL SCALE coo-coonoIOQOUI noooooooooooonuoo COIOOOOIOOOIOIOOII. cocoooooaoooao-uooo coo-ocoooaooocouo-oo 1966 oo-oo-uooo-coqu-o neocoooo-a-ooo-ooo-o FIGURE 11.——Low-water cross sections, Blue Creek gaging-station reach. shown in figure 12 clearly indicates that most of the increase in depth occurred during the rainy months of November through March of 1966—67, three seasons after the record flood of December 1964. Only one sec- tion shows a decrease in depth, a decrease that is very slight. Perennial streams with gravel beds commonly tend to scour over relatively long reaches (Leopold and others, 1964, p. 234). Although the net degrada- tion over the gaging-station reach is not surprising, it is indicative of the ability of Blue Creek to move rapidly large volumes of coarse material supplied to the channel. TOPOGRAPHIC SURVEYS The cableway test reach half a mile downstream from the gaging station was surveyed in 1966 and again in 1967. Both surveys were done during summer low— flow periods and were used to describe the net change in the 450-foot-long test reach during the study period. The areal distribution of bedrock and bed material of various sizes according to the Wentworth scale are shown (with the topography) in figures 13 and 14. The distribution of bed material is generalized and indicates that the areas mapped are overlain mainly by the indicated size. The most noticeable change from 1966 to 1967 is in flow direction (shown by large arrows) which was caused by local scour of as much as 3 feet along the left bank. Lesser scour along the right bank has exposed additional bedrock underlying the channel. Particle size increased from pebbles to cobbles and boulders in the downstream portion of the test reach. LARGE BED PARTICLE MOTION, BLUE CREEK, CALIFORNIA G15 102 EXPLANATION X Indicates location of surveyed 'cross section 100 7 ‘ l" IR“ October 26. 1965 ’ h r’ I §<:‘~.‘ .______ 1’ \\ \ September 26, 1966 s k \ \\ _ ___________ , \\\ September 26, 1967 1 i 98 I \\ ’ \ I \ s I- I V a ,I \ [L 2 II \ _ I \ i l ‘.\ A O 96 ' '\ ’: I \ . f§~ § II ‘ m l d I I l \ I ‘l 94 I II .~ I /’ ~~ 7’ I” ~~~~ I 92 904 X X X X X X 0 200 400 600 800 1000 1200 1400 DlSTANCE DOWNSTREAM, IN FEET FIGURE 12.—Thalweg profiles of a reach of Blue Creek extending approximately one-fourth of a mile down- stream from the gaging station. Figure 15 shows the change in streambed topography and the net degradation that occurred during the study period. The volume removed from the test reach was determined by planimetry of an area bounded by the upper and lowermost cross sections. The removal of approximately 2,800 cubic yards resulted in an average bed-elevation decrease of 1.2 feet. CONCLUSIONS The bed velocities necessary to initiate motion of coarse bed material, as calculated from a theory which considers particle size, shape, specific gravity, and orien- tation angle agree well with those determined by field observation. The initial movement seems to depend more on particle size and shape than on specific gravity and orientation angle. In fact, difference in specific Present data also suggest that threshold velocities necessary to move coarse material exists for at least 5 percent of the time in Blue Creek. Field data were collected on channel changes and were completed during a degradational phase of channel adjustment. Long reaches of the channel of Blue Creek have degraded considerably since the December 1964 flood, and most of the degradation occurred during the rainy season of 1966—67—three seasons after the flood. Cross-sectional and topographic surveys indicated that approximately 2,800 cubic yards of material were scoured from a 450-foot-long reach of Blue Creek be- tween September 29, 1966, and September 29, 1967. This demonstrates the ability of perennial mountain streams, such as Blue Creek, to transport very coarse gravity from 2.65—3.10 is almost completely compen- sated by difference in shape. debris. G16 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS EXPLANATION Sand Pebbles Boulders and cobbles gfluum...’ all Bedrock outcrops N0! xurveyed Position of water's edge Seplcmber 29. I966 [30— [29 Contours Dun-her! where approxinmle Centaur inlerva/ I fiml. G Survayed cud: of cross SECUOHS Flow direction IlOH'l-IANK @CAIL! SECYION l I l I I | l l l \ ,/ lEFT—IANK CABLE SECVION O 0 20 4O 6 0 80 100 FEET FIGURE l3.-——Ca.ble-section reach of Blue Creek, 1966. LARGE BED PARTICLE MOTION, BLUE CREEK, CALIFORNIA EXPLANATION Sand Pebbles Boulders and cobbles WW“ l ; Bedrock outcrops Na! :urm'ed Position :f’:w_al_e:'s edge September 29, 1967 —I50— I29 Contours Dashed when approximalt Contour inlerval I faoL O Surveyed epds of cross secuons Flow direction N @ RIGHI-IANK 4/ @(Alll SEC'ION ”J G17 [EFT-BANK CA ILE SEC'IION Q O 20 40 60 80 100 FEET FIGURE 14.—Cable-section reach of Blue Creek, 1967. G18 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS E E” E. " V o EXPLANATION “guns“ “4 Bedrock outcrops rm! xurveyed a._' __/_ Lines of equal scour or filld Numbers indicate fill or scour(—). in feel, between September 29.|966. through 9 September 29,|967 G) Surveyed ends of cross sections TOTAL SCOUR -2835 cubic yards TOTAL FILL -23 cubic yards " NET CHANGE ~28|2 cubic yards scour BED CHANGE (-) l.2 fee! r g / o 20 4o 60 so 100 FEET |__1_l___l___L___J FIGURE 15.—Cable—section reach of Blue Creek, showing change of streambed topography, 1966—67. LARGE BED PARTICLE MOTION, BLUE CREEK, CALIFORNIA REFERENCES CITED Bagnold, R. A., 1942, Physics of blown sands and desert dunes: London, Methuen and Co., 265 p. Corbett, D. M. and others 1962, Stream-gaging procedure, a manual describing methods and practices of the Geological Survey: U.S. Geol. Survey Water-Supply Paper 888, 240 p. Egiazarofl', I. V., 1967, Sediment transportation mechanics: Ini- tiation of motion: Am. Soc. Civil Engineers Proc., Jour. Hydraulics Div., v. 93, no. HY4, p. 281—287. Einstein, H. A., and El Samni, El-Sayed Ahmed, 1949, Hydro- dynamic forces on a rough wall: Review of modern physics: Lancaster, Pa., Am. Inst. of Physics, v. 21, no. 3, p. 520—524. Fahnestock, R. K., 1963, Morphology and hydrology of a glacial stream—White River, Mount Rainier, Washington: U.S. Geol. Survey Prof. Paper 422—A, 65 p. Gilbert, G. K., 1914, The transportation of debris by running water: U.S. Geol. Survey Prof. Paper 86, p. 16. Helley, E. J., and La Marche, V. C., 1968, December 1964—a 400-year flood in northern California: U.S. Geol. Survey Prof. Paper 600—D. Hickey, J. J., 1967, Variation in low-water streambed elevations at selected stream-gaging stations in northern California: U.S. Geol. Survey open-file rept. Hjulstriim, Filip, 1935, Studies of the morphological activity of rivers as illustrated by the river Fyris: Univ. Upsala [Sweden] Geol. Inst. Bull., v. 25, p. 221—527. Irwin, W. P., 1960, Geologic reconnaissance of the northern Coast Ranges and Klamath Mountains, with a summary of the mineral resources: California Div. Mines Bull. 179, 80 p., pl. 1. Krumbein, W. C., 1940, Flood gravel of San Gabriel Canyon: Geol. Soc. Amer. Bull., v. 51, p. 636—676. 1942, Flood deposits of Arroyo Seco, Los Angeles County, California: Geol. Soc. America Bull., v. 53, p. 1355-1402. Leliavsky, Serge, 1966, An introduction to fluvial hydraulics: New York, Dover Pubs, Inc., 245 p. G19 Leopold, L. B., Wolman, M. G., and Miller, J. P., 1964, Fluvial processes in geomorphology: San Francisco, Calif., W. H. Freeman and Co., 522 p. Mavis, E. T., and Laushey, L. M., 1949, Formula for velocity of beginning of bedload movement is reappraised: Civ. Eng., v.19, p. 38—39. Potter, P. E., and Pettijohn, F. J ., 1963, Paleocurrents and basin analysis: New York, Academic Press, Inc., 277 p. Rantz, S. E., and Moore, A. M., 1965, Floods of December 1964 in the far western states: U.S. Geol. Survey open-file rept. Raudkivi, A. J., 1967, Loose boundary hydraulics: New York, Pergamon Press, 321 p. Rubey, W. W., 1938, The force required to move particles on a stream bed: U.S. Geol. Survey Prof. Paper. 189—E, p. 121-140. Shultz, E. F., Wilde, R. H., and Albertson, M. L.. 1954, Influence of shape on the fall velocity of sedimentary particles: Omaha, Nebr., U.S. Army Corps of Engineers, Missouri River Division Sedimentation Ser., Report no. 5, fig. 25. Shepard, F. P., 1963, Submarine geology: New York, New York, Harper & Row Pubs, 487 p. Shields, A. 1936, Anwendung der Ahnlickeit—mechanik und der Trubulenz-forschung auf die Geschiebebewegung Mitt, preoss Versuchsanstalt fur Wasserbau und Schifl'bau, pt. 26. Stewart, J. H., and La Marche, V.C., Jr., 1967, Erosion and deposition produced by the flood of December 1964 on Coffee Creek, Trinity County, California: U.S. Geol. Survey Prof. Paper 422—K, 22 p. 1 p1. U.S. Inter-Agency Committee on- Water Resources, Project Report No. 12, 1957, Measurement and analysis of sediment loads in streams: Some fundamentals of particle size analy- sis: Washington, D.C., U.S. Govt. Printing Office, 55 p. Vanoni, V. A., 1966, Sediment transportation mechanics: Initi- ation of motion: Am. Soc. Civil Engineers Proc., Jour. Hydraulics Div., v. 92, no. HY2, March 1966. p. 291—313. White, C. M., 1940, The equilibrium of grains on the bed of a stream: Royal Soc. [London] Proc. (A) 174, p. 322—334. U.S. GOVERNMENT PRINTING OFFICE: 1969 0-359-778 . ‘1 , TC: 7 DAY 1:11:53 V. 562' H Flume Width and Water Depth Effects in Sediment-Transport Experiments GEQLOGICAL SURVEY PROFESSIONAL PAPER 562— H UM")? “(A Aw 9.: AUX f a H JUL 13 1970 "‘r; K‘ t 43' z x '1‘ ,- 3" ’ - I ‘ " \‘C‘N’Firnf HQ}; \i:; -\\;~;~’:. IL”. QM. Q g L U.S.S.D. Flume Width and Water Depth Effects in Sediment-Transport Experiments By GARNETT P. WILLIAMS SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS GEOLOGICAL SURVEY PROFESSIONAL PAPER 562—H UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1970 UNITED STATES DEPARTMENT OF THE INTERIOR WALTER J. HICKEL, Secretary GEOLOGICAL SURVEY William T. Pecora, Director For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 - Price 55 cents (paper cover) CONTENTS Page Page Abstract ___________________________________________ H 1 Results—~Continued Introduction _______________________________________ 1 Water discharge ________________________________ H6 Equipment and measurements ________________________ 2 Mean velocity __________________________________ 8 Flume _________________________________________ 2 Slope _________________________________________ 8 Water supply and discharge measurement---- - _ _ _ - _ 2 Stream power __________________________________ 13 Sediment infeed ________________________________ 2 Bed forms _____________________________________ 20 Sediment—transport measurement _________________ 2 Bed-form heights ___________________________ 20 Sediment ______________________________________ 2 Bed-form wavelengths _______________________ 21 Depth measurement _____________________________ 2 Travel velocity _____________________________ 21 Velocity _______________________________________ 4 Resistance factors ________________________________ 22 Slope __________________________________________ 4 Sidewall correction procedure-- ___________________ 24 Bed-form characteristics _________________________ 4 Test one ___________________________________ 25 Procedure ------------------------------------------ 4 Test two ___________________________________ 26 Results ____________________________________________ 5 Conclusions ________________________________________ 29 General _______________________________________ 5 References _________________________________________ 29 ILLUSTRATIONS Page FIGURE 1. Photographs of flume and associated equipment _________________________________________________________ H3 2—17. Graphs showing-— 2. Size distribution of sand ________________________________________________________________________ 4 3. Relation of unit water discharge to unit sediment-transport rate _____________________________________ 7 4. Mean velocity—unit transport relations ___________________________________________________________ 9 5. Mean velocity—unit transport relations ___________________________________________________________ 10 6. Slope—transport relations ----------------------------------------------------------------------- 11 7. Adjustment factors to correct slope for sidewall effect ______________________________________________ 12 8. Unit stream power—unit sediment-transport relations showing flume—width effect ----------------------- 14 9. Adjustment factors to correct stream power for sidewall efiect _______________________________________ 16 10. Single curve giving adjustment in slope, stream power, or shear stress to correct for flume sidewall influence- 17 11. Unit transport rate adjustment factors to correct for flume sidewall efl’ect ---------------------------- 18 12. Unit stream power—unit sediment-transport relations in an infinitely wide channel- - _ - - - - - - - _ - - - - _ - - -p. - 19 13. Variation of total sediment-transport rate with different water depths, for constant stream power -------- 19 14. Dune-height adjustment factors to correct for flume—width efl’ect ------------------------------------ 20 15. Flume-width effects on friction factor-transport relations ------------------------------------------- 23 16. Velocity—slope test of sidewall correction procedure ________________________________________________ 27 17. Slope-transport rate test of sidewall correction procedure ___________________________________________ 28 TABLES TABLES 1, 2. Summary of experimental data: 1"“ 1. English units _______________________________________________________________________________ H33 2. Metric units ________________________________________________________________________________ 35 III SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS FLUME WIDTH AND WATER DEPTH EFFECTS IN SEDIMENT—TRANSPORT EXPERIMENTS By GARNETT P. WILLIAMS ABSTRACT This paper reports 177 flume experiments made in channels of difierent widths and water depths, the purpose being to find how the flume width and flow depth influence experimental results. No attempt was made to derive a sediment-transport formula. Sediment transport rates, grain size (,nearly uniform-sized par- ticles with a 1.35 mm median diameter), water depth, and chan- nel width were controlled; the dependent variables were water discharge, mean velocity, slope (energy gradient), and bed-form characteristics. The flume widths were 0.25, 0.5, 1.0, and 2.0 ft. For each of these widths a series of runs (from slow to fast transport rates) was made at depths of 0.1, 0.3, 0.5, and 0.7 ft, that is at depths of about 20 to 160 grain diameters. The narrower flume widths affected some variables signi- ficantly, as explained below, but in a channel 2 ft Wide flume sidewall effects very nearly or completely disappeared. Relations from the narrower channels, Where wall effects were pronounced, could therefore be compared to the relations for wide channels in which wall effects were absent. The channel width did not affect the unit water discharge—unit sediment-transport relations, at constant water depth. The rela- tion between mean velocity and sediment-transport rate there— fore was not affected by the flume width, because for a given width and depth the mean velocity varies directly with the dis- charge. Water depth influenced these relations in that ,a greater discharge, and, at low transport rates, a faster velocity was needed to move sediment at a given rate as depth increased. The slope or energy gradient decreased as the channel became wider, for a given unit transport rate and water depth. This means that any factors involving slope, such as stream power and shear stress, showed the same trend. By measuring the change in these dependent variables with channel width it was possible to get an empirical adjustment equation to correct the slope, stream power, and shear stress for the flume sidewall efl’ect. Multiplying the laboratory value of slope, unit stream power, or shear stress by the adjustment factor 1 1+0'18(W%) Where D is water depth and W is flume width, gives the slope power, or shear for a wide channel (no sidewall influence) for the same water depth and unit sediment-transport rate. Adjustment factors also are given for correcting the unit sediment-transport rate for sidewall efiects, taking transport rate as a dependent variable and stream power as the flow quan- tity which governs transport rate. For a given stream power or bed shear stress in wide channels (negligible wall effects) the sediment-transport rate increased fourfold to sixfold as the water depth was decreased from 0.7 to 0.1 ft. The curves suggest that this depth effect may disappear at depths of about 1.0 to 1.5 ft. The flume width influenced the bed-form characteristics in various ways. Bed forms in wide channels can have heights and travel rates quite different from those observed in narrow chan- nels. Except for runs at the 0.1-ft depth, bed forms did not be- come three dimensional (curving from wall to wall) until the flume was widened to 1 ft (for fast transport rates) or 2 ft. Thus the disappearance of sidewall effects on the measured value of the energy gradient corresponded approximately with the ap- pearance of three-dimensional bed forms. Two different tests of the validity of the J ohnson—Brooks side- wall correction procedure showed that for the present movable- bed data the degree of agreement between predicted and measured flow depths varied with the hydraulic or transport con— ditions. Best agreement (predicted depths within about :30 per- cent of measured depths) usually occurred with channels E 1 ft wide and for runs which did not have extremely rough beds. A review of the literature suggests that for many rigid-boundary flows this sidewall correction procedure is reasonably reliable. INTRODUCTION The movement of solid particles by flowing water affects pollution, the rate at which land is eroded, the filling of reservoirs, and many related problems. Sedi- ment transport is difficult to study in nature because of the problem of accurately measuring the travel rates of sand and gravel during most flow conditions. Many investigators have therefore resorted to artificial watercourses (flumes) in the laboratory. Flume experi- ments use water and sediment in quantities small enough to control, and this valuable control of variables means a better understanding of the role of individual factors. Each laboratory, understandably, has built equip- ment to suit its particular interests, capacity, and needs. The sediment-transport experiments reported in the lit— erature therefore differ in type and size of apparatus H1 H2 used, experimental procedure, and in other respects. Consequently the data from any one investigation us- ually do not agree with the data of others. The present study explores the questions of how the results of sedi— ment—transport experiments can be affected by flume width and water depth—two features which usually have varied randomly from one study to the next. An equally important purpose of the investigation was to make some progress toward relating flume data to natural-river conditions by evaluating flume sidewall effects. This study makes no attempt to derive or test a sediment-transport formula. The encouragement and advice of Ralph A. Bagnold have been an invaluable support throughout this entire investigation. I am grateful to William W. Emmett, Harold P. Guy, Everett V. Richardson, Neil L. Cole- man, Edward J. ‘Gilroy, Emmett M. Laursen, J acob Davidian, and William H. Kirby for helpful sugges- tions or generous assistance. EQUIPMENT AND MEASUREMENTS FLUME Williams (1967) described in detail the 52-ft—long nonrecirculating flume (fig. 1) used for the experiments. The flume could be tilted from horizontal to a maximum slope of about 0.035 ft per ft, and the maximum usable width was 3.9 ft. For most of the experiments both walls were of transparent plastic (Plexiglas), although for some tests at widths of 0.25 and 0.5 ft one wall consisted of smooth plywood. The smooth wood surface probably was not appreciably rougher than the plastic. WATER SUPPLY AND DISCHARGE MEASUREMENT Three pipelines (diameters 8, 6, and 4 inches) sup- plied water to the flume. Water destined for the 6- and 4-inch lines went from the sump to a constant-head tank and then flowed through the pipelines to the flume. For the 8-inch line a second pump sent water directly from the sump to the stilling tank at the head of the flume. A valve in each pipeline regulated the flow rate. Elbow meters precalibrated at the Georgia Institute of Technology measured the discharge in the 6- and 4-inch lines. Another calibration of the meters in place (Washington, DC.) near the end of the investigation showed that they were accurate to i1.8 percent. The 8-inch line had a factory-calibrated orifice plate. For four runs at the very lowest discharges (depth 0.1 ft in a 0.25 ft-wide channel), the discharge had to be measured volumetrically. Maximum available dis- charges were 3.5, 2.0, and 0.8 cfs (cubic feet per second) in the 8-, 6-, and 4-inch lines, respectively. SEDIMIENT TRANSPORT IN ALLUVIAL CHANNELS VSEDIMEN T INFEED In the early stages of the investigation a submerged elevator just upstream from the flume test section fed sediment into the stream. This feed method was only partly satisfactory. Although the sand entered the test section at a constant rate, a minor amount of sediment leakage along the sides of the elevator prevented a computation of the exact sediment infeed rate. Sec- ondly, faster sediment-transport rates could not be studied because the 4-ft—long by 2.5-ft-deep sand supply was used up before a run could be completed. Changing to a vibrating feeder (fig. 1) partway through the study eliminated these problems, and this “drop-in” feed method turned out to be much better than the elevator system. The slowest infeed rates required a second vi- brating feeder, very small, and this is not shown in figure 1. SEDIMENT-TRANSPORT MEASUREMENT The water-sediment mixture leaving the flume fell into a sediment-collection box (figure 1). Water escaped through screens along the top of the box while all the sand settled to the bottom. Weighing the box and its contents periodically in place gave the sediment-trans- port rate (total sediment load) in submerged weight. During the early stages of the study, the volume of the collection box (which sat on a platform scale) was 9 cubic feet, but this box proved to be too small for transport rates greater than about 0.2 lb per sec-ft. The 44-cubic-foot collection box adopted partway through the investigation was much better. This larger box hung from a crossbeam, and the scale sat to one side of the box; one support of the crossbeam rested on the scale platform, and the recorded weight was adjusted by an appropriate factor to get the actual weight of the box and its contents. SEDIMENT The quartz sand used for the experiments was fairly uniform in size (2 percent <08 m and 2 percent >20 mm) with a median sieve diameter of 1.35 mm (fig. 2). Transported material trapped in the collection box had virtually the same size distribution as the material re- maining on the flume bed. The average fall velocity for 75 randomly selected grains was 14.5 centimeters per second at a water temperature of 315° C. Most of the grains were not particularly spherical, and their edges were of intermediate roundness. DEPTH MEASUREMENT Elevations of the water- and bed—surfaces were meas- ured to the nearest 0.001 ft with a point-gage at regular intervals along the test section, beginning at station 3.0 ft and ending at station 49.0 ft. The horizontal intervals FLUME WIDTH AND WATER DEPTH EFFECTS H3 n-n-C'. " “III: II. (ID-l .. _ ,. Willi? C FIGURE 1.—Flume and associated equipment. A, General view looking downstream with elevator feed system in use. B, Upstream View showing elevator feed system and preliminary channel. 0, Measurement of sediment-transport rates with collection box resting on scale platform. D, General view looking downstream with “drop-in” feed system. E, Upstream View of “dropin” feeder. F, Measurement of sediment-transport rates using the suspended collection box. H4 were usually 4 ft, occasionally 2 ft. After the elevations were plotted on arithmetic coordinate graph paper, straight lines of best fit by eye were drawn through the points for each surface. With uniform flow the lines were parallel, and the elevation difference normal to the two lines gave the mean water depth. VELOCITY Mean velocity equals the discharge divided by the product of mean depth times channel width. Travel times of small chips of wood over a 40-ft distance gave the surface velocity. The accepted surface velocity was the average of three observations made with a stopwatch. SLOPE The slope of the water surface, equal to that of the sand bed, is the sum of the flume slope (measured by a surveyor’s level) and the water-surface slope relative to the flume (obtained from the graphs of bed and wa- ter-surface profiles). After equilibrium (defined below) l00 I I I ITTI I Lu VIsual— _ g accumulatIon ‘0 tube anal sis Q 80 — V — L|J '— < 2 o E 60 — — z < I I— Q: E LL. i— z . . LLJ SIeve anaIySIs c: LIJ & 0 I ii I I 0.5 l 2 PARTICLE DIAM ETER, IN MILLIMETERS FIGURE 2,—Size distribution of sand. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS evolved, the inclination of any one profile usually devi- ated by no more than about 2 percent from the average of several such profiles. FOr some runs at a depth of 0.7 ft and for runs with very rough water and bed surfaces 1- 4 percent was the maximum deviation. BED-FORM CHARACTERISTICS The bed-form height recorded for each run represents an average value of 3 to 10 different bed features. Meas- urements were perpendicular to the bed slope and in the downstream half of the flumeggenerally using the point gage along the center of the channel, but for some of the early runs just from a scale on the flume wall. A count of the number of crests along the complete flume test section gave the average bed-form wavelength. The specific downstream location of each crest, at a given time, was also listed for some of the initial runs. The travel velocities of the bed forms were obtained in the downstream half of the test section by timing the bed form as it traversed a known horizontal distance. For some of the early runs only one bed form was timed, but generally the travel velocity is an average of the travel rate of five or six bed forms. PROCEDURE In a typical sediment-transport experiment, the ma— jor variables are the water discharge, mean velocity, mean depth, channel width, energy gradient (slope, for uniform flow), rate of sediment transport, bed rough- ness, and sediment characteristics (size, size distribu- tion, shape, and density). Other factors, such as water temperature, may have some influence under certain conditions. For the present study the independent variables—— those variables determined before beginning a run— were the sediment-transport rate, mean depth, channel width, and sediment characteristics. The dependent vari- ables—those factors whose Values were unknown until after the experiment—were water discharge (or mean velocity, at constant depth and width), slope, and bed roughness. In laboratory studies with movable (sand) beds it is practically impossible to set up an “ideal” ex- periment in which all variables are independent except one. The reason for controlling sediment-transport rates was that this is by far the most convenient way to op- erate a nonrecirculat-ing flume. (A study by Guy and others (1967) gave identical results for recirculating versus nonrecirculating flumes.) The purpose in keep- ing depth constant was to keep the wall drag and cross- sectional flow dimensions as constant as possible from run to run. Depth effects can then be evaluated sep- arately from flume-width efl'ects. FLUME WIDTH AND WATER DEPTH EFFECTS There was no convenient way of regulating the water temperature. It varied little if at all during a single run but ranged from 8° to 28°C during the investi- gation. The study by Colby and Scott (1965) suggests that such temperature changes should not significantly influence the transport rates of coarse sand and that temperature effects on transport rate are relatively minor compared to the effects of mean velocity and shear. However, no one has yet made a carefully con- trolled comprehensive study with different grain sizes to determine what influence water temperature has on sediment-transport rates. An individual run began with the sand bed scraped to approximately a flat surface. The flume slope was set at the estimated probable equilibrium slope. The next step was to start the steady sediment infeed, thus fixing the unit sediment-transport rate for the run. At the same time the water discharge was turned on and ad— justed to get the desired depth. The range of acceptance for water depth was about $7 percent of the desired mean depth. I then took repeated water and bed surface profiles, and if necessary changed the discharge and (or) the fiume tailgate-setting to get a uniform flow of the desired depth. The requirements for equilibrium were (a) constant slope with time and (b) no net gain or loss of sand in the flume with time. With the elevator feed system both of these requirements were judged by com- paring successive sets of profiles and successive transport measurements, as with recirculating flumes. The drop-in feed method made possible an additional verification, namely sediment input rate=sediment output rate. The run and measurements of the basic variables began after equilibrium conditions with uniform flow developed. Sediment-transport measuring periods were always long enough for many bed forms to migrate out of the flume. These relatively long collecting periods assured a reliable measurement of the sediment-transport rate. The final values of depth and of slope relative to the flume in nearly all cases are an average of several sets of profiles. Reproducibility of runs was good. A few runs using the drop-in feed method for situa- tions studied earlier with the rising-platform system showed that the feed method did not significantly in- fluence the experimental results. The experiments for each channel width and mean depth consisted of a series of runs from slow to fast sediment—transport rates. This was done for four con- stant water depths, at a fixed width. The whole process was then repeated for a different channel width, using the same depths as before. Transport rates and water discharges were reckoned in terms of unit (foot) width for comparison purposes. I systematically widened the 373—261 0—-70—2 H5 channel and made more runs until reaching the limits of the equipment or until the chief dependent variables (unit discharge and slope) no longer changed signifi- cantly with increasing flume width for a given water depth and unit transport rate. The depths and widths studied were: Width (fa) Depth (ft.) 0.25 0.1, 0.3, 0.5, and 0.7 0.5 0.1, 0.3, 0.5, and 0.7 1.0 0.1, 0.3, 0.5, and 0.7 2.0 0.1, 0.3, 0.5, and 0.7 3.9 0.7 (five runs). No attempt was made to directly determine threshold flow conditions at which sediment transport would just begin. RESULTS GENERAL Tables 1 and 2 at the end of the paper give all the experimental data, arranged in order of increasing sedi- ment-transport rates for each set of channel dimensions. All measurements except for water temperature were taken in English—system units, so table 2 is merely the basic data converted into metric units. For every run the sediment moved only as bedload, according to visual observations. The results may have been different for grains transported in suspension, and experiments of the present type should be repeated with finer (and coarser) grains and probably with hetero- geneous mixtures too. At the fastest transport rates (flat-bed stage) the grains, according to visual estimation, moved within a zone no more than about 1 centimeter high (about 8 grain diameters) regardless of water depth. The height of this layer of moving grains decreased as transport rate decreased. The many data obtained in this study could be ana- lyzed in various ways, but the discussion here will deal mainly with plots of the individual variables, in an at- tempt to isolate flume-width and water—depth effects. Any influence of the channel width should be dis- closed by plotting each of the dependent variables (wa- ter discharge, mean velocity, slope, and bed-form char— acteristics) as functions of the independent variable, sediment-transport rate, for a constant depth. The same plots for a constant width should reveal the effect of water depth. Such diagrams are intended only to relate a dependent variable to the independent variables, as is customary with experimental data. The purpose is not to recommend any one of the dependent variables by itself as an important indicator of sediment-trans- port rate. H6 WATER DISCHARGE GENERAL A logarithmic plot, not shown here, of unit water discharge (discharge (Q) per foot width (W)) as a function of unit sediment-transport rate (2') revealed an insensitive relation between these two variables in that the line of best fit was rather flat. In other words a large increase in sediment-transport rate required only a relatively small increase in discharge, particularly at low transport rates. The expected depth effect but no flume width effect appeared on the plot. The loga- rithmic diagram of figure 3 with the ordinate, unit discharge, expanded to about five times its usual length, permits a closer examination of these relations. All the lines in figure 3 were fitted by least squares, with the equations rectified to the general form (Q / W) —C=a(7§) b. 0 is a constant for each depth, a is a co- eflicient, and b is an exponent. Values of the constant 0 for this least-squares analysis were 0.087, 0.35, 0.68, and 1.07 for depths of 0.1, 0.3, 0.5, and 0.7 ft, respectively. WIDTH EFFECT In figure 3 the lines for all four flume widths at any constant depth fall within a narrow band which becomes narrower as transport rate increases. For any depth (D) and unit transport rate the lines for the different flume widths generally show no channel-width effect or, as at low transport rates for D=0.3 ft, any difference due to width is negligible. Deviations from the average unit discharge, at any transport rate and depth, range from 0 to 6 percent. The only exceptions are the 0.25- ft-wide channel at depths of 0.1 and 0.7 ft, where the maximum deviations are about 8 percent and 12 percent, respectively. The maximum percent discrepancy from an average unit discharge diminishes as transport rate increases. For the complete range of conditions cov- ered in the experiments the average deviation is about :3 percent. For all practical purposes, therefore, the flume width had no significant effect on the unit discharge—unit transport relations, at a constant water depth. DEPTH EFFECTS Water depth of course afi‘ects the unit discharge— unit transport relations—more discharge is needed to move sediment at a given rate as depth increases (fig. 3). The water depth is important in rivers and streams because of its relation to flooding, irrigation, and nav- igation. In most field situations discharge would be in- dependent or imposed on a given reach, and depth reacts to changes in discharge and resistance to flow. An im- SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS portant question concerning depth in natural rivers is: How does depth vary with water discharge at a constant slope? Laboratory flumes differ from most natural streams in that the flume width is fixed. Thus in a river the mean velocity, depth, and width all absorb a change in dis- charge, whereas in a laboratory flume any change in discharge will appear only in velocity and depth. Hence, the rate at which depth changes with discharge for flumes may be greater than the rate for natural streams. For the present data the rate at which depth changes with discharge, at constant slope, can be found analyt- ically (multiple regression) or graphically. A plot of unit discharge versus slope at constant depth revealed a power relation between any two of these variables, up to the stage where the washing out of bed forms re- duced the slope values (discussed on p. H13). Having the general form of the equation, I ran a multiple regres- sion analysis using (a) discharges from an average least-squares curve for each depth on a discharge-trans- port rate diagram and (b) slope values from the “wide- channe ” slope—transport rate curves (discussed on p. H8). The analysis revealed that at constant slope the depth varied with (Q/W)°-“. Let us compare this exponent, obtained on the basis of many flume experiments, with the exponent predicted by the minimum variance theory of Langbein (see Scheidegger and Langbein, 1966). The minimum var- iance theory postulates that the major dependent var- iables absorb any increase in discharge as equally as pos- sible under the existing constraints. If the major de— pendent variables are velocity, depth, friction factor (Darcy—Weisbach), and unit stream power (slope and width beng constant for the present question), the minimum variance analysis predicts that at constant slope and width the water depth varies with Q M“. At constant width Q is proportional to the product of velocity and depth, and if velocity (V) and depth have a power relation with discharge (Leopold and Maddock, 1953) then the exponents of velocity and depth add up to 1.0. Thus if the exponent of depth is 0.71 then V o: ( (2/ W) ”9- The relations shown in figure 3 converge as sediment- transport rate increases. The diagram magnifies this con- vergence by about five times compared to a regular logarithmic graph, so the convergence is less important than appears from figure 3. Thus the rate at which water discharge increased with increase in transport rate varied considerably with the particular range of transport rates and to a slight extent with the water depth. i w UNIT DISCHARGE , IN CUBIC FEET PER SECOND PER FOOT WIDTH FLUME WIDTH AND WATER DEPTH EFFECTS UNIT SEDIMENT-TRANSPORT RATE,’IN KILOGRAMS (IMMERSED WEIGHT) PER SECOND PER METER WIDTH 0.001 0.01 0.1 1.0 10.0 I | l T EXPLANATION wum. (11) — 300.0 . . 1.0 . 3.9 DEPTH 0.7 FT 30 Depth (11) 025 05 2° / (H A o u 0 DEPTH 0.5 FT 0.3 A o I 0 0.5 13- e e O 0.7 A m o — 200.0 2.0 — w=0.2s 11 W: ~ 100.0 1.0 — - 90,0 0'9 _ — 80.0 0.3 — — 70.0 0-7— DEPTH 0.3 'PT -— 60.0 0.6 — a 500 0.5% O — 400 °-4 — . w=2.0 I1 30.0 DEPTH 0.1 FT 0.3— — 20.0 0.2 — 0.1 l 1 I I 0.0001 0.001 0.01 0.1 1.0 10.0 UNIT SEDIMENT-TRANSPORT RATE, IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH UNIT DISCHARGE 3‘”, IN LITERS PER SECOND PER METER WIDTH FIGURE 3.—Relation of unit water discharge to unit sediment-transport: rate, at constant water depth (ordinate scale magnified about fivefold). H7 H8 MEAN VELOCITY WIDTH EFFECT For any constant flume width and water depth the mean velocity varies directly with the discharge. Thus a regular logarithmic plot (not included here) showed that mean velocity was not. very sensitive to changes in sediment-transport rate, as was true with discharge. Figure 4, with the mean—velocity scale magnified about five times, shows the velocity—transport relations for the various channel widths at constant water depth. For any one depth there is no distinction on the basis of flume width. The single line of best-fit for each depth was fitted by least squares. The range of scatter in ve- locity values is :6 percent, for any transport rate and depth, except for D=0.1 ft Where the velocity for some runs is 12 percent greater than that indicated by the curve. As with the unit discharge—unit trans- port relations, then, the flume width had no significant influence on the velocity—transport relations, at a con- stant water depth. DEPTH EFFECT Figure 5 contains the four lines of best fit from fig- ure 4, to see if water depth affects the velocity—trans— port relations. The strange result is that water depth had a pronounced influence at low transport rates but this influence gradually diminished as transport rate increased. At mean velocities greater than about 4 fps (feet per second) the depth effect disappeared for all practical purposes. At slower mean velocities, those common in flume studies, the curves diverge widely on the basis of water depth. The depth effect shown here at low mean velocities agrees qualitatively with the remarks of Colby (1964). Colby analyzed the influence of depth on the mean ve- locity—sediment transport relation but confined his attention to medium and fine sands. His graphs can- not readily be compared to the present data because of the uncertainties in extrapolating his curves to the coarse sand range. SLOPE WIDTH EFFECT Figure 6 shows the flume width effects on the slope- transport relations for each of the four constant water depths. Where the relations follow a power law, that is at intermediate transport rates, the lines for all widths and depths were fitted by least squares with the con— straint that for a given depth the lines for all four widths are mutually parallel. The curved lines at the extremes of the transport range were fitted by eye. The slope or energy gradient (8) is the loss of energy SEDIIVIENT TRANSPORT IN ALLUVIAL CHANNELS (in foot-pounds per pound of fluid) to overcome fric- tion per unit length of stream. As the channel becomes wider at a constant depth the sidewalls retard a lesser proportion of the cross-sectional flow area. This lesser retardation means a lesser rate of energy loss, that is, a flatter slope. The decrease in slope that occurred with increasing flume width (fig. 6) was greatest between the 0.25- and 0.5-fit-wide channels and gradually dimin- ished in wider channels. According to the least—squares analyses, the slope values in the 2-ft-wide channel were 0.0, 2.1, 2.9, and 7.7 percent less than those in the 1-ft— wide channel for depths of 0.1, 0.3, 0.5 and 0.7 ft, re- spectively (at any constant transport rate within the least-squares range). This result suggests that further increases in flume width would bring even lesser changes (if any) in slope values. To find the slope in an infinitely wide channel, for a given depth and unit sediment-transport rate, S was plotted as a function of W/D. More precisely, instead of W/D the abscissa was a parameter X=1 ’ 1 because in this manner X=1 when W,/D=infinity. Then a simple extrapolation of the curve from the four experimental points such that the curve levelled off at X=1 gave the value of S in an infinitely wide channel, for the given depth and unit transport rate. This method indicated that slope values in a channel of infinite width were about 1, 4, and 5 percent less than the slopes in the 2—ft-wide channel for depths of 0.3, 0.5, and 0.7 ft, Iespectively. (The five runs at W=3.9 ft for D=0.7 ft were omitted in this analysis because of the very limited range of transport rates covered by these runs.) The dashed lines in figure 6 represent these extrapolated slope-transport relations for infinitely wide channels. How much adjustment should be made to the slope value found in a narrow channel (laboratory flume) to find the slope that would pertain to the same depth and sediment-transport rate in a wide channel (for example, a natural liver)? In the absence of any theory which corrects the equilibrium slope for the sidewall (flume width) effect the present data provide the necessary “adjustment factors.” For example, at a depth of 0.5 ft and unit transport rate of 0.01 lb per sec-ft, the slope in the 0.5—ft-wide channel was 0.00326 whereas in a channel of infinite width the slope would be 0.00224. One must therefore adjust the narrow channel slope by a factor of 833:: or 0.69. Figure 7, based on computa— tions made in this manner, shows adjustment curves for each of the four depths. All lines on figure 7 were fitted by eye. H9 FLUME WIDTH AND WATER DEPTH EFFECTS GNOHS 83d SIHHWILND NI 'AIDO'HA NVSW 43825 ”Bonn gfinwafi 2.8m hfioo~w>lnaofiv £wa .8ng 25389 as $5323 ”Foams—Eu “Enlmfioofikr :onl.w 353% 28.; 80m x: 928mm a: 2.333 3335!: 32:2 2. .mp5. 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Ml 'AIDO‘IJII NVJW H10 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS UNIT SEDIMENT-TRANSPORT, IN KILOGRAMS (IMMERSED WEIGHT) PER SECOND PER METER WIDTH 0.001 0.01 0.1 1.0 10.0 I I I | 1 -— 300.0 8.0 — 7.0 — — 200.0 6.0 — 3 O V) a: M V) LU g 4.0 — 3 D. a: a E r: E E — 100.0 E ,>__-‘ 3-0— — 90.0 E g - > U z DEPTH 0.7 FT 3 5 — 70.0 g E 3 2-0 — DEPTH 0.5 FT * 60-0 E DEPTH 0.3 FT — 50.0 DEPTH 0.1 FT — 40.0 1.0 I I I I 0.0001 0.001 0.01 0.1 1.0 10.0 UNIT SEDIMENT-TRANSPORT RATE, IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH FIGURE 5,—Mean velocity-unit transport relations showing depth effect (mean-velocity scale magnified about fivefold). The lines on the slope—transport diagrams (fig. 6) seem to diverge at the lowest sediment-transport rates and then remain equidistant from one another at trans- port rate's greater than about 0.005 lb per sec-ft. The appropriate adjustment factor therefore depends in part on the sediment-transport rate. One set of curves (fig. 7B) suffices for rates greater than about 0.005 lb per sec-ft. For lesser rates a slightly different adjustment factor for each transport rate should be given, accord- ing to figure 6; however, because of the greater chance of error in slope measurements at extremely flat slopes only one set of curves (fig. 7A), representing average adjustment factors for any transport rate less than about 0.005 lb/sec-ft, is given here. This introduces some possible error for the extreme conditions of deep depths (0.5, 0.7 ft) in very narrow channels (0.25, 0.5 ft) at extremely low transport rates (<0.001 lb per sec-ft). Aside from these rare conditions the wide-chan- nel slopes obtained by the adjustment factors of figure 7 are accurate to Within about 1- five percent for the SLOPE, IN FEET PER FOOT FLUME WIDTH AND WATER DEPTH EFFECTS H11 UNIT SEDIMENT—TRANSPORT RATE, IN KILOGRAMSIIIMMERSED WEIGHT) PER SECOND PER METER WIDTH 0.0001 0.00I 0.01 0.I I0 I00 I I I EXPLANATION Width (ft) 0.25 0.5 1.0 2.0 3.9 Depth (It) __ 0.] A o D o 0.3 A o . 0 Width 0.25 h 0.5 -& e a 4+ Width 0.5 It _ 0.0] 0.7 A ¢> m I _ _ DEPTH 0.7 n W‘d'l‘ I-° I' Widths 2.0 and 3.9 It I 0.00I — , ’\ I D — Infinitely wide channel WIdIh 0.25 II I I l I '— Width 0.5 II 0.0] r— ._ - DEPTH 05 FT Widths 1.0 and 2.0 h _ _,_’ i I 0.001 I— __ I I Infinitely wide channel _ Width 015 It _ I I _ I | _ ————— Width 0.5 It 0.0I — _ PTH 0. FT ,_ DE 3 Widths Lo and 2.0 II _ 0.001 — —""\ I I Infinitely wide channel I I T I I Width 0.25 h '— _ I I _ 0.0] _ DEPT” °~I FT Widths 1.0 and 2.0 h._ — Width 0.5 h —I 0.001 I I I I 0.000I 0.00I 0.0I 0.I I.0 I0. UNIT SEDIMENT—TRANSPORT RATE, IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH FIGURE 6.—Slope—-transport relations showing influence of flume Width. 0.0I 0.0I 0.0I 0.001 0.0] 0.00] 0 H12 SEDINIENT TRANSPORT IN ALLUVIAL CHANNELS Width _ Width . __Depth who -——-> “Depth ”"0 """ 0.5 l.0 2.0 5.0 l0.0 20.0 0.5 l.0 2.0 5.0 l0.0 20.0 '0 llllllll l lTlllllI (; IIIIIII l I Illllll 5 I . f :1 T DEPTH 0.1 FT t 5‘ ,K" g 0.9 — DEPTH 03 FT ./ DEPTH 0.l FT — .- E 03 _ /- DEPTH 0.3 FT — DEPTHS<0.5 , 0.7 FT / E 0.7 —- / Crutt(l965), smooth -— 1.1.1 / . E / steel boundaries ‘ g 0-6— / (0.0925D50J4 f1) ‘ 3 ‘5 0.5 '— /\ e —‘ L” / :84 0 4 — / Lane (1955), / DEPTH 0.5 FT __ W I / nature of boundaries A . T 0'3 _ and actual depths DEPTH 07 F — not specified. A. i<0.005 lb per sec-it B. i>0.005 lb per sec~tt 1111111L 1 1111111| 1 1111111 111111111 11 EXPLANATION Width (f1) Depth (it) 0.25 0.5 l.0 2.0 0.] A o 1:1 0 0.3 A o I O 0.5 as 9 B 4% 0.7 43 ¢ it t FIGURE 7.——Adjustment factors to be multiplied by the laboratory value to correct slope for sidewall effect. present data. Greater accuracy would depend in part on greater precision in fixing the slope—transport rela- tion for an infinitely wide channel. Thus for a given water depth, one can change the slope obtained in a flume of one width to the different slope which would obtain at another width, at least for grain sizes and flow conditions comparable to those studied here (fig. 6). What is more important, one can adjust the slope obtained in a “narrow” channel (side- wall effect significant) to the “wide-channel” slope (no wall effect), for the same depth and unit sediment-trans— port rate. To use figure 7 for this purpose, take the nar— row channel width and depth and multiply the indi- cated adjustment factor by the narrow-channel slope. This gives the slope which would occur in a wide chan- nel for the same depth and unit transport rate. The slope—transport curves of figure 6 can be in- terpreted as plots of shear stress versus transport rate. This is because depth was contant and wide-channel shear can be defined as 708, where y: specific weight of water. The slope-adjustment factors of figure 7 therefore also represent adjustments in yDS. The sidewall influence for these movable- and rough- bed studies probably is less than that which occurs when all three boundaries are smooth and rigid. Cruff (1965) computed shear stresses by using data from a smooth rectangular flume; Lane (1955) took another approach and got a different curve. For comparison purposes figure 7A includes the relations proposed by Cruif and Lane. This diagram suggests that when the bed and sidewalls are smooth and rigid greater width/ depth ratios are needed to eliminate wall effects than are needed for channels of smooth walls and movable sand beds. FLUME WIDTH AND WATER DEPTH EFFECTS DEPTH EFFECT The slope—transport curves of figure 6 could be used to obtain a depth effect for a constant fiume' width, but the resulting relation would include the effect of a changing discharge. A more pertinent question about natural streams is: How does depth vary with slope at constant water discharge? The multiple regression analysis mentioned earlier disclosed that for the present data depth varied with S428, at a constant discharge. The negative exponent means that for a given discharge the depth decreases if the slope steepens. What value would the minimum variance theory assign to this exponent? If the major dependent vari- ables are velocity, depth, friction factor, and unit stream power (discharge and channel width being con— stant), the minimum variance theory predicts that depth varies with 8-0-27, for a constant discharge and width. The slope values at depths of 0.3 and 0.5 ft (fig. 6) show a curious change in trend at high transport rates (0.2 to 0.5 lb per sec-ft) . In this range of transport rates the slopes tend to become constant (or even decrease slightly) as transport rate increases. At higher trans- port rates the slopes resume increasing. Brooks (1958) reported a similar pattern for slope values; however, he used fine sands, for which the nonuniqueness of slope values covered a much wider range of transport rates. For the coarse sand used here the relatively short range of transport rates affected by the nonuniqueness reduces the importance of this phenomenon. A nonuniqueness not uncommonly appears in natural streams having beds of medium and fine sand (Dawdy, 1961). There, however, the effect shows up in the water depth rather than in the slope because a river slope usually stays virtually constant. There probably are not enough runs at the pertinent sediment-transport rates to determine how, if at all, the channel Width affected the nonuniqueness in slopes. There is a depth effect in that the phenomenon is absent at D=0.1 ft but shows up at D=0.3 ft. One feature of the bed configuration should be men- tioned at this time. The bed forms progressed from dunes to antidunes to flat bed as transport rate in- creased. (With finer sands the only flat-bed stage that has been reported for flume studies occurs between the dune and antidune ranges rather than after the anti- dunes.) The flat-bed stage arrived gradually: as 2' increased, the flat bed occupied a greater upstream portion of the flume, with antidunes occupying a correspondingly shorter and shorter reach at the downstream end. The washed-out or flat-bed zone upstream had a shallower depth and flatter slope than the downstream antidune 373—261 0—70—3 H13 reach. (In some ways this is similar to the “sand wave” described by Vanoni and Brooks, 1957, p. 41.) For this particular range of transport rates, therefore, a uniform flow over the full flume test section was not possible. The slope profiles drawn for these runs were single “aver- age” straight-line profiles representing the whole flume, and discharge was regulated on the basis of these average profiles. (In tables 1 and 2 such runs are labelled “antidune” runs, and only those runs where antidunes disappeared completely are called “flat bed” runs.) The dip in slope values shown in figure 6 occurs pre- cisely in the range of “nonuniform” flow, where both antidunes and flat bed existed simultaneously in the flume. Slopes resumed their “normal” rate of increase with transport rate only after the flat bed occupied the full flume length. The major findings about flume width and depth effects on the energy gradient are as follows: 1. A lesser slope evolved as the channel become wider, for the same unit transport rate and depth. Such a trend might have been predicted, but the present study actually measures this change. The resulting adjustment factors give slope values in an infinitely wide channel, the proportion of the energy gradient due to sidewall effects in narrow channels, and a means of correlating slopes from flumes of different widths. 2. Flume width did not affect the rate of change of slope with change in unit sediment-transport rate as long as water depth remained constant. 3. For depths ranging from 0.1 to 0.7 ft the sidewall effects became virtually insignificant at a flume width of 2 ft. 4. The large difference in roughness between bed and sidewalls seems to contribute to an elimination of wall effects at lesser width/depth ratios than in flumes of smooth rigid boundaries. 5. At constant unit discharge, depth varied with 84-23. The minimum variance theory predicts this same relation. 6. The nonuniqueness of slope values associated with the washing out of bed forms seems to be less impor— tant with coarse sands than with medium and fine sands. STREAM POWER GENERAL Stream power (Bagnold, 1966) is the’rate at which a stream loses energy per unit boundary area. The power per unit bed area, a), is equal to yQS/ W. Figure 8 shows the unit stream power-unit transport rela- tions for the present data. H14 , IN POUNDS PER SECOND PER FOOT 705 W UNIT STREAM POWER SEDMENT TRANSPORT IN ALLUVIAL CHANNELS UNIT SEDIMENT—TRANSPORT RATE, IN KILOGRAMS (IMMERSED WEIGHT) PER SECOND PER METER WIDTH 0.001 0.0I O.I 1.0 10.0 I EXPLANATION I I I I Width (ft) Depth (“I 0.25 0.5 I.0 2.0 3.9 _ '00 °-' A 0 U 0 Width 0.25 it 0.3 A o I Q _ 5'0 0.5 a e 4} 0 WidIIT 0.5 ft 1.0 0.7 d 0 E I X Width 1.0 H _ 2'0 . A Lo 05 — WIdIITs 2.0 and 3.9 II DEPTH 07 FT _ 0 5 0.2 0.] I00 0.05 5.0 0.5 0.2 0.I DEPTH 0.5 FT Width 0.25 II WidIITs Lo and 2.0 II Width 0.5 H _ I 2 'o I 9 .5 o L11 0 UNIT STREAM POWERyoS, IN KILOGRAMS PER SECOND PER METER 0.05 Width 0.5 It — 2.0 3 I0 0.5 — 0.5 0.2 __ DEPTH 0.3 FT — 0.2 0,] 0.05 I — 2.0 0.02 _ 1.0 0'0] — 0.5 0.2 — 0.2 0.1 — 0] 0.05 DEPTH 0.1 FT — 0.05 O 0.02 — — 0.02 0.01 1 I | I 0.000] 0.00] 0.0I 0.] IO 10.0 UNIT SEDIMENT—TRANSPORT RATE, IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH FIGURE 8.—Unit stream power—unit sediment-transport relations showing flume—width efiect. FLUME WIDTH AND WATER DEPTH EFFECTS The graphs reveal that the change in trend at high transport rates which appeared on the slope-transport diagrams (fig. 6) disappears on the power—transport plots. This is because a discharge slightly greater than expected accompanied the lesser slope ,values for the pertinent transport rates, in order to maintain the same constant water depth. The result is a unique relation between stream power and sediment transport for a con- stant water depth, regardless of bed configuration. The unit stream power—unit transport relations for the three deeper depths (and approximately for D=0.1 ft) follow a power law over most of the range of transport rates covered. As with the discharge— transport and slope—transport relations, flume width did not affect the rate of increase in unit power with increase in transport rate, at constant water depth. The straight-line portions for the three greater depths in figure 8 and nearly all of the relation for D=0.1 ft were fitted by least squares by using the constraint that the lines for all widths at a given depth are mutually parallel. The curved lines at the lowest transport rates on all four diagrams were fitted by eye. Unit stream power varied with the 0.61 power of unit transport rate, at constant channel width, within the range of transport rates covered by the least-squares analysis (0.005 éié 1.0 lb per sec—ft and 0.3 éDé 0.7 ft). If we consider stream power as the independent variable then 2' 0: (01'64. WIDTH EFFECT The transportation of an imposed sediment load re- quires a certain basic stream power or work rate. In narrow channels the sidewalls take up a significant part of the total available power. Consequently, narrow chan- nels need a greater stream power (w’)~—the basic work rate required to move the sediment load plus the power used up on the sidewalls. For the present study the data permit a determina- tion of these two powers for a given depth and width. Moreover, the unit power measured in a narrow channel can be corrected to yield the lesser power needed to move the same unit transport rate in a wide channel at the same depth. This can be done because the sidewall effect disappeared at the 2-ft width, according to the least-squares computations, except for D=0.7 ft. For D=O.7 ft the same extrapolation method as on the slope—transport relations was used. The dashed line in figure 8 represents this extrapolated relation for D=0.7 ft in an infinitely wide channel. Figure 9 gives the adjustment factors to correct unit stream power for the flume sidewall effect, at a con- stant depth and unit transport rate. These factors rep- resent simply the Wide-channel unit power a) divided H15 by the narrow-channel value w’. For any given channel width and depth, multiply the narrow-channel unit pOwer by the adjustment factor shown in figure 9 to find the unit power needed to transport the same unit sediment load in an infinitely wide channel, at the same water depth. ' Figure 9 shows that the stream power adjustment factor depends primarily on the width/depth ratio, as expected, but that the adjustment also varies slightly with both water depth and sediment transport rate. In fact, since unit discharge (2/ W did not vary significantly with flume width (fig. 3) one might ex- pect that the unit power yQS/ W adjustment factors would be the same as the slope-adjustment factors of figure 7. A comparison of figures 7 and 9 shows that the two diagrams are indeed virtually the same. The chief exception is for a depth of 0.1 ft, where narrow chan- nels need a greater adjustment for (0 than for slope. This is probably due to the slightly different unit dis- charge—unit transport relation that appeared for the 0.25-ft-wide channel at this depth (fig. 3). A minor difference between the power- and slope- adjustment factors is that with stream power the side- wall influence, according to figures 7 and 9, may be eliminated at slightly lesser W/D ratios. There seems to be no ready explanation for this. For practical purposes it might be better to ignore the minor influence of sediment-transport rate and to concentrate on the general similarity in the adjustment factors of slope, shear stress, and stream power (figs. 7 and 9). Because all these curves have the same shape, a simple curve-fitting procedure will permit one curve to describe all the data. For the present data the plot which brings all the points reasonably close to a single curve is the adjustment factor as a function of (W/Dh/fi. Figure 10, which has all the slope (or shear) and stream power adjustment factors (figs. 7 and 9) for the complete range of transport rates studied, shows this plot. Figure 10, in other words, includes the same data as figures 7 and 9 but with (W/DND— rather than W/D on the abscissa. One advantage to this type of diagram is that no interpolation is needed to get the adjustment factors for widths and depths intermediate between those studied here (for example, a depth of 0.4 ft and (or) width of 0.75 ft). The single greatest deviation of the curve from a measured adjustment factor is 26 percent, but in 73 percent of the cases the discrepancy between the meas- ured values and the curve is é 5 percent, the arithmetic average. Data for the deeper water depths in narrower channels tend to show the largest deviations, owing to the steepness of the curve for these widths and depths (fig. 10). H16 SEDMENT TRANSPORT IN ALLUVIAL CHANNELS WidIh , Width raho —> ratIo—-> Depth Depth . 0.5 1.0 2.0 5.0 10.0 20.0 0.5 1.0 2.0 5.0 10.0 20.0 33 llllllll I llllllll I llllllll I IIIIIIIj I H 1.0 a 0 I: 0 H D ()— M 2 0.9— O — U E 0 8 _ DEPTH 0.1 FT .— - DEPTH 0.1 FT ‘ E E 0.7— DEPTH 0.3 FT — 3 DEPTH 0.3 FT 3 0.6 — — < E 0.5 w _ E A ‘2‘ 0‘4 T \ 4\ DEPTH 0.5 FT - E 0.3 — DEPTH o.5,o.7 FT — E DEPTH 0.7 FT m E A. i<0.005 lb per sec-H B. i>0.005 11) per sec-ff 3 IIIIIIII I lll||l|1 I lllll|l1 I Illlllll I EXPLANATION Width (ft) m 0.25 0.5 1.0 2.0 0.1 A o u o 0.3 A o I O 0.5 a: e B 0 0.7 A d> m t FIGURE 9.—Adjustment factors to be multiplied by the laboratory value to correct stream power for sidewall effect. The equation of the general adjustment-factor curve of figure 10 is X2 Y=0.18+X2’ where Y is the adjustment factor for slope, stream power, or shear stress and X is (W/D) {5. This equation reduces to Y—~——1 - —1+0'18(1/%) The coefficient (0.18) has dimensions of length (feet), and the adjustment factor Y is dimensionless. Using coeflicients of 0.10 and 0.24 in place of 0.18 produces two curves which include nearly all of the plotted points. The coefficient of 0.18 was determined by least—squares from the data of the narrower chan— nels, as the predicted adjustment factors for these data (steep portion of curve in fig. 10) are the most sensitive to changes in the coefficient. (For the wider channels small changes in the 'coefiicient have a negligible in- fluence on the predicted adjustment factor.) With the above formula the adjustment factor varies not only with the width/ depth ratio but also with the actual magnitudes of width and depth for the same W/D ratio. (The separate adjustment curves, such as those in fig. 9, show this same feature.) For example, at a Width/ depth ratio of 3 the adjustment factor com— puted from the general equation progresses from 0.82 at a depth of 0.1 ft to 0.94 for D=0.3 ft to 0.96 for FLUME WIDTH AND WATER DEPTH EFFECTS H17 (W/Dufi, IN (FEETIV’ 0.0 0.5 l.0 1.5 2.0 2.5 A3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 1.0 I RI J'j I K—l—i—A- ' I l I I 24 | _ I b E i’g f I _ & seek a: 0.9 — A xEF p I _ E _ A ADJUSTMENT FACTOR=Y= _ u [IT D E l + 0.l8(—2) ,_ 0.8 — w —~ 5 l _ 2 — 9 5 o 7 — 11> — s w < — 9 “ g g 0.6 —— / —- n. — kg '— E g 0-5 — as EXPLANATION - s — I: — g 0.4 __ A . Symbols Sample use of tick-marks __ a _ f Deplh(fll)N|dlh l“) 0.25 05 1.0 20 Slope (or shear) adiuslmenl factor: _ g 0.3 — if 0.] A o D O i<0.005lb per sec-Her _ E _ {I 0.3 ‘ . I . i>0.005lb per sec-Hr _ E: 0.2 —,l 0.5 19* 9 5“ e Stream power adiustmeni factor: fl E —II' 0.7 4: ¢ [I] i? i<0.005|b per sec-liq — m (H fl" i>0.005lb per sec-HP — 0'0 " I l | | I l I l I I I l I FIGURE 10.——Adjustment factors to be multiplied by the laboratory value of slope (energy gradient), unit stream power, or shear stress to correct for the flume sidewall effect. D=0.5 ft, the width in each case being three times the depth. Similarly, at a width/depth ratio of 5 the calcu- lated adjustment factor is 0.93 for D=0.1 ft (W=0.5 ft), 0.98 for D=0.3 ft, and 0.99 for D=0.5 ft. More ad- justment is needed, in other words, as water depth de- creases, for a given W/ D ratio. The above equation for finding the necessary adjust- ment in the “narrow-flume” value of slope, shear stress, or unit stream power is one of the main results of this study. The formula may or may not apply to other flow conditions and sediments. The unit power may often be independent or constant, and one would like to know how to adjust the sediment- transport rate (considered as a dependent variable) to correct for the sidewall influence. Figure 8 also pro- vides the information needed for these adjustment fac— tors. The adjustment to transport rate varies depending on the specific unit power, in addition to depth and width/depth ratio. Figure 11 shows the necessary ad- justment in unit sediment—transport rate for various values of unit stream power. (Fig. 11 therefore does not reflect the control of variables for the experiments—it comes from the measured power—transport relations but pretends that stream power was independent and transport rate was dependent.) One of the most striking revelations of figure 11 is that the unit sediment-transport rate in a wide channel can easily be 2 to 5 times greater than in a narrow channel, for the same unit stream power and water depth. Also the sidewall efl'ect is much more pronounced at low flow rates (low values of stream power). DEPTH EFFECT In addition to flume-width effects the present data reveal the influence of water depth on the power—trans- port relation. The discussion here deals with the more H18 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS l IIIIII I I IIIIII_IO.0 1 3.0 — w = 003 II) per set“ " DEPTH 0.I FT : _. 1 a: 2 0 / — w— 0' (a): 0.07 lb per SEC-h _ 5 0 z . I— \ " "‘ . _ . g \ 0.065w5l.0Ibpersec-H — lb per sec-ft _ E :5 ‘s DEPTH 0.3 FT E 5 10 l \_ ‘ *5 w - ' ' ' = o.osI - E 2.0 5.0 we _ ‘° 5 P" s“ “_ 2 o :‘g‘ g Width/Depth ralio—> ' S 3 20.0 I I I I I I1 3 : w= 0.2 lb per sec-h 0155‘” '30”) Persec'“ : ’E DEPTH 0.7 FT I I I I II I ,0 I; 0‘ 0.5 I.0 2.0 5.0 I0.0 °‘ 30; 10.0 : Width/Depth ratio—> '00—: “- _ A. Q ’ DEPTH 0.5 FT - I I I I I II I I d g < ’— F. _ _ 55, 5.0 ~ w: M lb per sec-It \— ‘\\°" °-' '5 P" 5“ I' — 5.0 E '— z " " " z "2" to: 0.08 lb per sec-ft \ w: 006”) per ”2" E L _ sec-ft " E 3 3 E 2.0 — L ~ 2.0 g 2’ 0.2Ews4.0 = 0.55w52.0|b per sec-It Ib per sec-It ‘0 I I l I I I I I I '0 0.5 I.0 2.0 5.0 Width/Depth ratio —> 0 .5 I.0 2.0 Width/Depth ratio ——> FIGURE 11,—Unrit transport rate adjustment factors to be multiplied by the laboratory value to correct for flume sidewall effect. common field situations where stream power is usually the imposed or independent variable and depth and transport rate are dependent. Figure 12 shows the power-transport curves for “wide” channels (wall effect negligible) for the four flow depths studied. For a given unit power the trans- port rate increased as depth decreased. This means that power for power a shallow stream transports sediment at a faster rate than a deeper stream, within the range of depths studied here. The transport rate increased four to six times as depth was decreased from 0.7 to 0.1 ft (that is, from about 160 to 20 grain diameters), for a given stream power. The depth effect in the power-transport relations diminished as the water became deeper. The curves of figure 13, prepared from figure 12, suggest that at some depth greater than 0.7 ft (probably around 1.0 to 1.5 ft) the unit transport rate may no longer decrease with increase in depth, for a given stream power. The transport rate at zero depth should be zero. For this reason it seems unlikely that the transport rate could go on increasing at depths much below 0.1 ft. The curves showing the depth effect at depths less than 0.1 ft (about 20 grain diameters) therefore might be simi- lar to the broken extensions shown in figure 13 (R. A. Bagnold, written commun., 1968). Bagnold (1966, p. I9), in comparing shallow depths where saltating grains reach the water surface to large depths where the saltation height is a negligible por— tion of the flow depth, predicted strictly on theoretical grounds that the bedload transport rate at the shallow depth would be three times the rate at the greater depth, for a given stream power. Figures 12 and 13 suggest that a factor of about 4 to 6 applies to the present data, except for very low flow rates For unit stream powers from 0.1 to 1.0 lb per sec-ft (that is, for most of the conditions covered in the ex- periments), the unit sediment transport rate changed at the same rate with depth, regardless of the stream power (fig. 13). Further experimentation with grains larger and smaller than 1.35 mm would be useful in determining whether the depth effect as observed here is influenced by such features as (a) depth/grain—size ratio, as con- trasted to depth alone, (b) bed-form heights relative to water depth, and (c) the ratio of bedload to sus— pended load. FLUME WIDTH AND WATER DEPTH EFFECTS UNIT SEDIMENT-TRANSPORT RATE, IN KILOGRAMS (IMMERSED WEIGHT) PER SECOND PER METER WIDTH '— . § 10 0.001 0.01 0.1 1.0 10.0 n. g _ § 011111 0.5 11 D V) a F 011111 0.3 11__ Q. 3 1.0 -— 011111 0711’; 3 x — 1.0 o __ n. z _ 8 z — e~ 0.1 —- II 0: 011111 0.1 11 D 0.1 u-1 1— 3 O _ O. 2 L— :5 m '- 0.01 I I I 1 2 0.0001 0.001 0.01 0.1 1.0 10 § 01111 SEDIMENT-TRANSPORT 11111, IN 10uuos (111111111510 w11e111) 111 SECOND 1111 1001 WIDTH FIGURE 12.—Un.it stream power—unit sediment-transport relations in an infinitely Wide channel. H19 1 IN KILOGRAMS PER SECOND PER METER 05 W UNIT STREAM POWER 7 UNIT SEDIMENT—TRANSPORT RATE, IN KILOGRAMS (IMMERSED WEIGHT) PER SECOND PER METER WIDTH DEPTH, IN FEET 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.I o . 0.00I 0.0I 0.I I.0 I I I I 1—- | I _ I I I I I _ I F ‘ I w_ 0.I lbs per sec-II l __ \ I I: 0.067 kg per sec-m) I _ \\ I‘ “ w = ID lbs per sec-II 1— v (= 0.67 kg per sec-m) —_ v —_ I— Bw= 0.05 lbs per sec-II V V v _ _(: 0.034 kg per sec-m) \ \ — v v v \ \ _ _ _I _____ ’ I 3 I \II ___=_=_'—__'_'_-'_n-———_—_—— ————————— — 0.00I 0.0I 0.I I.0 30.0 25.0 20.0 I5.0 DEPTH, IN CENTIMETERS 10.0 5.0 0 UNIT SEDIMENT—TRANSPORT RATE, IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH FIGURE 13.-—Variati0n of total sediment-transport rate with difierent water depths, for constant stream power. H20 BED FORMS The sizes, shapes, and travel rates of the sand features which form on a streambed influence the level to which the water will rise in a channel of fixed width and slope,‘ the navigability of a watercourse, and the depth to which bridge piers must extend. The types of bed configuration (Kennedy, 1966) which appeared with increasing sediment-transport rates were flat bed (at very low transport rates, for some runs only), dunes, antidunes (always moving down- stream), and flat bed (sheet flow) . This order of appearance differs from that found with medium and fine sands (Simons and others, 1965) . With increasing transport rate medium and fine sands produce a bed of ripples, ripples on dunes, dunes, flat bed, antidunes, and chutes and pools. The chief differ- ences between such sands and the present coarse mate- rial are that with the latter (a) the bed often remained flat at the very lowest transport rates (possibly because the run began with an artificially flattened bed), (1)) no ripples formed, and (c) a fla -bed stage came after rather than before the antidune stage. No dunes occurred at a depth of 0.1 ft. At widths of 1 and 2 ft the runs at slow transport rates for D=0.1 ft produced bars which alternated or meandered from wall to wall (see Williams, 1967, p. B21). In the 0.25- and 0.5-ft-wide channels, the bed forms at all depths were mostly two dimensional, except for the antidunes at D=0.1 ft in the 0.5—ft-wide channel. At widths of 1 ft or more, the bed forms for the three deeper water depths were two dimensional during slow transport rates but gradually became three dimensional (curving from wall to wall) as transport rates increased. Thus the disappearance of sidewall efl’ects on such fac- tors a-s slope and stream power corresponded roughly with the onset of three dimensionality in the bed forms. The following analyses are based on graphs (not included here) of the individual bed-form character— istics as function of the independent variable unit sedi- ment-transport rate. BED-FORM HEIGHTS 1. General. Neither flume width nor water depth af- fected the rate of growth of bed-form height with increasing unit transport rate. Dune heights, for example, increased with 2"”. The specific height corresponding to any unit transport rate, however, usually changed significantly with flume width and depth. 2. Width efl'ect. Least-squares lines of best fit for the dune height—unit transport relations (keeping the lines for the various flume widths parallel to one another for each depth) showed that dune heights SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS increased as the channel became wider, for a given unit transport rate and depth. For the 0.3 and 0.5 ft depths this width effect disappeared in the two wider channels. For D=O.7 ft the width effect ap— peared to be almost eliminated at W=2.0 ft, but this conclusion is only tentative because dunes in the five runs in the 3.9-ft—wide channel seemed to be higher than those in the narrower channels. Figure 14 gives the necessary adjustment fac- tors to correct dune height for the channel width effect (0.3éDé0.5 ft). Notice that this effect can be substantial. Dunes in the 0.25-ft-wide channel were only about half as high as those in the 1- and 2-ft-wide channels, for a given unit transport rate and water depth. Flume width had no significant influence on an- tidune heights. This is strange in View of the channel width effect on dunes. 3. Depth effect. Dune heights increased considerably with increase in water depth, at constant flume width and unit sediment-transport rate. The least- squares lines indicate that in the 2-ft-wide chan- nel, where sidewall effects were negligible (or at least minor, such as for D=O.7 ft), dune heights . increased with Do“, for any selected unit sediment- transport rate. Narrower channels gave slightly different ex- ponents. In the 025-, 0.5- and 1.0-ft-wide chan- nels dune heights grew about with the 1.0, 1.0, and 0.7 powers of water depth, respectively, at con— stant unit transport rate. Thus the exponent de- creased slightly as the channel became wider. Antidune heights at constant unit transport rate increased with water depth for depths at 0.1 to 0.5 ft, especially in going from the 0.1- to the 0.3-ft depth. Heights for D=O.7 ft, however, were not significantly different from those at D=0.5 ft, for the same unit transport rate. ( ' ' ‘ ' ' ‘ 'l ' EXPLANAT|ON g Depthin it E 2.5 —— DEPTH 0.5 H DEPTH 0.3 FT .3 0.5 ”- A .25 A A g 2.0— \t\ .3 : e E . a a 15— .0 o e a 9: 1.0 — 9—4—— .. g I I l I l 1 ll l l l I l l l '5; 05 1.0 2.0 50 10.0 ‘“ Width . z 1 —> 2 Depih ru I0 FIGURE 14.—Dune—height adjustment factors to 'be multiplied by the laboratory value to correct for flume—width effect. FLUME WIDTH AND WATER DEPTH EFFECTS H21 BED-FORM WAVELENGTHS 1. Width effects. The flume width did not influence the bed-form wavelength—unit transport relation for a given water depth. However, the channel width may have had an effect (data are inconclu- sive) in that the effect of water depth (m the wave— lengths seemed to vary with the flame width, as will be mentioned below. 2. Depth effects. For unit transport rates less than about 0.01 lb per sec-ft (about half the range covered) the water depth had no influence on the bed-form (dune) wavelengths. As transport rate increased, however, a depth effect became more and more pronounced, at least in the two narrower channels: bed-form wavelengths increased with increase in water depth. The plots suggested that this effect may not exist for channel widths El ft, at depths of 0.3 to 0.7 ft. But there are not enough runs in this range to say with certainty. Even in the wider channels the wavelengths for D=0.1 ft (anti- dunes) were considerably shorter than those for greater depths, at any selected unit transport rate. Antidunes tended to form at lesser unit trans- port rates as water depth decreased, at least in the two narrower channels. In fact at D=0.1 ft anti- dunes always formed. at slower transport rates, regardless of channel. width. (By the. same token the flat-bed stage which followed also came at. slower unit transport rates.) For depths between 0.3 and 0.7 ft the data. for the 1- and 2-ft-wide channels are inconclusive on this issue. TRAVEL VELOCITY 1. General. Bed forms travelled faster with increasing sediment-transport rate. The rate of dune move- ment increased about with z" “8, with no significant difference due to depth. or width. For antidunes the exponent. was less, about 0.7 to 0.4, depending on the flume width. 2’. Width effects. Least-squares lines. for the travel ve- locity—sediment transport relations (keeping the lines for all four widths parallel to one another, for a given depth) revealed a definite width ef- fect: dunes in the two narrower channels, where sidewall effects were significant, travelled, faster than dunes in wider channels, for a given water depth and unit. sediment-transport rate. For depths of 0.3 and 0.5 ft the order of magnitude of this in- creased travel velocity was about 1.5 times. Side- wall effects disappeared at the two wider channels for depths of 0.3 and 0.5 ft but were still present for D=0.7 ft, according to the least-squares lines. The travel velocities for 0:07 ft showed more scatter than those at lesser depths, so the sidewall effect may or may not have been eliminated at D= 0.7 ft. Plots of the calculated travel-velocity adjust- ment factors as a function of W/D, for depths of 0.3 and 0.5 ft, showed too much scatter to permit drawing reliable curves. Analyzing antidune travel velocities by least- squares was not feasible because of the small num- ber of antidune runs for any one width and depth combination. But the scatter on the plots was gen- erally small enough for representative lines to be fitted by eye. These lines suggest the following: (a) no width effect occurred at D=0.1 ft and (b) a width effect occurred for the three deeper depths in that the rate at which vantidune travel-velocities in- crease with 2' probably decreased as the channel widened, for 0.25 éWél.0 ft. 3. Depth effects. For a given channel width and unit sediment-transport rate, dunes travelled faster as water depth decreased. The dune travel velocity increased about With D'L5 for Wide channels where sidewall effects were negligible (W: 1.0 ft and 2.0 ft for the two shallower depths, and assumed to be W=2.0 and 3.9 ft for D=0.7 ft). The exponent was less in narrower channels, however. For the 0.5- ft-wide channel dune travel velocity increased about with D'”, while for W=0.25 ft the ex— ponent was about —1.0. Antidune travel rates showed no depth effect for 0.3 éDé0.7 ft. However, at D=0.1 ft the anti- dunes fer a given transport rate moved nearly twice as fast as. those at the greater depths, at least in the two narrower channels. The effects of. flume width and. water depth on bed- form. characteristics, at constant unit sedimentrtrans— port rate, are summarized as follows: 1. In the two narrower channels where sidewall. effects- were significant, dune heights were less but these dunes travelled faster, for a. given depth. Anti- dunes heights and bed-form wavelengths remained virtually the same regardless of channel width. Data are inconclusive concerning flume Width, effects- on the travel velocities of‘antidunes. 2'. With increase in. water depth. at constantflume width. the dunes grew higher and travelled. at a slower rate. Antidune heights also increased. with depth, with the possible exception, of depths. from 0.5 to 0.7 ft. Travel rates of antidunes showed no marked depth effect for the three greater depths, but. antidunes at, D=0.1 ft travelled faster than those at deeper depths. No depth influence onbed- form wavelengths appeared for transport rates less H22 than about 0.01 lb per sec-ft, but as-z' increased beyond this value (involving some dune runs and all antidune runs) the wavelengths probably in— creased with water depth, at constant transport rate. The width and depth effects mentioned above suggest that many bed-form characteristics meas- ured in narrow flumes probably cannot be applied with assurance to wide channels. Why did the dunes grow higher as the flume be- came Wider, at constant unit transport rate and depth? The most likely reason is that the increase in width brings a different velocity distribution within the cross-sectional flow area. Rouse (1961, p. 276—277 ) shows that in narrow rectangular chan— nels the velocity near the bed increases more rapidly with height and the maximum velocity oc- curs closer to the bed than in wide channels. These velocity characteristics would restrict bed-forms to lower heights in narrow channels. Higher dunes by themselves should cause a steeper slope, if the bed roughness alone governed the slope (transport rate and depth constant). But the general trend with increasing width was a lesser slope, in spite of the higher dunes Hence the greater width pre- dominated over the increase in bed roughness, in re- gard to the slope that evolved. A wider channel at the same depth meant a proportionally smaller retarda- tion of the flow by the sidewalls, as discussed earlier. RESISTANCE FACTORS GENERAL The resistance factor or friction factor as an indicator of boundary resistance is important in river and canal hydraulics because this resistance directly affects the size of the cross—sectional flow area and the rate at which a channel conveys water. Table 1 includes two commonly-used resistance fac- tors: Manning 71. (21.49 132/381/2/ V) and Darcy-Weis— bach f (= 89138 / V2) , in which R is the hydraulic radius and g is the acceleration due to gravity. (The values of n and f in metric units are the same as those for English units.) Both of these resistance factors changed in the same way as functions of the independent variable 2', so only one of them need be examined here. WIDTH EFFECT Figure 15 shows how the Darcy-Weisbach friction factors changed with flume width, for a constant depth and unit transport rate. The straight portions of the lines were fitted by least-squares with the constraint that the lines for the various widths be mutually parallel, SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS for any one depth. The curved lines at fast transport rates were fitted by eye. At a constant depth the relations for all widths are similar in that the friction factor gradually increased as bed forms grew higher. This trend extended over about the first two-thirds of the range of transport rates studied. The highest friction factors (greatest bed re- sistance) occurred when antidunes covered the full flume test section. The friction factor began declining when antidunes started washing out at the upstream end of the test section, even though the remaining antidunes in the downstream zone were higher than in runs at lesser transport rates. With further increase in transport rate, the decline in friction factor continued as antidunes occupied a lesser and lesser zone downstream, and in fact the de- cline continued during the subsequent flat-bed stage throughout the remainder of the range of transport rates investigated. The friction factor began decreasing at transport rates slightly less than those rates at which the change in trend of slope values occurred (compare fig. 6 to fig. 15). At still faster transport rates the friction factor declined regardless of how slope was changing. The friction factor at constant depth and width varies with 8/172, and at fast transport rates V2 increased with 73 faster than S changed with 75. Since the channel width did not affect the mean veloc- ity, for a given transport rate and depth, any changes in the friction factor due to flume width must be due to the changes in the hydraulic radius and the slope. Figure 15 shows that the Darcy-Weisbach friction fac- tor increased as the channel became wider, for a constant depth and unit transport rate. Thus with increase in flume width the hydraulic radius increased more sub- stantially than the slope decreased. The B and S values in tables 1 and 2 verify this. Knowing the effect of flume width on the variables 13,8, and V, it was possible to compute the friction fac- tors for an infinitely wide channel. Mean velocity was the same for any flume width, at a given depth and transport rate, so the best-fit curves of figure 4 provided values of V. The hydraulic radius in an infinitely wide channel equals the mean depth D. Figure 6 was the most convenient source for the wide-charmel slopes, although the slope-adjustment factors of figures 7 or 10 could be used as well. For each selected transport rate and depth the appropriate R, S, and V values provided the friction factor in an infinitely wide channel (dashed lines in fig. 15). The empirical system used here to correct friction fac- tors for the sidewall effect keeps the same depth for both the narrow flume and the infinitely wide channel. FLUME WIDTH AND WATER DEPTH EFFECTS H23 UNIT SEDIMENT-TRANSPORT RATE, IN KILOGRAMS (IMMERSED WEIGHT) PER SECOND PER METER WIDTH 8gRS V FRICTION FACTOR f 0.00] 0.0] 0.] I0 I I I I 0' dunes —-—+— anIidunes 0.05 0.02 0.0I 0.1 0.05 0.02 0.0T OI dunes—+— anIidunes—+—flut bed ' I I I I 0.05 r- ._ 0.02 -— _, DEPTH 0.3 FT I I I I 0.0I 0‘ HM bed——+— anIidunes —+— “(II bed ' I ___L _________ I F o “““““ o___—— if Dog 9 0 EI“‘“~\ Infinitely wide 0.05 — ‘3 1v U U 0 V” 0 A Nchunnel ‘ PM 0.02 _ . o — 0.0] DEPTH 0.I FT I I I I 0.000] 0.00I 0.0] 0.] 1.0 UNIT SEDIMENT-TRANSPORT RATE, IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH EXPLANATION Width (II) DepIh (II) 0.] 0.3 0.5 0.7 0.25 0.5 I.0 2.0 3.9 bitbp 9000 Emir: oo<> FIGURE 15.—Flume-width efiects on friction factor—transport relations. H24 Mean velocity also stays the same, but the two channels have different slopes. Some investigators regularly use a theoretical method to adjust friction factors for the sidewall eifect. This system, known as the sidewall cor— rection method (see Vanoni and Brooks, 1957), keeps both velocity and slope the same for the two channels and changes only the hydraulic radius. The section “Sidewall correction procedure” deals with the sidewall correction method in more detail. DEPTH EFFECT An increase in depth at any fixed width and transport rate brought an increase in R, a decrease in S (fig. 6), and an increase in V (fig. 5). The change of the quotient [BS/V2 With depth should therefore be calculable from a lmowledge of how R, S, and V changed with depth, at a. fixed transport rate and flume width. An easier method simply compares the curves for the various depths for any chosen Width, as taken from figure 15. Such a comparison shows that there is little if any significant difference between the friction factor-trans- port relations for the three greater depths. The curves for all three depths reach their peak and begin declining at about the same unit transport rate. The trends of 8 alone (fig. 6) indicate this might be expected for depths of 0.3 and 0.5 ft but would not be expected for D=0.7 ft, because at the latter depth no dip or nonuniquiness in slope values appeared. More runs at D=O.7 ft would be needed to clarify this point. At low transport rates the friction factors for D=O.1 ft are about 1.5 times greater than those for the other three depths. Antidunes at D=O.1 ft began washing out at much lesser transport rates, however, so the curve begins to decline correspondingly earlier (about one log cycle of transport rates sooner). At transport rates of about 0.1 lb per sec-ft or a little less, the friction factors for all depths are nearly the same, differing by a factor of about 1.2. The labelling of the bed configuration in figure 15 (with flat-bed zones determined from narrow-channel data) shows a feature mentioned in the bed-form discus- sion: antidunes and the subsequent flat-bed stage appeared at slower unit transport rates as depth decreased. The scatter on the friction factor—transport diagrams prevents drawing conclusions more specific than those mentioned here. SIDEWALL CORRECTION PROCEDURE The results presented thus far show that flume width can have a considerable influence in sediment-transport experiments. Clearly, a reliable means of evaluating and eliminating sidewall effects would be a very useful tool SEDIMIENT TRANSPORT IN ALLUVIAL CHANNELS indeed. Whenever poSsible such tools should be sup- ported by theory rather than being empirical rules based on limited observations. Several “theories” or formulae for sidewall correction have been proposed but are not very popular. The few investigators in the United States who use a sidewall correction prefer a method which has evolved gradually over the past 55 years. Schoklitsch (1914) outlined the foundation of this particular sidewall cor- rection. method. After about 20 years two more papers appeared, almost simultaneously: Horton (1933) in November of 1933 and Einstein (1934) in February of 1934. Though starting from different viewpoints and prepared independently of one another, these two pa- pers arrived at the same general formula. Colebatch ( 1941) , apparently unaware of the Schoklitsch and Ein- stein papers, proposed a variable correction factor to Horton’s equation. These correction factors presumably apply to canals and ditches cut in earth and rock and have received very little attention. Also in 1941, Ein- stein gave an example Showing 'how to apply his 1934 treatment to flume studies of sediment transport (Ein- stein, 1942). Johnson (1942) took Einstein’s equation and added the refinements of (a) showing how to com~ pute the hydraulic radius of smooth sidewalls and (b) changing the basic friction formula from that of Man- ning to that of Darcy-Weisbach in order to include a viscosity factor. Brooks simplified the procedure, and it is explained in detail by Vanoni and Brooks (1957). The method as proposed applies only to fully rough flow, where the bed resistance coefficient stays constant for varying flow conditions (Reynolds number) for a given bed roughness. The general approach is to imag- inarily divide the cross-sectional flow area into three subsections, each representing a separate “channel” in which only one particular boundary (bed or sidewall) affects the flow. You assume that the mean velocity and energy gradient for each subchannel equal the mean velocity and energy gradient for the entire flume. The calculations involve any of the resistance formulae (for example, Darcy—Weisbach or Manning), with variables V, S, R, and the resistance coefficient. The goal is the friction factor and hydraulic radius of just the bed; for this bed section you can then compute any other quantity involving the hydraulic radius or depth, such as the discharge. Any such factor supposedly is free of sidewall influence. Many people do not use the sidewall correction pro- cedure, partly from theoretical objections but primarin because of the scarcity of data showing whether or not the method gives accurate answers. Some advocates of the procedure claim as one verification of its validity the results of flume experiments with a fixed, rough FLUME WIDTH AND WATER DEPTH EFFECTS bottom and smoother sidewalls (for example, the tests of Johnson, 1944). Runs at various depths in such tests give different composite resistance coefficients but al- most identical values of the predicted “wide-channel” friction factor. The literature contains at least five instances where authors devoted specific attention to testing this side- wall correction method. Colebatch (1941) made from one to three runs in each of three types of board-and—dirt model channels and concluded that the method (Horton’s formula) gave errors up to :15 percent of the composite resistance coefficient. Haywood (1940, 1942) analyzed data from two en- vironments: (a) eight natural drainage ditches with boundaries that had a uniform roughness at low stage and a different but also uniform roughness along the banks (higher flow depths) and ('b) a rectangular flume with smooth walls and sand-roughened bottom. Hay- wood remarked that the data check very closely the lines predicted by the sidewall correction formula, and he decided that the method (that is, the composite resist- ance equation of Einstein’s 1934 paper) was “sum- ciently accurate.” Yassin (1953) studied uniform but difi’erent fixed roughnesses on a flume bed and sidewalls. He first de— termined the resistance coefficients of various boundary surfaces individually, for a range of flow conditions. Then he installed channels of composite roug‘hnesses (for example, bed rough and sidewalls smooth), using the surfaces whose coefficients he had measured in the initial tests. Yassin found that the sidewall correction equation, with the separately-measured boundary re- sistance-coefficients, gave theoretical values of the com- posite resistance coefficient which agreed with the measured coefficients to within about :5 percent. Taylor (1961) did flume experiments on flow over a fixed cobblestone bed. He found that by applying the sidewall correction procedure the resulting bed friction. factor-relative bed roughness relation agreed quite well with the relation predicted by the Karman-Prandtl re- sistance equation for rough, two-dimensional channels. In spite of this good agreement, Taylor expressed seri- ous misgivings about the theoretical considerations on which the sidewall correction method is based, and con- sequently he cautioned against applying the method to situations where it is not previously known to work. The available evidence therefore favors use of the sidewall correction procedure, at least for fixed-bound- ary situations and for flow conditions common in laboratories. H25 The present movable-bed tests either eliminated side- wall effects or came close enough to doing so to permit a safe extrapolation to infinitely wide channels. These wide-channel relations can test the sidewall correction method for the sediment-transport experiments reported herein. For this purpose the present data were analyzed in two ways. TEST ONE The sidewall correction procedure specifies that the velocity and slope for a narrow channel will be the same as for an infinitely-wide channel but that a different depth (Rb) will evolve for the wide channel. The method predicts the value of Rh. Needed for the first test was a master graph showing the wide-channel velocity—slope relations for the four depths studied. For any combina- tion of V and S (for example from a narrow-channel experiment) one could then interpolate on the wide- channel graph to get the applicable depth in a. wide channel. This depth should equal 13;, as given by the sidewall correction method. Specifically, the steps in this test were: 1. Plot slope as a function of mean velocity for a con- stant depth, to show the influence of flume width. 2. Apply a least-squares fit to the points for each width- depth combination. (The runs at D=0.1 ft showed no width effect, so only one line was fitted to all of these points.) 3. Determine by extrapolation the slope-velocity rela- tion for an infinitely wide channel, for each water depth. The procedure here was firstly to select any velocity on the S—V diagram and plot slope values as a function of the corresponding W/D ratios. The resulting graphs verified a power law between these variables. Assuming that for a given depth the channel could eventually become so wide that further increases in width would no longer affect the slope, the applicable function was of the form 1 B 1+‘W/‘D where A and B are the coefficient and exponent to be determined. As W/D approaches infinity the right—hand side of this equation ap-proaches'A. Thus in an infinitely wide channel the value A represents the slope corresponding to the given velocity and depth. . The procedure for getting the wide-channel S—V relation for each depth was therefore to (a) choose a velocity, (b) read the values of S from the least— squares S—V lines for the successive W/D values, H26 and (c) perform a final least-squares analysis with WTD Such an analysis produced the coefficient A (equal to the wide-channel slope) for the given velocity and depth. The wide-channel S—V relation could then be drawn by using the same inclination ob- tained in step two for the narrow-channel relations. For each depth the procedure had to be done twice, as the power relation between slope and velocity changed inclination at higher velocities. 4. Make a single graph containing the four wide channel slope—velocity curves (one curve for each depth). 5. Draw lines for intermediate depths on this graph by interpolation. 6. For each individual run, take the slope and velocity values and consult the above graph to find the depth that would obtain in an infinitely wide channel for this same slope and velocity. 7. Compare each such depth (Dmeas) to that predicted by the sidewall correction procedure (Rb). Figure 16 shows the results of this test, with the dis- crepancy ratio Dmeas/Rb plotted as a function of sedi- ment-transport rate. Runs at D=0.1 ft could not be tested because the wide channel depths would be less than 0.1 ft, and there was no reliable way of finding Dmeas for such depths. The 142 runs involved in this test had discrepancy ratios ranging from 0.41 to 1.90; the median was 0.98, the arithmetical average 1.01, and the standard devia- tion 0.29. Thus about 67 percent of the discrepancy ratios fall between 0.72 and 1.30. The agreement varies with the hydraulic and (or) sediment-transport conditions. At the lowest transport rates (flat slopes, low mean velocities) the discrep- ancy ratios range from about 1.0 to 1.9, with a slight tendency for the poorest agreement to be associated with the two narrowest channels. The ratios improve considerably at intermediate transport rates. Agree- ment becomes poorest at those rather fast transport rates at which bed forms (antidunes) reach their great- est heights. At this stage the most discrepant values again seem to be associated with the narrower chan- nels. The predicted depths show immediate improve- ment as soon as the flat-bed stage arrives. Over some of the range of conditions studied the agreement is good. This tends to support those investi- gators who believe in the sidewall correction method. 1 variables log 8 and log [”1 1 :|. SEDIIMENT TRANSPORT IN ALLUVIAL CHANNELS Some possible causes of the poorer agreement where it occurs, in no special order of probability, are: (a) imprecise measurements (such as might occur for very 'flat slopes, especially at deeper depths where bed and water-surface irregularities are higher) ; (b) effect of bed configuration (for example, well-de- veloped antidunes)— that is, large differences in relative roughness between bed and sidewalls; (c) effect of sediment in motion ; (d) the method used to analyze the slope—velocity data; (e) defects in the theory of the sidewall correction procedure. I tried a variation of this test by obtaining the wide- channel velocity—slope relations in a different way, so as to avoid extrapolating the S—V data. The procedure here for each depth was to choose values of unit trans- port rate and for a given transport rate take (a) the slope from the 3—6 relation for infinitely wide channels (fig. 6) and (b) the corresponding velocity from the least-squares lines on the velocity—transport graphs (fig. 4). Repeating for the other depths gave the wide-chan- nel velocity—slope relations. Then for each run an inter- polation on this master graph gave the wide-channel depth corresponding to each narrow-channel velocity and slope, as before. The results of this test showed no significant differences from the first velocity—slope test. TEST TWO The second major test of the sidewall correction pro- cedure involved only the slope and sediment-transport rate. Mean velocity, as seen earlier, did not change with flume width for a constant depth. That is, for a given unit transport rate and depth the wide-channel V was the same as the narrow-channel V. The assumption in this test is that if the sidewall correction procedure changes the hydraulic conditions (depth and unit dis— charge) then no simultaneous change should be made in the unit sediment-transport rate. In other words, the same unit transport rate applies to both the narrow flume and the infinitely wide channel (Johnson, 1942). The master chart for this test therefore was the wide- channel slope—transport relations (from fig. 6). For each individual run the question asked was: what is the wide-channel depth corresponding to the narrow- channel slope and transport rate? This depth should equal 131,, the depth predicted by the sidewall correction procedure. Figure 17 shows the results of this second major test of the sidewall correction method. The agreement between predicted and “observed” depths is better here than with the first test. Of the 133 runs which could be tested, the discrepancy ratios ranged from 0.47 to 1.95; Rb DISCREPANCY RATIO = 0““ FLUME WIDTH AND WATER DEPTH EFFECTS H27 UNIT SEDIMENT-TRANSPORT RATE, IN KILOGRAMS (IMMERSED WEIGHT) PER SECOND PER METER WIDTH 0.00I 0.0I ' O.I LG I I I I EXPERIMENTAL DEPTH 0.7 FT 2.0 — A q: — “it” ‘9“; A CI) 4 IO _— ------------- x-m--9 ------ a) -------- [3‘- ¢ ------------------ —_ : x I EDI x A” I : ._ x x @A [ITA (I) _ 0.5 :' A j I I I I I I I I 2.0 — EXPERIMENTAL DEPTH 0.5 FT — e ‘5 15915 e, _ _____ .9.-- -_ _ ___________________________ _ 1.0 ___ .9. s—gq- cage #96 Be a 9* $9 9 tea} t 9 : — 6 _. 0.5 _— e. e ‘% —_: I I I I I I I I EXPERIMENTAL DEPTH 0.3 FT 2.0 —- ._ I \ Q A 3 ‘ o ‘ A A _____'___ __u- _ _- c- __ ‘___ _ _ _ __ ___ __9__‘ _____ __ * L" * --*- we 2.51.“: H s I I I I 0.000] 0.00I 0.0I O.I I.0 UNIT SEDIMENT-TRANSPORT RATE, IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH EXPLANATION Width (f1) Depth (II) 0.25 0.5 I.O 2.0 3.9 0.3 A o I 9 0.5 war 0 fr + 0.7 4 ¢ [11 A x FIGURE Iii—Velocity—slope test of sidewall correction procedure (Vanoni and Brooks, 1957). H28 DImeas Rb DISCREPANCY RATIO SEDIIVIENT TRANSPORT IN ALLUVIAL CHANNELS UNIT SEDIMENT-TRANSPORT RATE, IN KILOGRAMS (IMMERSED WEIGHT) PER SECOND PER METER WIDTH 0.00I 0.0I 0.I I.O I I I EXPERIMENTAL DEPTH 0.7 FT 2.0 — n; _ O c» ”Ix a ‘9 m 1.0 r—————-;, ——————— ;5-—E5-‘¢m«n--oi”-L-A—TI—3 —————————————— —_ I A (I) I 0.5 __ A A __. I I I I I I I I 2 0 _ 6 EXPERIMENTAL DEPTH 0.5 FT _‘ 9 9 8656 SEE a B 9 6 1.0 :— ————— £-—A-—A---—6—— ,eg-g—fi;é—§—5;—§-B—e—'-——GTA%-& ———————— —:4 0.5 L t 9 E _: I I I I I I I I EXPERIMENTAL DEPTH 0.3 FT 2.0 "' —‘ O A f A I I.O r- __._'_ .31-- E.._'_t'__a_ !.__5¢!_1_._$39_!__,t“1:_: __________ __ I: A . A 2‘ 0.5 " _ I I I I 0.000I 0.00I 0.0I 0.I I.0 UNIT SEDIMENT-TRANSPORT RATE, IN POUNDS (IMMERSED WEIGHT) PER SECOND PER FOOT WIDTH EXPLANATION Depth (H) w'dII‘ (“I 0.25 0.5 1.0 2.0 3.9 0.3 A o I O 0.5 fr 9 a {L 0.7 A ¢ :1: I x FIGURE 17,—Slopev—transpom: rate tbest of sidewall correction procedure (Vanoni and Brooks, 1957). FLUME WIDTH AND WATER DEPTH EFFECTS the median was 1.09 and the arithmetical average 1.05. The standard deviation of 0.22 means that about 67 percent of the discrepancy ratios fall between 0.82 and 1.27. To a lesser extent the same tendencies noticed with the first test show up here. The predicted depths are slightly small at low transport rates. Where bedforms attain their greatest heights the predicted depths are a little too large, and this trend disappears as soon as the flat—bed stage appears. The two tests applied here to the sidewall correction method do not rigidly prove or disprove its validity. On balance, however, the degree of agreement as shown in figures 16 and 17—together with the studies of Hay- wood, Yassin, and Taylor—support using the pro- cedure. With sediment-transport studies the procedure may be more reliable with smooth rather than with very rough beds. The wide-channel slopes, stream powers, and shear stresses for the present flume experiments can easily vary by a factor of 3 from the narrow-channel values (see figs. 6 and 8), at a given depth and unit transport rate. If these factors involving slope are considered constant (independent) then the depths and unit trans— port rates vary severalfold from narrow to wide chan- nels. Hence if data from narrow flumes are to be related to wide streams some sort of sidewall correction must be applied. At the present time the only feasible ways to do this are to use either a sidewall correction pro- cedure, for example the one described most recently by Vanoni and Brooks (1957) for adjusting the hydraulic radius, or empirical correction factors of the sort given in the present study. CONCLUSIONS 1. Flume width had no measurable influence on the unit discharge—unit sediment-transport relations and the mean velocity-transport relations, at constant water depth. 2. The energy gradient (slope), unit stream power, and shear stress decreased as the flume became wider, for a constant depth and unit sediment-transport rate. For experimental depths from 0.1 to 0.7 'ft, a 2-ft-wide flume was wide enough to eliminate sidewall effects on the slope, power, and shear stress. (Values of these variables in the 2-ft-wide channel were within 0 to 5 percent of the values estimated for an infinitely Wide channel.) 3. Multiplying the laboratory value of slope, unit stream power, or shear stress by the adjustment factor 1+0 18 1(W—,) H29 gives the slope, power, or shear for a wide channel (no sidewall effect), for the same water depth and unit sediment-transport rate. 4. Depths from 0.1 to 0.7 ft affected the unit stream power—unit sediment-transport relations in that for a given stream power the transport rate increased about fourfold to sixfold as depth decreased from 0.7 to 0.1 ft. 5. Bedforms in narrow channels (widths less than 1 ft) differed in various ways from those in wider channels, for the same unit transport rate and depth. 6. For a given depth and unit transport rate the Darcy- Weisbach friction factor increased as the flume became wider, and this increase can be determined from a knowledge of the flume width effects on the individual variables 13,8, and V. 7. Five studies by other investigators, together with the present data, support the use of the sidewall correction procedure (Vanoni and Brooks, 1957) for relating flume data to infinitely wide channels, at least for most of the common laboratory flow conditions. The procedure may not be reliable, however, for those particular sediment-transport rates associated with high antidunes. Further checks should be made of the sidewall correction procedure to determine the range of widths and depths and the boundary roughnesses to which the method applies. REFERENCES Bagnold, R. A., 1966, An approach to the sediment transport problem from general physics: U.S. Geol. Survey Prof. Paper 422—I, 37 p. Brooks, N. H., 1958, Mechanics of streams with movable beds of fine sand: Am. Soc. Civil Engineers Trans, v. 123, p. 526—594. Colby, B. R., 1964, Discharge of sands and mean-velocity rela- tionships in sand-bed streams: U.S. Geol. Survey Prof. Paper 462-A, 47 p. Colby, B. R., and Scott, C. H., 1965, Effects of water temper— ature on the discharge of bed material: U.S. Geol. Survey Prof. Paper 462—G, 25 p. C-olebatch, G. T., 1941, Model tests on Liawenee Canal roughness coefficients: Journal of the Institution of Engineers Aus- tralia Trans, v. 13, no. 2, p. 27—32. CrufE, R. W., 1965, Cross-channel transfer of linear momentum in smooth rectangular channels: U.S. Geol. Survey Water- Supply Paper 1592-B, 26 p. Dawdy, ID. W., 1961, Depth-discharge relations- of alluvial streams discontinuous rating curves: U.S. Geol. Survey Water-Supply Paper 1498-0, 16 p. Einstein, H. A., 1934, Der Hydraulische oder Profil-Radius: Schweizerische Bauzeitung, V. 103, no. 8, p. 89—91. 1942, Formulas for the transportation of bed load: Am. Soc. Civil Engineers Trans, v. 107, p. 561—577. H30 Guy, H. P., Rathbun, R. E., and Richardson, E. V., 1967, Recir— cu'lation and sand—feed type flume experiments: Am. Soc. Civil Engineers Proc., v. 93, no. HY5, p. 97—114. Haywood, O. G., J r., 1940, Flume experiments on the trauma- tation by water of sands and light weight materials: Ph.D thesis, Massachusetts Inst. Technology, 122 p. 1942, Discussion of “Formulas for the transportation of bed load2” Am. Soc. Civil Engineers Tnans., v. 107, p. 583- 590. Horton, R. E., 1933, Separate roughness coeflicients for channel bottom and sides: Engineering News-Record, Nov. 30, 1933, p. 652—653. Johnson, J. W., 1942, The importance of considering sidewall friction in bed-load investigations: Civil Engineering, v. 12, p. 329—331. 1944, Rectangular artificial roughness in open channels: Am. Geophys. Union Trans, 25th Annual Meeting, part V1, p. 906—912. Kennedy, J. F., Chairman, 1966, Nomenclature for bed forms in alluvial channels, Report of the task force on bed forms in alluvial channels: Am. Soc. Civil Engineers Proc., v. 92, no. HY3, p. 51—64. Lane, E. W., 1955, Design of stable channels: Am. Soc. Civil Engineers Trans, v. 120, p. 1234—1279. Leopold, L. B., and Maddock, T., J r., 1953, The hydraulic geom- etry of stream channels and some physiograiphic implica- tions: U.S. Geol. Survey Prof. Paper 252, 57 p. SEDMENT TRANSPORT IN ALLUVIAL CHANNELS Rouse, H., 1961, Fluid mechanics for hydraullic engineers: New York, Dover Pubs.., Inc., 422 p. S-cheidegger, A. E., and Langbein, W. B., 1966, Probability con— cepts in geomorphology: U.S. Geol. Survey Prof. Paper 500—0, 14 p. Schoklitsch, A., 1914, Uber Schleppkraft und Geschiebebewe- gung: Leipzig and Berlin, W. Englemann, 66 p. Simons, D. B., Richardson, E. V., and Nordin, C. F., Jr., 1965, Sedimentary structures generated by flow in alluvial chan- nels, m Soc. Econ. Paleontologists and Mineralogists, Pri- mary sedimentary structures and their hydrodynamic in- terpretation—a symposium: Soc. Econ. Paleonto'logists and Mineralogists Spec. Pub. 12, p. 34—52, 253—264. Taylor, R. B., Jr., 1961, Exploratory studies of open-channel flow over boundaries of laterally varying roughness: Calif. Inst. Technology Div. of Engineering, Report no. KH—R—4, 65 p. Vanom‘, V. A., and Brooks, N. H., 1957, Laboratory studies of the roughness and suspended load of alluvial streams: Calif. Inst. Technology Sedimentation Laboratory, Report E—68, 121 p. (also published as US Army Corps of Engineers, M.R.D. Sediment Series 11, 121 p. ). Williams, G. P., 1967, Flume experiments on the transport of a coarse sand: U.S. Geol. Survey Prof. Paper 562—B, 31 p. Yassin, A. M., 1953, Mean roughness coeflicient in open channels with diflerent roughnesses of bed and side walls: Mitt. aus der Versuch-san-stalt fiir Wasserbau und Erdbau, Eidg. Tech. Hoch. Zurich, no. 27, 90 p. TABLES FLUME WIDTH AND WATER DEPTH EFFECTS TABLE 1.—Summary of experimental data, in English units H33 Unit Sediment trans- Bed forms 2 Friction factor water port ‘ Unit dis- Depth, Mean ——-—— Sediment Sur- Water ———————— s t Hy- Run charge, Slope, S D veloc- Unit infeed 1 face ve— temp- 3:2?“ draplic Q (ft per It) (it) ity, V Measur- transport (lb per locity er- Height Length Travel p ' radlus, Manning Ty (fps) ing period fife, 1 sec) (fps) aguge (it) (ft) velocity (lhaéer R (it) n ' (cfs per ft) (sec) se(c pgfi) ( ) (fps) sec per ft) ((0/0 Channel width=0.25 ft. 0. 148 0. 00529 0. 101 1. 46 2, 580 0. 00212 0. 000500 . 0. 056 0. 0108 .164 . 00640 . 104 1. 58 1,800 . 00472 . 00116 9. 0 . 057 . 0111 196 . 00840 107 1. 83 1, 200 . 0100 00250 5. 5 . 058 . 0112 200 . 0132 095 2.10 1, 500 . 0252 00660 . 5 A . 054 0116 232 0166 097 2. 39 5, 400 . 0572 0144 . 0 A . 055 . 0116 256 . 0213 093 2. 75 6, 540 . 101 0243 . 5 A . 053 . 0111 352 . 0262 099 3. 55 4 200 . 220 0556 . 0 A . 055 00985 440 00272 304 1. 45 55, 140 . 000540 . 000111 . 65. 0 D . 089 . 0107 460 . 00258 303 1. 52 17, 400 . 000920 ........... 1. 70 73. 0 D . 014. . 6. 06 00155 . 0743 089 . 0099 488 . 00295 300 1. 61 11, 340 . 00141 ........... l. 83 76. 5 D . 015. . 5. 55 4 . 0892 088 . 0099 476 . 00310 294 l. 62 7, 320 . 00218 ........... 1. 86 76. 5 D . 017. . 4. 40 00321 . 0916 087 . 0101 540 . 00371 304 1. 77 15, 180 00476 ........... 2. 00 75. 0 D . 020.. 2. 69 00480 . 125 089 0102 584 . 00435 303 1. 93 4,860 00617 ........... 2. 20 71 5 D . 027. . 2. 66 00640 . 158 089 . 0101 . 648 . 00595 306 2. 12 3, 330 0144 ........... 2. 52 69 5 D 030. . 2. 14 0167 . 250 089 0108 780 00942 300 2. 60 2, 595 0370 ___________ 3. 12 68 0 {AD 3 - 3g; - i {g 3%? . 459 088 . 0110 868 0131 305 2. 81 1, 740 . 060 ........... 3. 38 68 5 A . 103. . 1. 30 0185 . 706 088 . 0120 948 0133 307 3. 09 6, 780 . 0688 . 0167 3. 57 67. 5 A . 093. . 1. 34 0190 . 784 089 . 0110 ' 1 048 . 0177 3. 45 780 . 149 ........... 3. 71 69. 5 A . 160. . 1. 46 0278 1. 152 089 . 0114 l 080 . 0174 292 3. 70 3, 540 . 164 . 0406 4. 00 51. 0 A . 147. . 1. 45 0417 1. 174 088 . 0105 l 120 . 0208 301 3. 72 480 . 208 ........... 3. 85 69. 5 A . 180. . l. 30 0435 1. 452 088 . 0114 1 120 . 0205 287 3. 90 2, 970 . 273 . 0646 4. 12 65. 5 A . 160. . 1. 50 0455 1. 432 087 . 0108 280 . 0197 293 4. 37 2, 700 . 401 . 0833 4 50 67. 5 A . 142. . 1. 53 0654 1. 568 089 . 00950 1 352 . 0222 299 4. 52 3, 900 . 412 . 108 4 62 69. 5 A 217. . 1. 62 0526 1. 868 088 . 00972 1. 800 . 0288 . 303 5. 94 1, 980 . 997 238 5 92 67. 0 Flat bed ................... 3 230 089 00850 2. 160 . 0350 . 307 7. 04 900 1. 390 ........... 6 84 67. 5 . .. .. 0 ...................... 4 710 089 00790 . 820 . 00237 . 507 1. 62 70, 920 . 000380 . 0000754 1. 62 74. 0 ..... o ...................... . 121 099 . 00960 . 860 . 00271 . 501 1. 72 14, 280 . 00105 ........... l. 93 75. 0 D 030. . 6 68 . 00138 145 100 . 00971 . 916 . 00288 . 502 1. 82 8,340 00252 ........... 2. 12 75. 5 D 033. . 3 57 . 00403 165 100 . 00946 . 964 . 00363 . 500 1. 93 12, 780 . 00484 ........... 2. 20 69. 5 D 050_ . 3 74 . 00275 218 100 . 0100 1. 064 . 00485 . 501 2. 12 7 200 . 0102 ........... 2. 46 68. 5 D . 060. . 3. 38 . 00471 . 322 . 100 0105 1. 208 . 00651 . 502 2. 40 3, 120 . 0198 ........... 2. 85 70. 0 D . 062. . 2. 26 . 0142 . 490 . 100 0108 1. 292 . 00763 . 498 2. 60 2, 460 0325 ........... 3. 22 70. 0 D . 067. _ 2. 09 . 0196 . 614 100 . 0108 1. 520 . 0104 . 505 3. 01 , 0 76 ___________ 3. 63 68. 5 D . 080_ _ 3. 20 . 0286 . 985 . 100 . 0108 l. 720 . 0123 . 502 3. 42 5, 790 . 0964 0244 3. 94 65. 0 A . 180. . 1. 85 . 0270 1. 32 099 0103 1 712 . 0158 514 3. 33 360 . 144 ........... 3 79 73. 0 A . 220. . 2. 00 . 0323 1. 69 100 . 0125 1 840 . 0212 495 3. 72 240 . 284 ........... 06 73. 5 A . 280_. 2. 50 . 0439 2. 43 100 . 0125 2 280 . 0188 491 4. 64 4, 020 . 426 100 5 08 63. 0 A . 226.. 2. 08 . 0700 2. 67 099 00940 2 756 . 0238 492 5. 56 1, 320 . 737 191 6 01 63. 5 A . 216. . 2. 42 . 0971 4 07 0 3 068 . 0309 470 6. 53 2, 040 1. 20 300 6 81 59. 0 Flat bed ................... 91 099 00860 1. 248 . 00250 . 702 1. 77 11,640 . 000386 . 000155 1. 91 . 60. 0 D 026 .......... . 000476 194 106 . 00959 1. 240 . 00234 . 704 1. 76 4, 500 . 000612 . 000186 1. 89 64. 0 D . 024 .......... . 000280 . 181 106 . 00920 1. 392 . 00300 . 714 1. 95 5, 640 . 00382 . 000889 2. 11 56. 0 D . 050. . 3. 83 . 00204 . 261 106 . 00930 1. 720 . 00539 . 726 2. 37 6, 000 . 0194 . 00486 3. 04 59. 0 D . 108. _ 3. 33 . 00770 579 106 . 0103 2. 220 . 00793 . 711 3. 12 5, 520 . 0572 . 0125 3. 66 65. 0 D 100.. 2. 97 . 0305 1. 10 . 106 . 00950 2. 468 . 0101 . 701 3. 52 5, 340 . 0888 . 0238 3. 82 62. 5 D 122. . 2. 56 . 0333 1. 57 106 . 00950 2. 700 . 0146 . 692 3. 90 3, 720 . 216 . 0511 4. 59 63. 0 {AD ' 21,33 ‘ ; if,” ' 8218} 2. 46 106 0104 2. 960 . 0183 . 686 4. 31 2, 940 . 328 . 0791 4. 73 61. 5 A . 22. .. 2. 58 . 0546 3. 38 106 0104 3. 288 . 0225 . 679 4. 84 3, 120 . 543 . 131 5. 39 62. 0 A 27. . . 2. 67 . 0833 4. 62 106 0103 Channel width=0.5 ft 0 110 0. 00383 0 101 1. 09 19, 260 0. 000149 0. 000111 1. 57 68. 5 Flat bed ................... 0. 0262 0. 072 . 0147 - 128 . 00481 101 1. 27 7, 740 . 00181 ........... l. 74 71. 5 . .do..._ _ . 0384 . 071 . 0141 144 . 00558 102 1. 41 5, 160 79. 5 . .d0.. . . 0500 . 072 . 0137 150 . 00617 102 1. 47 8, 700 71. 5 . .do. . . 0578 . 072 . 0139 166 . 00758 . 104 1. 60 3, 420 80. 0 A? . _ . 0. 40 ......... . 0786 . 073 . 0142 . 180 . 0117 097 1. 86 1, 920 73. 0 A 0.040 . . . 60 . 0283 . 131 . 071 . 0147 208 . 0162 098 2. 12 1, 380 74. 5 A .055- - . 70 . 0406 . 210 . 070 . 0152 264 . 0202 100 2. 64 840 75. 5 A .068 . . . 80 . 0500 . 334 . 071 . 0138 . 294 . 0217 098 3. 00 75. 5 Flat bed .. . 398 070 . 0125 . 384 . 0303 087 4. 41 46. 5 . ..d0..._ . . 726 . 065 . 00950 460 0367 082 5. 69 46. 5 _ _.do ________________________ 1. 07 . 062 . 00790 430 00177 293 1. 47 69. 5 D .020. . 6. 63 . 0017 . 0474 . 135 . 0106 476 . 00183 306 1. 55 68. 5 D .022 - - 3. 44 . 0024 . 0543 . 138 . 0110 536 . 00251 308 1. 74 67. 5 D .025 . - 2. 55 . 0067 . 0835 . 138 . 0114 . 600 00374 300 2. 00 66. 0 D .035. . 1. 85 . 0147 . 140 . 136 . 0120 . 654 00553 288 2. 27 65. 5 D .045 .. 1. 50 . 0182 . 226 . 134 . 0128 . 756 00795 294 2. 57 64. 0 A .070 _ . 1. 10 . 0154 . 375 135 . 0136 8 00901 294 2. 72 63. 5 A .10 - . . 1. 10 . 0172 . 449 135 . 0137 964 0120 307 3. 14 65. 0 A .13 - _ . 1. 25 . 0312 . 720 137 . 0139 1 . 0136 307 3. 48 64. 5 A .15 . . . 1. 65 . 0333 . 9 137 . 0133 1 180 . 0149 312 3. 78 63. 5 A .18- _. 1. 50 . 0456 1. 09 139 . 0129 1 244 . 0165 300 4. 15 64. 5 A .20- . . l. 80 . 0700 1. 28 . 136 . 0122 1. 500 . 0179 286 5. 25 50. 5 1. 68 . 134 . 0100 1 920 . 0234 300 6. 40 53. 5 2. 80 . 136 . 00940 744 . 00123 493 1. 51 72. 0 0571 . 166 . 0104 792 . 00161 500 1. 58 79. 5 0797 . 167 . 0115 820 . 00191 492 1. 66 79. 0 0980 . 166 . 0119 . 880 . 00227 . 506 1. 74 80. 0 125 . 167 0124 . 924 . 00260 . 502 1. 84 79. 0 150 . 167 0125 See footnotes at end of table. H34: SEDIMENT TRANSPORT 1N ALLUVIAL CHANNELS TABLE 1.—Summary of experimental data, in English units—Continued Unit Sediment trans- Bed forms 3 Friction factor water port 1 Unit 1118- Depth, Mean -—-————~—— Sediment Sur- Water ————-——~— stream Hy- Hy- ————— R1111 charge, Slope, S D veloc- Unit infeed 1 face ve— temp- power, draulic draulic Darcy- Q (ft per It) (ft) ity, V Memur- transport (lb per locity er- Height Length Travel (5 radius, radius Weis- Mannin 7,? (fps) ing(pez;'od gage, 1' sec) (fps) 8233;“? (It) (ft) velocity (lb pea) R (ft) gt lies, bach, n 5, sec per sec per . (cfs per it) sec perft) (fps) f (11116) Channel width=0.5 ft—Continued 976 .00300 500 1.95 6,240 2.28 77. 5 D 183 167 .312 .0340 0127 1.140 .00458 493 2. 31 3,000 3. 00 76. 5 D 326 166 .324 .0366 0132 1 360 .00639 505 2.69 2,040 3. 37 79.0 D 541 167 339 .0379 0134 1 580 .00931 512 3. 08 840 3. 79 79. 5 A? 916 168 362 .0425 0142 1 676 .0111 492 3.40 3,120 4.20 52.0 A 1.15 166 348 .0411 0139 1 720 .0141 504 3.41 490 4.01 79.5 A 1 51 167 381 .0521 6157 1 856 .0141 480 3.86 5,580 4 85 49.5 A 1 63 164 .339 .0400 0138 2 0144 515 4.84 1,980 . 5 32 52. 5 A 2 23 167 .304 .0265 0112 3 40 0230 443 7.67 960 1.95 1.00 7.85 48.0 Fl 4 88 161 205 .0162 00870 1 150 .00115 .700 1.64 55,800 000350 .000184 1 79 61.0 D 0825 184 .242 .0202 01000 1 240 .00127 702 1.77 14, 400 000816 .000248 1 89 65.5 D 0981 185 .234 .0193 0098 1 320 .00145 715 1.85 12,900 00121 .000695 1 92 73.5 D 119 186 .260 .0203 0100 1 4 0 .00211 711 2.04 18,000 00532 .00229 2 22 75.0 D 191 186 .328 .0243 0109 1 742 .00324 702 2. 48 14,640 0181 .00916 2 80 75.0 D 352 184 .341 .0250 0111 2 12 .00456 722 2.94 6, 0434 .0212 3 43 57.0 D 185 360 .0251 0111 2 58 .00951 694 3.72 3,420 .184 .0875 4 29 54.5 A 1 53 183 .425 .0324 0125 .30 .0135 693 4.76 2,250 .526 268 5.44 53.5 A 2 77 183 .403 0281 0116 Channel width=l.0 ft 95 _____ 0.115 0.00407 0 093 1.24 226,620 0.000541 0.000519 1.66 57.0 Flat bed .................... 0.0292 0.078 0.091 0.0531 0.0140 96 ..... 127 .00411 100 1.27 17,940 .00145 ___________ 1. 68 65. 5 ___do_.. - .0325 .083 .092 .0546 .0142 97 ..... 142 .00495 100 1.41 10,140 1.89 66.5 ...do. . .0438 .083 .092 .0533 0141 98 ..... 158 .00590 102 1.55 5,400 2.08 70.0 o _ 0581 .085 .094 .0537 0142 99 ..... 154 .00751 101 1.53 2,460 2.22 54.5 A ......... 0 50 ......... 0724 .084 .094 0692 0161 100-... 166 .0108 095 1.75 1,440 2.41 53.5 A 021.. 50 0200 112 .080 090 0727 0163 101.... 191 .0128 101 1.89 1,684 2.67 63.5 A 042.. 60 0216 .152 .084 095 0775 0170 102.... 220 .0151 099 2. 22 2,183 2.86 60.0 A 083.. 70 0300 .206 .083 093 0647 0155 103.... 233 .0199 094 2.48 960 3.39 74.5 A 053.. 1 00 0683 .289 .079 089 0660 0155 104.... 292 .0222 097 3.01 473 3.85 76.5 A 073.. 0 60 0683 .404 .081 090 0511 0137 105.... 400 .0331 .094 4.26 1,530 5.22 66.5 Flatbed ____________________ 826 .079 086 0371 0117 106.... 405 .00110 .297 1.36 24,180 1.56 70.5 .. 77 186 .221 .0284 0117 107.... 440 .0012 314 1.40 26,040 1.67 73.0 D 0332 193 .238 .0307 0123 108.... 440 .00136 313 1. 41 23,820 1. 76 67.5 Flat bed ................... 2 193 .244 0339 0129 109.... 438 .00162 294 1.49 23, 400 1. 85 65.5 D .042.. 8.9 .0017 0443 185 .232 0347 0130 110.... 452 .00182 294 1.54 12,240 1.87 61.5 D .042.. 5.8 .0027 0513 185 .235 0367 0133 111.... 470 .00200 300 1.57 14,040 2.06 65.0 D .053.. 4.8 .0015 0585 188 .243 0393 0138 112.... 498 .00210 303 1.64 ,360 2.16 63.0 D .063.. 4.3 .0035 0655 189 .242 0360 0133 113.... .503 .00211 304 1. 65 2,400 2.10 64.0 D .042.. 3.6 .0050 0661 189 .244 0374 0135 114.... .512 .00236 295 1.74 5,040 2.14 63.0 D .053._ 3.5 .0027 0755 186 .238 0371 0134 115.... .530 .00272 294 1.80 3,620 2.30 64.0 D .053.. 2.3 .0075 0899 185 .241 0398 0139 116.... .551 .00318 290 1.90 2,340 2.31 61.0 D .053... 2.4 .0117 109 183 .239 0417 0142 117.... .570 .00397 288 1.98 2,160 2.50 61.0 D ...063 2.0 .0158 141 183 .245 0475 0152 118.... .650 .00509 287 2. 26 1,980 2. 92 60. 5 D .073.. 1.8 .0267 206 182 .243 0469 0151 119.... .741 .00557 297 2.49 2,130 2.92 54.0 D .167.. 1.3 .0250 258 186 .248 0430 0145 120.... .760 .00594 293 2. 59 1,140 3.00 68. 5 A .150.. 1.4 .0200 281 185 .245 0422 0139 121.... .760 .00592 296 2. 57 1, 200 3. 05 71. 5 A .150.. 1.3 .0250 280 186 .248 0430 0146 122.... .794 .00643 306 2.59 1,353 3.05 60.0 D .125.. 1.5 .0384 318 190 .260 0467 0151 123.... .860 .00721 307 2.80 960 3.33 71.0 A .167.. 1. 5 .0083 386 190 .259 0449 0148 124.... 1. 05 .00824 324 3. 24 720 3. 67 74. 5 A .250.. 1. 6 .0400 539 197 .268 0396 0140 125.... 1.12 .0109 321 3.49 510 3. 74 77.0 A .250.. 1.6 .0350 760 196 .272 0452 0148 126.... 1.30 .0129 324 4. 01 900 4.65 68.5 A .21... 1.73 .0500 1 05 197 .270 0406 0144 127.... 1. 97 .0162 323 6.10 27 ........ 67. 5 Flat bed ................... 99 197 .240 0221 0105 128.... .768 .00106 503 1.53 172,500 1. 76 66.0 D .044._ 10.7 000421 0507 252 .348 0294 0127 129.... .845 .00137 509 1.66 4,040 1.91 70.0 D .083.. 5.2 0012 0723 252 .364 0323 0132 130.... .795 .00133 485 1.64 9,180 1.92 79.0 D .042.. 3.9 00070 0661 246 .346 0313 0129 131.... .866 .00144 505 1.72 10,020 1.97 73.0 D .104.. 3.7 0017 0780 .251 .358 0314 0130 132.... .905 .00172 517 1. 75 8,460 2.02 74.5 D ...063 2.8 0018 .0972 .254 .386 0367 0141 133.... .960 .00184 512 1. 87 18,420 2.25 74.0 D .042.. 2.9 0022 110 253 .377 0343 .0136 134.... .958 .00216 502 1.91 3,840 2.20 64.0 D .063.. 2. 5 0020 129 250 .380 0379 0143 135.... 1.05 .00251 517 2.03 6,300 2.38 65.5 D .167.. 2.0 0072 165 254 .397 0400 0147 136.... 1.10 .00314 504 2.18 2,640 2 54 69.5 D .167.. 2.2 0063 215 250 .394 .0424 0151 137.... 1.32 .00416 .510 2. 59 1,800 3.14 69. 5 D .167.. 1.8 .0217 342 252 .398 0403 0147 138.... 1. 64 .00842 .486 3.37 2,820 3.77 66.0 A .18... 1.88 0307 861 246 .396 0470 .0159 139.... 1.87 0118 .480 3.90 1,380 4.45 66.0 A .28... 2.19 0417 1 37 245 .398 0489 0163 140.... 2. 49 0113 .477 5. 22 1,380 5. 63 66. 5 A .27... 2.56 0546 1 75 244 .344 0260 0119 141.... 1.17 00081 .696 1.68 186,720 .000467 .000465 1.82 71.5 D .050.. 7.9 000312 0591 .291 .382 0215 0111 142.... 1.24 00079 .711 1. 74 86,520 .00143 .00135 1.83 61.0 D .064__ 5.3 000754 0611 294 .365 0198 0106 143.-.. 1. 32 00131 .703 1.88 106,800 .00323 .00322 2.04 70.5 D .083.. 3. 7 00163 108 292 .450 0278 0126 144.... 1.42 .00178 .716 1.98 28,380 .00583 .00563 2.16 69.0 D .082.- 2.6 00218 158 295 .504 0346 0141 145.... 1. 64 00272 .707 2.32 14,400 .0201 .0200 2.53 66.0 D .154.. 4. 5 00376 278 293 .518 0381 0148 146.... 2.26 .00454 .695 3.25 3,240 .0806 .0813 3.60 66.0 A .134.. 1.9 0263 .640 290 .491 .0320 0135 147.... 2.79 .00955 .645 4.33 2,160 .307 .319 4.36 68.0 A .273.. 2.3 0403 1.66 282 .490 .0370 0144 Channel width=2.0 ft 148.... 0.120 0.00489 0.098 1.22 56,280 0.00170 0.00330 1. 85 80.0 B 0.12... 11.0 ......... 0.0366 0.089 0.094 0.0751 0.0170 149.... .146 .00569 .091 1.60 19,560 .00354 .00782 198 78 0 B .03... 5 3 0.00148 .0518 .083 .087 .0475 .0133 150.-.. .175 .00816 .091 1. 92 11, 550 .0119 .0241 2.30 B .03.-. 4.1 .0041 .083 .087 .0472 .0133 77'“ AI .02... 0.5 .022 -°391 151.... .180 .0117 .089 2. 02 6,000 .0272 .0574 2.58 80 0 A .06... 0.6 .022 .131 .082 .086 .0606 .0150 152.... .260 .0172 .093 2.80 3,945 .0775 .164 3.17 80.0 A .08... 0.82 .039 .278 .085 .089 .0480 .0134 153.-.. .320 .0234 .099 3. 23 900 . 188 .403 4. 23 79. 0 Flat bed ___________________ .465 .090 .095 .0520 .0142 See footnotes at end of table. FLUME WIDTH AND WATER DEPTH EFFECTS H35 TABLE 1.—Summary of experimental data, in English units—Continued Unit Sediment trans— Bed forms 2 Friction factor water port 1 Unit (115- Depth, Mean —-—- Sediment Sur- Water —————— stream Hy- Hy- ——— Run char e, Slope, S D veloc- Unit infeed I face ve- temp- . power, draulic draulic Darcy- 5 (it per ft) (it) ity, V Measur- transport (lb per locity er- Helght Length Travel a: radius, radius Weis- Mannin W (fps) ing period 11:66, 7' , sec) (fps) M3169 (it) (It) velocity (lb per.It R (ft) (£21969, been, 71. 3' (cfs per 16) (39°) g“ 33;“) (fps) 5“ p“ ) b ( t) f (nu/o) Channel width=2.0 ft—Continued 154... . . 428 . 00118 .287 1.49 2'5, 340 . 000670 . 00139 1. 94 75. 0 D 0.029. . 6. 2 . 00132 .0315 . 223 .247 . 0305 . 0127 155. .. . .450 . 00154 . 293 1. 54 48, 900 . 00120 00239 1. 97 78.0 D .035. . 3. 28 . 00204 .0432 .226 . 258 .0378 . 0141 156. . . . 500 . 00210 286 1. 75 5, 700 . 00420 00859 2. 22 83. 0 D . 049. . 2. 38 . 00334 . 0655 . 222 . 254 . 0392 . 0143 15 . .. . 590 . 00330 290 2. 04 7, 770 . 0124 0250 2. 70 83. 0 D . 070 .......... . 00920 . 121 . 225 . 263 . 0459 . 0155 158... . . 845 . 00714 289 2. 92 6, 510 . 0700 150 3. 33 83.0 A . 11. . . 1. 3 . 0278 . 376 . 224 . 264 .0482 .0159 159. .-. 1. 105 .0113 293 3. 77 2,605 . 192 437 4. 40 76. 5 A . 18. . . 1. 46 . 0322 . 781 .226 . 267 . 0462 . 0155 160.. .- . 780 . 00106 478 1. 63 83, 940 . 000710 00150 1. 89 74. 5 D . 040. . 5. 8 000489 . 0516 . 324 . 396 . 0332 . 0141 161... . 855 . 00097 490 1. 75 53, 940 . 00131 00248 1. 92 79. 5 D . 054. . 3. 63 00105 . 0517 . 329 . 388 0268 0126 162. . _ . 880 . 00137 496 1. 77 , . 00305 00599 2.05 80. 0 D .072. . 3. 10 00160 . 0751 331 . 416 0373 0149 1 ... . 1 110 . 00281 496 2. 24 7, 650 . 0141 0288 2. 62 76. 5 D . 11... 3. 42 . 194 . 331 . 434 . 0477 0169 164.-. . . . 00445 . 483 2. 67 3,830 . 0362 0713 2. 96 79.0 D . 13.. . 2. 53 0200 . 358 327 . 431 0526 0177 165.-. . 1. 605 . 00643 .490 3. 28 3, 595 . 100 194 3. 77 80. 0 A . 16-. . 2. 2 0228 . 644 329 .436 0506 . 0174 166. .. . 1. 710 . 00877 .452 3. 78 l, . 197 413 4. 55 79.0 A 20... 2. 1 0400 . 936 311 . 403 0492 . 69 167... . 1. 120 . 00060 . 692 1. 62 103, 080 . 000585 00120 1. 76 72. 5 D . 071. . 3. 75 000494 . 0419 . 408 . 500 0240 0124 168.. . . l. 285 . 00080 . 681 1. 89 32, 700 . 00150 00280 1. 95 80.0 D . 068.. 3. 5 00104 . 0641 . 405 . 492 0233 0122 169. ._ . 1. 370 . 00147 . 711 1.93 11,940 . 00410 00799 2.04 77. 5 D .09... 3. 1 000651 .126 .415 . 589 .0421 0165 170... . 1. 405 . 00172 . 700 2. 01 4, . 00730 0150 2. 22 82. 0 D . 11.. . 3. 6 00188 . 151 412 . 590 0451 0170 171.... 1. 800 . 00280 . 702 2. 56 1, 205 . 0296 0583 2. 80 82. 0 D . 13... 3. 1 00398 . 314 . 412 . 595 0454 0170 172..-. 2. 290 . 00560 .66 3. 47 585 . 116 275 3. 96 81.0 A? .16... 2. 5 0343 . 800 .399 . 574 0478 0174 Channel width= 3.9 ft 173... . 1 29 0. 00096 0. 730 l. 77 20, 820 0. 00156 0. 00644 2. 00 82. 5 D . 07-.- 3 6 0. 000566 0. 0772 0. 531 0. 650 0. 0419 0. 0171 174.... 1. 28 . 000912 . 705 1.82 16, 530 . 00205 . 00800 2. 01 77. 0 D . 13... 4 3 . 000556 .0730 .519 . 622 .0368 . 0160 175... . 1. 36 . 00115 . 708 1. 92 12, 480 . 00367 .0152 2. 22 83. 5 D . 13... 4 2 . 000790 .0974 .521 .635 . 0419 . 0170 176. .. . 1 43 . 00191 .694 2 06 15, 600 . 00830 . 0308 ........ 81.5 D . l5--. 2 5 . 00114 . 170 .512 .640 . 0594 .0202 177.... 1 47 . 00214 .67 2 20 4, 290 . 0112 .0420 2. 68 79. 0 D . 18.. . 3 0 . 00287 . 197 . 498 . 616 .0568 .0196 l Immersed weight. 3 Both dunes and antidunes occurred. Letter A in height column indicates bed forms were antidunes; B, bars; D, dunes. 4 Both bars and antidunes existed, simultaneously. TABLE 2.—-Summary of experimental data, in metric units [Precision of measurements indicated by table 1, not table 2] Unit Sediment transport 1 Bed forms 1 Unit water Mean —— ——— stream (“50113me Depth, velocity, Unit Sediment Surface Water power, Hydraulic Hydraulic Run 2 Slope, D V Measuring transport infeed 1 velocity, tempera- Travel a: radius, radius of W S (cm) (cm er period rate, 1' (kg per (cm er ture Height Len th velocity, (kg per R bed, R1 (liters per . sec (sec) (kg per sec) sec (°C) (cm) (cm (cm per sec per (cm) (cm) sec per 111) 5631?” sec) 111) Channel width 7.5 cm 13.8 0.00529 3.1 44.5 2.580 0.00315 0.000227 52.5 21.2 1.7 2.1 15.2 .00 3.2 48.0 1,800 .00702 .000526 56.0 26.2 d 1.7 2.2 18.2 00840 3.3 56.0 1,200 0149 .00113 65.5 24.2 d 1.6 2.3 16.6 0132 3.0 64.0 1,500 0375 .00299 77.0 21.6 A 1.6 2.1 21.6 .0166 3.0 73.0 5,400 0851 .00653 84.5 22.2 A 1.7 2.2 23.8 .0213 2.6 64.0 6,540 150 .0110 97.5 23.6 A 1.6 2.2 32.8 0262 3.0 108. 0 4,200 327 .0252 117.5 24.6 A 1.7 2.0 40.8 .00272 9.3 44.0 55,140 .000803 53.0 18.2 D . 2.7 4.3 42.8 .00258 9.2 46.5 17,400 .00137 ............ 52.0 22.8 D . 2.7 3.8 45.4 .00295 9.1 49.0 11, 340 00210 _ 56.0 24.8 D . 2.7 3.8 44. 2 .00310 9.0 40. 5 7, 920 00324 _ 56. 5 24.8 D . 2.7 3.8 50.2 .00371 9.2 54.0 15,180 00706 . 61.0 23.8 D . 2.8 4.0 54.2 .00435 9.2 59.0 4,860 00918 . 67.0 22.0 D . 2.8 4.2 60.2 .00595 9.4 64.5 3,330 0214 ............ 77.0 20 8 D . 2.8 4.8 72.4 00942 9.0 79.0 2,595 0551 ............ 95.0 20 0 {2, 1'8 35 32} 683 2.6 5.0 80.6 .0131 9.5 65.5 1,740 0905 ............ 103.0 20 2 A 3.2.... 40 .56 1 051 2.6 5.6 88.0 .0133 9.5 94.0 6,780 102 00756 109.0 19 6 A 2 8.... 41 .58 1 167 2.6 5.2 97.4 .0177 9.5 105.0 780 222 ............ 113.0 20 6 A 4 9.... 45 .85 1 714 2.8 5.6 100.4 .0174 9.0 113.0 3,540 244 0184 122.0 10 6 A 4 4.... 1.27 1 747 2.6 4.8 104.0 .0208 9.0 113.5 480 .310 ____________ 117.5 20.8 A 5 4.... 40 1.33 2 161 2.6 5.4 104.0 .0205 9.0 119.0 2,970 .406 .0293 125.5 16.6 A 4 8.... 46 1.39 2 131 2.6 5.0 119 0 .0197 9.0 133. 0 2,700 .597 0376 137 o 19.6 A 4 4.... 47 1.99 2 333 2.8 4.4 125 6 .0222 9.0 138.0 3,900 .613 141.0 20.6 A 6.... 49 1.60 2 780 2.6 14 167 2 .0288 9.0 161.0 1,980 1.434 108 180 5 19.6 Flat bed ...................... 4 606 2.8 3. 6 200 6 .0350 9.5 214.5 900 2.068 ............ 208 5 19.6 o ........................... 7 2.8 3.0 4 76 2 .00237 15. 5 49 5 70,920 000565 0000342 49. 5 23. 2 ...do ........................... .180 3.0 4. 79 6 .00271 15.3 52 5 14,280 00156 ............ 59.0 24.0 D 1.0.... 204 .042 216 3.0 4.8 85 0 .00288 15.3 55 5 8,340 00375 ............ 64.5 24.2 D 1.0.... 100 .12 246 3.0 4.5 89 6 .00363 15.2 59 0 12,780 00720 ............ 67.0 20.8 D 1.6.... 114 .084 324 3.0 5.5 98 8 .00485 15.2 64.5 7,200 0152 ............ 75.0 20.4 D 1.6.... 103 .14 .479 3.0 6.4 See footnotes at end of table. H36 SEDJJVIENT TRANSPORT 1N ALLUVIAL CHANNELS TABLE 2.-—Summary of experimental data, in metric units—Continued mew o omnv—wccoocoofikoo “OOhOONfi omuumchmmuwmwm OIOIUIOOOUIOJNOOUIOI DOOIUICJIOIUNIKIQ‘I Umt Sediment transport 1 Bed forms 2 water Mean —— ——-—————— Unit discharge, Slope, Depth, velocity, Unit Sediment Surface Water stream Hydraulic Hydraulic Run 3 S D V Measuring transport infeedl velocity, tempera- Height Length Travel power, radius, radius of W (cm) (cm er period rate, 1' (kg per (cm pet ture velocity, u: R bed, Rb (liters per sec (sec) (kg per sec) see) (°C) (cm) (cm) (cm (kg per (cm) (cm) sec per 111) sec r sec sec Fer m m Channel width 7.5 can—Continued 112. 2 00651 15 4 73 0 87.0 21. 2 D 1.8.... 69 .43 .729 3. 0 7. 120. 0 00763 15 2 79 0 98.0 21. 2 D 2. 0.... 64 .60 . 914 3. 0 7. 141. 2 0104 15 4 91 5 110. 5 20. 2 D 2. 4.... 98 .87 1. 466 3. 0 7. 159.8 .0123 15 5 104 0 120.0 18. 4 A 5. 4.... 56 .82 1. 964 3. 0 7. 159.0 0158 15 5 101 5 115.5 22.8 A 6. 8.... 61 . 98 2. 515 3. 0 9. 171.0 0212 15 0 113 5 123.5 23.0 A 8.6.... 76 1.34 3.616 3.0 9. 211. 8 .0188 15 0 141.5 155.0 17. 4 A 6.8.... 63 2.13 3. 973 3. 0 6. 256 0 .0238 15 0 169. 5 183.0 17. 6 A 6. 6.... 74 2. 96 6.056 3. 0 5. 285 0 0309 14 5 199 207.5 15.2 Flat bed ...................... 8.794 3.0 5. 116 0 00250 21 4 54 0 58.0 15.6 D 0.8 .015 . 9 3.2 5. 115 2 00234 21 4 53 57.5 17.8 D 0.8 .0085 .269 3.2 4. 129 4 00300 21 8 59 5 64.5 13.4 D 1.6 .062 .388 3.2 5. 159 8 00539 22 2 72 0 92. 5 15. 0 D 3.2 .23 .862 3. 2 8. 206 2 00793 21 6 95 0 111.5 18.4 D 3.0 .93 1. 637 3.2 6. 229 2 0101 21 4 107 5 116.5 17.0 D 3. 1.01 2.336 3.2 7. 250 8 0146 21 o 119 0 140.0 17.2 {E 3' fig} 3.660 3.0 9. 275 0 0183 21 O 131 5 144.0 16.4 A 6. 1.66 5.029 3.0 9. 305 5 0225 21 0 147 5 164.5 16.6 A 8. 2.54 6.875 3.0 9. Channel width 15.0 cm 10 2 0.00383 3. 1 33.0 19, 260 0.000222 0.0000503 48.0 20. 2 2. 2 2. 11 8 .00481 3. l 38. 5 7, 740 . 00269 ............ 53. 0 22.0 2. 2 2. 13 4 .00558 3.1 43.0 .5 26.4 2.2 2. 14 0 .00617 3.1 45.0 .0 22.0 2. 2 2. 15 4 .00758 3. 2 49.0 .0 26.8 2.0 2. 16 8 .0117 3. 0 56. 5 .0 22.8 2. 0 2. 19 4 .0162 3.0 64.5 . 23.8 2.0 2. 24 6 .0202 3.0 80.5 24.2 2.0 2. 27 4 .0217 3.0 91.5 24.2 2.0 2. 35 6 .0303 2.6 134.5 8.0 2.0 2. 43 2 .0367 2.4 173.5 8.0 2.0 2. 40. 0 . 00177 8. 9 45.0 20. 8 4. 1 5. 44. 2 .00183 9.3 47.0 20.4 4. 2 5. 49. 8 . 00251 9. 4 53. 0 19. 8 4. 2 5. 55. 8 00374 9. 2 61. 0 19. 0 4. 2 6. 60. 8 00553 8. 8 69. 0 18. 6 4.0 6. 70. 2 00795 9.0 78. 5 17.8 4. 2 6. 74. 4 0090] 9.0 83. 0 17.4 4.0 6. 89. 6 0120 9. 5 95. 5 18. 2 . 4.0 7. 99. 2 0136 9. 5 106. 0 18. 0 .348 4.0 7. 109. 6 0149 9. 5 115.0 17.6 .622 4.0 7. 115. 6 . 0165 9.0 126. 5 18. 0 .905 4. 0 6. 139.4 .0179 8.8 160.0 10.4 .500 4.0 5. 178. 4 . 0234 9. 2 195. 0 12. 0 4. 166 4. 0 5. 69.2 .00123 15.0 46.0 22.2 D . .0850 5.1 6. 73. 6 . 00161 15. 2 48.0 26. 4 D 1. . 119 5. 1 8. 76 2 .00191 15. 0 50. 5 26.2 D . . 146 5. 1 8. 81 8 .00227 15.4 53.0 26.8 D . .186 5.1 9. 85 8 .00260 15.3 56.0 26.0 D . .223 5.1 9. 90 6 .00300 15. 2 59. 5 25.4 D . .272 5.1 9. 106 0 .00458 15. 0 70. 5 24.8 D 2.4 . 485 5. 0 9. 126 4 .00639 15. 4 82.0 26.0 D 2.4 .805 5. 0 10. 146 8 .00931 15.5 94.0 26 4 A? 4.2 58 91 1.363 5. 0 11. 155 8 . 0111 15.0 103. 5 11.0 A 6. 1. 711 5. 0 10. 159 8 0141 15 5 104 0 26.6 A 7. 2. 247 5.0 11. 172 4 0141 14 5 117 5 9.8 A 6. 2.425 5.0 10. 232 2 0144 15 5 147 5 11.6 A 7. 3 318 5.0 9. 315 8 0230 13 5 234 0 8.8 F 5.0 6. 106 8 .00115 21 4 50.0 16.0 5.6 7. 115 2 .00127 21 4 54.0 18.6 5.6 7. 122 6 .00145 21 8 56.5 23.0 5.6 8. 134 8 .00211 21 6 62.0 23.8 5.6 10. 161 8 .00324 21 4 75. 5 24.0 5.6 10. 197 0 .00456 22 0 89.5 14.0 5. 6 11. 239. 6 .00951 21 0 113. 5 12.6 5. 5 13. 306. 6 . 0135 21 0 145. 0 12. 0 5. 5 12. 10. 6 0. 00407 2. 8 38. 0 226, 620 50. 5 2. 4 2. 11 8 . 00411 3. 0 39.0 17. 940 . 51.0 2. 5 2. 13 2 .00495 3. o 43.0 10,140 . 57. 5 2. 5 2. 14. 6 . 00590 3. 2 47. 0 5, 400 . 63. 5 2. 6 2. 14. 4 . 00751 3. 0 46. 5 2, 460 . 67. 5 2. 6 2- 15. 4 .0108 3. 0 53. 5 1, 440 . 73.5 2- 4 2- 17. 8 . 0128 3. 0 57. 5 1, 684 . 81. 5 2. 6 2. 20. 4 . 0151 3. 0 67. 5 2, 183 87. 0 2. 6 2. 21. 6 . 0199 3. 0 75. 5 960 . . 103. 5 2. 4 2- 27. 2 .0222 3. 0 91. 5 473 . ............ 117. 5 2. 4 2. wmmmmmmmmm See footnotes at end of table. FLUME WIDTH AND WATER DEPTH EFFECTS TABLE 2.—Summary of experimental data, in metric units—Continued H37 Uréit M Sediment transport 1 Bed forms 3 U i we er ean —————-—-——— n t discharge, Sloge, Depth, velocity, . Unit Sediment Surtece Water stream Hydraulic Hydraulic Run Q D V Measprmg transpprt mieed I veloclty, tempera— Height Length Travel power, radius, radius of W (cm) (cm per period rate, 1 (kg per . (cm per ture velocity. u.- R bed, (liters per sec) (see) (kg per sec) sec) (" 0) (cm) (cm) (cm per (kg per (cm) R; see per 1n) sec per sec) sen per (cm) m) 111) Channel width 30.5 «cm—Continued 37. 2 .0331 3.0 130.0 159.0 19. 2 Flat bed ...................... 1. 229 2.4 2. 6 37. 6 . 00110 9. 1 41. 5 47. 5 . . 0412 5. 7 6. 7 40. 8 . 00121 9. 6 42. 5 51.0 . . 0494 5. 9 7. 3 40. 8 . 00136 9. 6 43. 0 53. 5 . . 0554 5. 9 7. 4 40. 6 . 00162 9. 0 45. 5 56. 5 . . 0659 5. 6 7. 1 42. 0 . 00182 9. 0 47. 0 57. 0 . . 0763 5. 6 7. 2 43. 6 . 00200 9. 1 48. 0 63. 0 . . 0870 5. 7 7. 4 46. 2 . 00210 9. 2 50. 0 66. 0 . . 0975 5. 7 7. 4 192 $2 3'3 33 2‘23 ‘ '33“ 2'2 2'3 49. 2 . 00272 9. 0 55. 0 70. 0 . . 134 5. 6 7. 4 51. 2 . 00318 8.8 58.0 70. 5 . . 162 5. 6 7. 2 232 22232 22 222 232 2 232 22 68. 8 . 00557 9. 0 76. 0 89. 0 12. 4 40 . 76 . 384 5. 6 7. 6 70. 6 . 00594 9.0 79.0 91. 5 20. 4 .418 5. 5 7. 5 70. 6 . 00592 9. 0 78. 5 93. 0 22. 0 . 417 5. 5 7. 5 73. 8 . 00643 9. 5 79. 0 93. 0 15. 6 . 473 6. 0 8. 0 79.8 . 00721 9. 5 85. 5 101. 5 21. 8 . 574 6. 0 8. 0 97. 6 . 00824 10. 0 99. 0 112. 0 23. 6 . 802 6. 0 8. 0 104.0 .0109 10.0 106.5 114. 0 25.0 1.131 6.0 8. 5 120. 8 0129 10. 0 122. 0 141. 5 20. 4 1. 562 6. 0 8. 0 183.0 0162 9. 8 186. 0 .......... l9. 8 2. 961 6.0 7. 4 71. 4 . 00106 15.3 46.5 53. 5 19. 0 D .0754 7. 7 10. 6 78. 6 . 00137 15. 5 50. 5 58.0 21.0 D . 108 7. 7 11. 1 73.8 . 00133 14.8 50. 0 58. 5 26. 0 D . 0984 7. 5 10. 5 80. 4 . 00144 15. 4 52. 5 60. 0 22. 8 D . 116 7. 7 10. 9 84.0 .00172 15.8 53.5 61. 5 23.6 D .145 7. 7 11.8 89.2 . 00184 15.6 57.0 68.5 23.2 D .164 7. 8 11.4 89.0 . 00216 15.4 58.0 67.0 17. 8 D . 192 7. 6 11.6 97. 6 . 00251 15. 8 62. 0 72. 5 18. 8 D . 246 7. 8 12. 2 102. 2 . 00314 15. 4 66. 5 77. 5 20. 8 D . 320 7. 6 12. 0 122. 6 . 00416 15. 5 79. 0 95. 5 20.8 D . 509 7. 6 12. 2 152. 4 .00842 15.0 102. 5 115.0 18.8 A 1. 281 7. 5 12.0 173. 8 . 0118 14. 5 119.0 135. 5 18.8 A 2. 039 7. 5 12.0 231. 4 . 0113 14.5 159. 0 171. 5 19.0 A 2. 604 7. 5 10. 5 108. 6 . 00081 21.2 51. 0 55. 5 22.0 D 0879 8. 9 11. 6 115.2 . 0079 21. 7 53. 0 56. 0 16.0 D 0909 9. 0 11. 1 122.6 . 00131 21.4 57.5 62.0 21.6 D . 161 9.0 13.8 132. 0 . 00178 21. 8 60. 5 66. 0 20. 6 D . 235 9. 0 15. 4 152.4 . 00272 21.6 71.0 77.0 19.0 D .414 9.0 15. 8 210. 0 . 00454 21. 0 99. 0 . . 109. 5 18. 8 A . 952 9. 0 15. 0 259. 2 . 00955 20. 0 132. 0 2, 160 . 457 . 145 133. 0 20. 0 A 2. 470 8. 5 15. 0 Channel width 61.0 cm 11. 2 0. 00489 3. 0 37. 0 56, 280 0. 00253 0. 00150 56. 5 26. 6 B 3. 0. 0545 2. 7 2. 9 13. 6 . 00569 2. 8 49. 0 19, 560 . 00527 . 00355 60. 5 25. 6 B 0. . 0771 2. 5 2. 7 16.2 . 00816 2. s 58.5 11, 550 .0177 . 0109 70.0 25.0 {E} 3 .133 2. 5 2. 7 16. 8 . 0117 2. 7 61. 5 6, 000 . 0405 . 0260 78. 5 26. 8 A 2. . 195 2. 5 2. 6 24. 2 0172 2. 8 85. 5 3, 945 . 115 . 0744 96. 5 26. 8 A 2. . 414 2. 6 2. 7 29. 8 3. 0 98. 5 900 . 280 . 183 129. 0 26. 0 Flat . 692 2. 8 2. 9 39. 8 . 00118 8. 7 45. 5 23, 340 . 000997 . 000631 59. 0 24. 0 D 1.0 . 040 . 0469 6. 8 7. 5 41. 8 . 00154 9.0 47.0 48, 900 . 00179 . 00108 60.0 25.6 D 1.0 .062 .0643 6. 8 7.8 46. 4 . 00210 8. 8 53. 5 5, 700 . 00625 . 00390 67. 5 28. 2 D 1.5 . 10 . 0975 6. 8 7. 8 54. 8 . 00330 8. 8 62. 0 7, 770 . 0185 . 0113 82. 5 28. 2 D 2.0 . 28 . 180 6. 8 8. 0 78. 6 . 00714 9.0 89. 0 6, 510 . 104 . 0680 101.5 28. 4 A 3.5 .85 .559 7.0 8. 0 102.6 .0113 9. 0 115.0 2, 605 .286 . 198 134.0 24. 8 A 5.5 . 98 l 162 7.0 8.0 160 ........ 72. 4 . 00106 14. 6 49. 5 83. 940 . 00106 . 57. 5 23. 6 D 1.0. . . 015 . 0768 9. 8 12. 0 161 ........ 79.4 . 00097 15.0 53.5 53, 940 . 00195 . 00112 58.5 26.4 D 1.5. __ . 111 .032 0769 10.0 11.8 162 ........ 81. 8 . 00137 15. 2 54.0 7, 860 . 00454 . 00272 62. 5 26. 8 D 2.0. ... 94 .049 . 112 10.0 12.6 163 ........ 103. 2 . 00281 15.2 68.5 7, 650 . 0210 . 0131 80.0 24. 8 D 3.5. . . . 104 . 12 . 289 10. 0 13. 2 164 ........ 119.8 . 00445 14.8 81.5 .830 0539 .0323 90.0 26.0 D 4. 77 .61 .533 10.0 13.2 165 ........ 149. 2 . 00643 15. 0 100. 0 3, 595 . 149 . 0880 115. 0 26. 8 A 5. 67 .69 . 958 10. 0 13. 5 166 ........ 158. 8 . 00877 14.0 115. 0 1, 150 . 293 . 187 138. 5 26.2 A 6. 64 1. 22 1. 393 9. 5 12. 5 167 ........ 104.0 . 00060 21.1 49.5 103, 080 . 00870 . 000544 53.5 22. 4 D 2. 114 . 015 .0623 12.4 15.2 168 ........ 119. 4 . 00080 20. 8 57. 5 32. 700 . 00223 . 00127 59. 5 26. 6 D 2. 107 . 032 . 0954 12.4 15. 0 169 ........ 127. 2 . 00147 21.6 59. 0 11,940 . 00610 . 00362 62.0 25.2 D 2. 94 .020 187 12.6 18. 0 170 ........ 130. 6 . 00172 21.5 61.5 4, 440 .0109 . 00680 67.5 27.8 D 3. 110 .057 .225 12.5 18. 0 171 ........ 167. 2 . 00280 21. 5 78. 0 1, 205 . 0440 . 0264 85. 5 27. 8 D 4. 94 . 12 . 467 12. 5 18. 0 172 ........ 212. 8 . 00560 20. 0 106. 0 585 . 173 . 125 120. 5 27. 2 A? 5. 76 1. 05 1. 190 12. 0 17. 5 Channel width 119.0 cm 119. 8 0. 00096 22. 5 54. 0 20, 820 0. 00232 0. 00292 61. 0 28. 0 D 110 0. 017 0. 115 16. 0 20. 0 119.0 . 00091 21.5 55. 5 16, 530 . 00305 . 00363 61.5 25.0 D 131 .017 . 109 16.0 19.0 126. 4 . 00115 21. 5 58. 5 12, 480 . 00546 . 00689 67. 5 28. 6 D 128 . 024 . 145 16. 0 19. 5 132. 8 . 00191 21. 0 63. 0 15, 600 . 0124 . 0140 .......... 27. 6 D 76 . 035 . 253 15. 5 19. 5 136. 6 . 00214 20. 5 67. O 4. 290 . 0167 . 0191 81. 5 26. 2 D 91 . 087 . 293 15. 0 19. 0 1 Immersed weight. 3 Letter A in height column indicates bed forms were antidunes; B, bars; D, dunes. 3 Both dunes and antidunes occurred. 4 Both bars and antidunes existed, simultaneously. US. GOVENMENT PRINTING OFFICE: 1970 0—373- 26 I wk 9' l mu QB? Z5 7 DAY $53 ”"5“” Transport and Dispersion of Fluorescent Tracer Particles for the Flat-Bed Condition, Rio Grande Conveyance Channel, Near Bernardo, New Mexico GEOLOGICAL SURVEY, PROFESSIONAL PAPER 562—1 U.S.S.D._ Transport and Dispersion of Fluorescent Tracer Particles for the Flat-Bed Condition, Rio Grande Conveyance Channel, Near Bernardo, New Mexico By R. E. RATHBUN, V. C. KENNEDY, and J. K. CULBERTSON SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS GEOLOGICAL SURVEY PROFESSIONAL PAPER 562—1 UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1971 UNITED STATES DEPARTMENT OF THE INTERIOR GEOLOGICAL SURVEY William T. Pecora, Director Library of Congress (taming-card Nor 76-609684 For sale by the Superintendent of Documents, US. Government Printing Office, Washington, DC. 20402 - Price 65 cents (paper cover) CONTENTS Page Abstract .......................................................................... 11 Presentation and discussion of results ................................... Introduction ..................................................................... 1 Lateral-dispersion characteristics of the tracer materials ...... Design of the experiment .................................................... 2 Application Of fluorescent tracers ‘0 the measurement 0f the Selection of site .......................................................... 2 sediment-transport rate """""""""""""""""""""""" . . . “Dustpan” samples at cross section D Type of injectlon ......................................................... 3 . . . . Depth-integrated samples at the weir ........................ Quantity of fluorescent material ..................................... 3 Velocities of the centroids 0f the tracer masses ............... The “dustpan” sampler ................................................ 3 Longitudinal-dispersion characteristics of the tracer ma- Sampling arrangement ------------------------------------------------- 4' terials .................................................................... Experimental procedure ................................................... 4- Evaluation of the fluorescent tracer technique.. Preparation of the fluorescent materials .......................... 4- Summary... ------------------------------------------------------------------ Injection of the fluorescent materials ............................. 6 Literature Clted'.......:. .................................... , . . Appendix A— CllSCUSSlon of the washmtr effect ........................ Hydraullc and sediment-concentration measurements ........ 10 Appendix B— determination of the weighting factors IIIII Sampling procedure .................................................... 11 Appendix C —calcuiation of the sediment- -transport rates from the Analysis of the samples ................................................ 12 depth-integrated samples at the weir ................................... ILLUSTRATIONS FIGURES 1—4. Photographs of: 1. Rio Grande conveyance channel and the weir used for total sediment concentration sampling ............................... 2. Weir and baflies in the Rio Grande conveyance channel ................................................ 3. Study reach viewed in an upstream direction from the weir. 4-. “Dustpan” sampler .................................................................................................................................. 5. Detailed sketch of the “dustpan” sampler .............................................................................................................. 6. Plan-view sketch of the study reach ...................................................................................................................... 7'9. Photomicrographs of: 7. Two sieve classes of bed material from the Rio Grande conveyance channel .......................................................... . ...... 8. Three sieve classes of fluorescent materials, run 1 ................................................................................................... 9. Four sieve classes of fluorescent materials, run 2 .................................................................................................... 10. Photograph showing injection of the fluorescent materials, run 1 11. Discharge hydrograph ........................................................................................................................................ l2. Cross-section measurements ............................................................................................................................... 13. Photograph showing three boatcrews “dustpan” sampling at cross section I) ................................................................ _ 14-. Photograph of equipment used for determining the number of fluorescent particles ...................... 15—42. Graphs showing: 15. Variation with time of the concentration of the 0.177- to 0.250-mm sieve class of green quartz ........................... 16. Variation with time of the concentration of the 0.350- to 0.500-mm sieve class of yellow quartz .......................... 17. Variation with time of the concentration of the 0.707- to LOO-mm sieve class of red quartz... 18. Variation with time ofthe relative concentrations of the quartz and monazite at lateral positions ofz=18. 24. 30. and 36 feet ......................................................................................................................................... 19. Variation] with time of the relative concentrations of the quartz and monazite at lateral positions ofz: 42, 4-8, and 54 feet ................................................................................................................ 20. Variation of the area under the curve of concentration versus time with lateral position, 2. for different sieve classes of quartz tracer, run 1 ..................................................................................................................... 21. Variation of the area under the curve of concentration versus time with lateral position. 2. for different sieve classes of quartz tracer, run 2 ............................................................................................ 22. Variation of the area under the curve of concentration versus time with lateral position. z. for different sieve classes of garnet tracer. run 2 ..................................................................................................................... 23. Variation of the area under the curve of concentration versus time with lateral position, 2. for different sieve classes of monazite tracer, run 2 ................................................................................................... 24. Variation with fall diameter of the mean lateral postions of the tracer distributions. run 1 ................................ 25. Variation with fall diameter of the mean lateral positions of the tracer distributions. run 2 ............................... 26. Variation with fall diameter of the variances of the lateral distributions of the tracer masses, run 1 .................... III Page 113 17 28 14 15 16 18 20 22 23 24 25 27 27 28 IV CONTENTS FIGURES 15-42: Graphs showing: TABLE 1. gxmtpww coo—q 11. 12. 13. 14. 15. 16. 17. 18. 19. . Summary of the Z. 0'3. and 0'? (corrected) values for the dye-dispersion test ........................ . Summary of the calculation of the sediment-transport rate. “dustpan” samples at cross section D, run 1 ............................... 27. Variation with fall diameter of the variances of the lateral distributions of the tracer masses. run 2 .................... 28. Variation with time of the relative mean fluorescent tracer concentrations of the weir samples, run 1 ................. 29. Variation with time of the relative mean fluorescent tracer concentrations of the weir samples. run 2 ................. 30. Variation with time of the relative mean concentration of yellow quartz. run 1 ................................................ 31. Variation with time of the relative mean concentration of green quartz. run 1 ................................................. 32. Variation with time of the relative mean concentration of red quartz. run 1 .................................................... 33. Variation with time of the relative mean concentration of quartz tracer. run 2 ................................................ 34. Variation with time of the relative mean concentration of garnet tracer, run 2 ................................................ 35. Variation with time of the relative mean concentration of monazite tracer. run 2 ............ 36. Variation with fall diameter of the velocities of the centroids of the tracer masses. run 1 ................................. 37. Variation with fall diameter of the velocities of the centroids of the tracer masses. run 2 ................................. 38. Variation with fall diameter of the variances of the mean concentration versus time curves, run 1 ..................... 39. Variation, with fall diameter of the variances of the mean concentration versus time curves, run 2... 40. Variation with lateral position of the sediment-transport weighting factors. runs 1 and 2 ................................... 4-1. Sieve-size distributions of two depth-integrated samples obtained at the weir ................................................. 4-2. Visual-accumulation-tube size distributions .............................................................................................. TABLES Summary of the median fall diameters of the various sieve classes of fluorescent tracers from runs 1 and 2 and the bed material from the Rio Grande conveyance channel ............................................................................................................ . Summary of the amounts of fluorescent material injected for each sieve class, runs 1 and 2 ................................................ . Summary of the hydraulic data for the study reach ...................................................................................................... . Total-sediment-concentration measurements at the weir. run 1. December 13. 1966 ........................................................... . Total-sediment-concentration measurements at the weir. run 2. December 14-. 1966 ........................................... Numbers of fluorescent particles per gram of fluorescent material for the sieve classes of fluorescent tracer materials used in runs 1 and 2 ................................................................................................................................................... . Summary of the z‘ and 0% values for the lateral distributions at cross section D. run 1 ........................................................ . Summary of the Z and 0% values for the lateral distributions at cross section D. run 2 Summary of the calculation of the sediment-transport rate. “dustpan” samples at cross section D. run 2 ............................... Summary of the calculation of the sediment-transport rate, depth-integrated samples at the weir. run 1 ................................. Summary of the calculation of the sediment-transport rate, depth-integrated samples at the weir. run 2 Summary of the l. At. tom. and 17 data. run 1 ............................................................................................................. Summary of the 5. At, £0.01, and I7 data. run 2 ............................................................................................................. Summary of the 0-? values of the mean concentration at cross section D as a function of time data, run 1 .............................. Summary of the a"? values of the mean concentration at cross section D as a function of time data, run 2 ....... . .. Comparison of the median diameters and the gradations of the size distributions of selected “dustpan.” core, and depth- integrated samples .......................................................................................................................................... Comparison of the (113, (150, d“. and 0' values for selected “dustpan” samples at cross section D, run 2 ................................. Page [28 32 33 35 36 37 38 40 42 43 4-4 46 4-6 54 55 55 15 10 10 10 11 C(t) am C(t) ém C(z) Cfld C'(t) C§(t) 0m dlti (150 (134 KI, KZ CONTENTS SYMBOLS Area under the experimental concentration as a function of time curve at lateral position 2, in gram-hours per gram. Relative area, equal to A(z) divided by the total area under the A(z) as a function of 2 curve. Area under the concentration as a function of time curve for the depth-integrated samples at the weir, in particle- hours per gram. Area under the concentration as a function of time curve for size class i of the depth-integrated samples at the weir, in particle-hours per gram. Width of the channel, in feet. Concentration of fluorescent tracer in a size split of a “dust- pan” sample, expressed as grams of fluorescent tracer per gram of total material in the size split. Relative concentration of fluorescent tracer, equal to the concentration divided by the area under the concentration as a function of time curve. Mean concentration of fluorescent tracer across the channel width, in grams per gram. Relative mean concentration of fluorescent tracer, equal to the mean concentration divided by the area under the mean concentration as a function of time curve. Concentration of fluorescent tracer at lateral position 2, in grams per gram. tMay also refer to the concentration of fluorescent dye at lateral position 2 in the dye-dispersion test, milligrams per liter.) Concentration of sediment at lateral position 7., determined from a depth—integrated sample at z, milligrams per liter. Concentration of fluorescent tracer in a depth-integrated sample, expressed as number of fluorescent particles of a specific color per gram of total sediment in the sample, in particles per gram. Relative mean concentration of fluorescent tracer in a depth- integrated sample, equal to the concentration divided by the area under the concentration as a function of time curve. Mean concentration of fluorescent tracer in a depth-inte- grated sample, determined from a composite of depth-inte- grated samples taken across the weir at equally spaced intervals, in particles per gram. Particle diameter for which 16 percent by weight are smaller, in millimeters. Median particle diameter, in millimeters. l’article diameter for which 84- percent by weight are smaller, in millimeters. Dispersion coefficients in the x, z directions, in square feet per second. Total number of fluorescent particles of all sizes of a specific color injected at the beginning of the experiment. an Q Q (13(2) n. tum At WU) w(z) Az Nt Total number of fluorescent particles of size class L'ofa specific color injected at the beginning of the experiment. Total number of fluorescent particles of a specific color in a depth-integrated sample at time 1. Percent of the total weight of a depth-integrated sample that is in sieve class i, in percent. Total water discharge, in cubic feet per second. Water discharge per unit of width at lateral position z, in cubic feet per second per foot. Total sediment-transport rate, in tons per day. Total sediment-transport rate for size class i, in tons per day. Sediment—transport rate per unit of width at lateral position 7., in tons per day per foot. Mean sediment-transport rate per unit of width, in tons per day per foot. Fraction of the total water discharge in the width increment Az centered at lateral position 2. Time. in hours. Time required for the centroid of the tracer mass to reach the measurement section, in hours. Time required for the mean concentration at the measure- ment section to decrease to 1.0 percent of the maximum mean concentration, in hours. Time correction for the finite time interval required for injection of the fluorescent materials, in hours. Velocity of the centroid of the tracer mass. in feet per second. Weight of fluorescent material injected at the beginning of the experiment, in pounds. Total weight of sediment in a depth-integrated sample at time t, in grams. Weighting factor relating the unit sediment-transport rate with the mean unit sediment-transport rate for the cross section. at lateral position 2 Lateral distance, measured from the. right bank of the channel. in feet. Increment of width, in feet. Mean lateral position of the tracer mass at the measurement section, measured from the right bank. in feet. Specific weight of the water-sediment mixture, in pounds per cubic foot. A measure of the gradation, equals %(([34/lfso+ (150/1115) Variance of the mean concentration as a function of time curves, in hours'-’. Variance of the lateral distributions of the tracer materials at the measurement section, in feet“. VI CONTENTS ENGLISH-METRIC CONVERSIONS Principal ilem English unit Factor Metric unit 0.3048 .......................... meter Length .................................................. feet ..................................... 30.48 ........................ centimeter 304.8 ........................... millimeter Area ..................................................... square feet ........................... $9290 """""""""""""" square centimeters .09290 .......................... square meters Weight .................................................. pounds ................................. £4536 """""""""""""" grams .4536 ........................... kilograms Velocity ................................................. feet per second ...................... 303048 """""""""""""" meters per second 30.48 ........................... centimeters per second Water discharge ...................................... cubic feet per second ............. {(102832 """""""""""" CUbiC meters per second 2.832X10‘1 ..................... cubic centimeters per second Sediment-transport rate ............................ tons per day ........................... 0.9072 .......................... metric tons per day Specific weight ........................................ pounds per cubic feet... ......... 0.01602 ........................ grams per cubic centimeter SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES FOR THE FLAT-BED CONDITION, RIO GRANDE CONVEYANCE CHANNEL, NEAR BERNARDO, NEW MEXICO By R. E. RATHBUN, V. C. KENNEDY, and J. K. CULBERTSON ABSTRACT A fluorescent tracer technique was applied to a study of the rates of transport and dispersion of sediment particles of various diameters and specific gravities for the high-velocity flat-bed condition of alluvial- channel flow. Two runs were conducted in the Rio Grande conveyance channel near Bernardo, N. Mex., on December 13 and 14-, 1966. An instantaneous point source of fluorescent material was used in each run. Samples of the bed material moving on or near the bed surface were obtained throughout the passage of the tracer masses with the “dustpan” sampler especially designed for this study. The mean lateral positions of the distributions of tracer materials tended to follow the thalweg of the channel and shifted toward the right bank in moving from the injection point to the measurement section. The amount of shift increased with increasing particle fall diameter. The lateral dispersion of the tracer masses as represented by 0'3, the variance of the lateral distribution of fluorescent material at the measure- ment section, decreased with increasing fall diameter. The sediment-transport rates calculated from the fluorescent tracer experiments were about 57 and 14 percent larger than the sediment- transport rates measured at the weir in runs 1 and 2, respectively. The agreement in run 2 was good because positive and negative errors for the different sieve classes were compensating. The variation of the centroid velocities of the quartz tracer masses with fall diameter was approximately U‘shaped: the minimum velocity occurred for tracer particles having fall diameters comparable to or slightly larger than the median fall diameter of the bed material in trans- port. The maximum centroid velocities observed were for the 0.125— to 0.177-millimeter sieve class of quartz tracer. and these were approxi- mately 26 and 16 percent of the mean water velocity in runs 1 and 2, respectively. The centroid velocities of the garnet and monazite tracer masses were about an order of magnitude less than the centroid velocities for quartz tracer particles of comparable fall diameter. The longitudinal dispersion of quartz tracer particles as represented by 0"7’, the variance of the curves of mean concentration as a function of time at the measurement section, varied with fall diameter approxi- mately inversely to the manner in which the centroid velocities varied with fall diameter. The of values for the garnet and monazite tracer particles showed relatively little variation with fall diameter but were about an order of magnitude larger than the of values for quartz particles of comparable fall diameter. The fluorescent tracer technique is a simple and sensitive experi- mental method for the study of the transport and dispersion of groups of particles in a natural or laboratory alluvial channel. However, con- siderable improvement in technique is still needed. INTRODUCTION Problems associated with rates of transport of sediment by natural and artificial waterways are many, both in number and in type. Among the problems are those in- volving river management, design and operation of canals and reservoirs, and degradation around bridge piers and below dams. A problem closely related to the rate of sediment transport is the rate of dispersion of the sediment. De- velopment of nuclear energy industries and the increas- ing use of agricultural chemicals have resulted in the undesirable presence of radioisotopes, pesticides, and herbicides in the environment. Furthermore, there is considerable evidence that these substances are ad- sorbed by sediment particles. Thus, in the event that toxic material is discharged or accidentally spilled into a stream, the sediment may remove most of it from solu- tion. Thereafter, the rate of transport and of lateral and longitudinal dispersion of the sediment will control the movement and the concentration level of the toxic substance. An understanding of the laws governing transport of sediments of differing size and specific gravity is also important in geomorphology, in stratigraphic studies, and in the search for concentrations of valuable heavy minerals. Fluorescent tracers have been used extensively in the study of sediment transport and dispersion, but these investigations have been limited almost exclusively to research on beach erosion. Exceptions are the labora- tory work of De Vries (1966) and Lean and Crickmore (1966) and the field study of Crickmore (1967). The 11 12 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS application of the fluorescent tracer technique to a study of the transport of sand-size particles in a gravel-bed stream by Kennedy (1968) and Kennedy and Kouba (1970) served as the foundation for the present research and suggested the possibility of a large-scale field study of the transport and dispersion of sand-size particles in a sand-channel stream. This report describes a field study of the transport and dispersion of sediment particles of various sizes and specific gravities coated with fluorescent dye. Two experi- ments were conducted in the Rio Grande conveyance channel near Bernardo, N. Mex., on December 13 and 14, 1966. A high-velocity flat-bed condition existed for both experiments. In the preliminary experiment, run 1, three size ranges of quartz, each coated with a difi'erent color of fluorescent dye, were used. In the second experi— ment, run 2, four materials of different specific gravity were each coated with a different color of fluorescent dye. These materials were quartz, garnet, monazite, and lead, and each material contained a range of particle Sizes. . This study was the joint effort of Water Resources Division personnel from Denver, Colo., Albuquerque, N. Mex., and Fort Collins, Colo. V. C. Kennedy originated and coordinated the project with the assistance of F. C. Ames. The Albuquerque Field Research Unit (J. K. Culbertson and C. H. Scott) provided extensive logistic support for the fieldwork. Fort Collins personnel con— ducted preliminary laboratory experiments with the “dustpan” sampler, and C. F. Nordin, Jr., and W. W. Sayre helped in the supervision of the experiments and contributed many ideas and suggestions during the analysis of the data and the preparation of the report. Personnel from the New Mexico District who assisted with the fieldwork included J. P. Borland, B. M. Delaney, J. D. Dewey, Trancito Diaz, N.D. Haffield, V. W. Norman, David Ortiz, and J. W. Shomaker. Graduate students from Colorado State University who assisted with the fieldwork included J. P. Bennett, W. E. Gaskill, and J. N. Loyacano. Graduate students assisting with the analysis of the samples included N. S. Grigg, Ziad Mughrabi, C. H. Neuhauser, and C. A. Ramirez. Norman Prime of Menlo Park, Calif., prepared the photomicrographs of the fluorescent materials. DESIGN OF THE EXPERIMENT The experiment was designed to permit a study of the longitudinal- and lateral-dispersion characteristics of particles of various diameters and specific gravities in the sand-size range and also to permit an evaluation of the fluorescent tracer technique as a means of measuring the total sediment-transport rate of the bed material. SELECTION OF SITE The site chosen for the study was the Rio Grande conveyance channel near Bernardo, N. Mex. The channel contained a weir at which total sediment concentrations could be sampled. Figure 1 is a photograph of the channel and the weir. A series of baffles on the weir upstream of FIGURE l.—Rio Grande conveyance channel and the weir used for total sediment concentration sampling. the crest created suflicient turbulence to suspend all of the sediment in transport as it passed over the weir. The sediment suspended by the action of the baffles was sampled with the standard US DH—48 depth-integrating hand sampler (Guy and Norman, 1970). Figure 2 is a photograph of the baffles and the weir. Details of the FIGURE 2.—Weir and baflies in the Rio (‘yrande conveyance channel.- TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 13 design, construction, and operation of the weir have been presented by Harris and Richardson (1964) and Gonzalez, Scott, and Culbertson (1969). The BOO-foot straight reach immediately upstream of the weir was selected as the study reach so that the total sediment-transport rates computed at the weir could be used to check the sediment-transport rates computed from the fluorescent tracer experiments. Figure 3 is a photograph of the study reach as viewed in an upstream direction from the weir. FIGURE 3.—Study reach, viewed in an upstream direction from the weir. TYPE OF INJECTION Possible types of injection procedures are the instan- taneous line source, the continuous line source, the instantaneous point source, and the continuous point source. The mechanical requirements for a line source are more demanding than for a point source, and information on the lateral-dispersion characteristiCS of the channel cannot be obtained. The continuous source has the ad- vantage that only a few samples are necessary after equilibrium has been attained at the measurement sec- tion. However, the continuous source must be maintained until equilibrium is obtained, and continuous feeding is demanding of both manpower and fluorescent materials. On the basis of these considerations, the instantaneous point-source method of injection was chosen for the study. QUANTITY OF FLUORESCENT MATERIAL One of the requirements of any tracer procedure is that the quantity of material introduced be small enough so that the natural sediment-transport process is not disturbed. At the same time, sufficient tracer material 405-770 0L - '71 - 2 must be injected so that statistically significant numbers of particles are obtained in the samples. The quantity of fluorescent material required was estimated in the following way. It was assumed that the injected tracer material was instantaneously and uniformly mixed throughout the length of the study reach. This assumption was obviously conservative and resulted in estimated peak fluorescent tracer concentrations that were smaller than the 'actual experimental values. Concentration of fluorescent ma- terial in a sample as used in this report is defined as the ratio of the weight of tracer material in a specific size range of the sample to the total weight of all sediment in that size range of the sample. For the flat-bed condition, mOSt of the material in transport is concentrated in a thin layer near the bed surface. Opinions differ as to the thickness of this moving layer. However, for the purpose of illustration, assume that the moving layer is 0.1 foot thick and that the water-sediment mixture in the moving layer is 50 percent sediment by volume. The study reach was 800 feet long from the injection point to the weir, and the mean channel width was about 70 feet. Thus, the total dry weight of sand participating in the transport process and present in the study reach at any instant is estimated as 800 X 70 X 0.50 X 2.65 X 62.4 = 463,000 pounds. For the flat-bed condition in the Rio Grande con- veyance channel, approximately 50 percent of the material in transport is in the size range from 0.125 to 0.250 mm (millimeter). Therefore, about 231,000 pounds of sediment in active storage in the 0.125- to 0.250-mm size range is present in the study reach at any instant. Fluorescent tracer concentrations of the order of 10‘3 to 10"4 are adequate for purposes of analysis; and if the mean fluo- rescent tracer concentration in the reach is of this order, then the quantity of tracer material in the 0.125- to 0.250-mm size range should be between about 23 and 231 pounds. THE “DUSTPAN” SAMPLER The application of the fluorescent tracer technique to the study of the transport and dispersion rates of sedi- ments for the high-velocity flat-bed condition required a different type of sampler from those usually used in sedi- ment-transport studies. Because the concentrations of fluorescent tracer could not be determined in situ, it was necessary to obtain samples from the channel for laboratory analysis. These samples had to contain all sizes of the bed material in transport, and the sample time was necessarily as short as possible so that several samples could be obtained as the tracers moved through the measurement section. Thus, the sampling position best suited to meet these requirements was on or just above the bed surface. 14 Sampling the moving bed material for a fluorescent tracer experiment, however, has one major advantage over sampling the bed-material discharge with any of the bedload samplers described by Hubbell (1964). This advantage is that the efficiency of the sampler is unim- portant in fluorescent tracer experiments, provided that the fluorescent tracer particles of any specific size behave identically with nontagged particles of the same size. Efficiency was defined by Hubbell (1964) as “the ratio of the weight of bedload collected during any single sampling time to the weight of bedload that would have passed through the sampler width in the same time had the sampler not been there.” The significant factor in the “dustpan” sample is the ratio of the number of fluorescent particles of a given size to the number of nonfluorescent particles of the same size. A rear view of the “dustpan” sampler designed for this study and used in the experiments is shown in figure 4. FIGURE 4-.— “Dust an” sampler‘ rear view. p 7 The flow expansion in both the horizontal and vertical directions resulted in a decrease in flow velocity and deposition of sediment in the sampler. The sampler was constructed from galvanized sheet metal, and a 6-foot length of 3/4-inch pipe was used as the handle. The fin on the top of the sampler served to stabilize the sampler in SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS high-velocity flows. A small wooden baffle was positioned‘ across the inside of the sampler on the bottom about 6 inches from the inlet. Dimensions of the sampler and the position of the baffle are shown in figure 5. SAMPLING ARRANGEMENT A plan-view sketch of the study reach is shown in figure 6. The injection point was 800 feet upstream of the weir. The injection point was not positioned nearer the highway bridge because of possible effects from the slight bend just upstream of the bridge. Measurement sections A, B, C, and D were 100, 300. 500, and 700 feet, respectively, downstream from the injection point. The position of the thalweg, or line of maximum depth, for the study reach is shown also in figure 6. Because information concerning the rates of movement of sediment particles for the high-velocity flat-bed condi- tion was nonexistent, sampling was concentrated initially at cross section D so as to insure that the fluorescent particles did not pass completely through the study reach before they could be sampled. Subsequent adjustments to the sampling arrangement were dependent on the qualita- tive examination of the samples from cross section D. EXPERIMENTAL PROCEDURE PREPARATION OF THE FLUORESCENT MATERIALS The fluorescent materials used in the preliminary experiment, run 1, were some of the materials prepared by Kennedy and Kouba, and the preparation procedure used for this material has been described previously (Kennedy and Kouba, 1970). This material was prepared from a natural river sand that contained minerals other than quartz; hence, it should correctly be called quartzose sand. However, for brevity, it will be referred to as quartz in this report. The amounts available were 281 pounds of green quartz (approximately 0.15 to 0.30 mm), 252 pounds of yellow quartz (approximately 0.30 to 0.52 mm), and 295 pounds of red quartz (approximately 0.52 to 1.29 mm). The fluorescent materials for run 2 were prepared by a procedure similar to that of Kennedy and Kouba (1970). The fluorescent dyes used were the A series of Day-Clo pigments (Switzer Brothers, Inc., Cleveland, Ohio).' The rocket red (A—13), are yellow (A—16), signal green (A—18), and horizon blue (A-19) dyes were chosen for use because they were the most easily distinguishable from each other by the human eye. A vinyl plastic VAGH, blend 1508 (Union Carbide Corp., South Charleston, W. Va.) was also used with the dye to produce an abrasion-resistant coating. ' Use of company names is for identification purposes only and does not imply official endorse- ment of any product. ' TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION [5 Sng‘l 7/! ____ T R Wooden baffle E .L i4—3"—>l ———— TX— : , __—_ Q EV % L1 :::l :::El ‘1 : : I I I I I Flow 7n FIGURE 5.—Detailed sketch of the “dustpan” sampler. Commercial grade acetone was used as the solvent. A quantity of acetone was saturated with the vinyl plastic by adding the vinyl powder slowly to the acetone with constant stirring. The vinyl-acetone solution was then saturated with the appropriate dye. About 100 pounds of the material to be coated was placed in a small motor- driven cement mixer. As the material tumbled, a small quantity of the solution was mixed into the material and the acetone allowed to evaporate. When the coating was completely dry, more ot the dye solution was added. This process was continued until fluorescence of the material under an ultraviolet light indicated that an adequate coating had been obtained. If no loosely cemented aggregates of particles existed in the dry material, the material was placed in canvas bags. If aggregates of particles existed. the material was passed between rubber rollers to break the aggregates into single particles. TABLE 1,—Summary ofthe medianfall diameters ofthe various sieve classes offluorescent tracers/ram runs 1 and 2 and the bed materialfrom the Rio Grande conveyance channel Median fall diameter (mm) Run 1 Run 2 Sieve class (mm) Bed material Green quartz Yellow quartz Red quartz Quartz Garnet Monazite Lead (1) 0.125-0.177 0.156 0.150 ............................................. 0.152 0.232 0.235 ............... (2) 0.177-0.250 .201 .204 .300 .305 0.715 (3) 0250-0350 .270 .289 .405 .484 1.12 (4) 0350—0500 .446 .420 .578 .721 1.36 (5) 0500-0707 .630 .541 .690 ................................. (6) 0.707-1.00 ................................... . .694 .................. (7) > 1.00 ....................................................... .839 ............................................................... ............................... 2.65 4.08 4.79 11.3 Specific gravity ........................................................................... I6 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS \~\ Thalweg 0 Injection [ point — 100 ____ ———A Measurement ‘ site — 200 l- m u u. E ,_‘ _ 300 ____ ___.B Measurement E site 0 n. z 9 5 m — 400 g E 2 O 0: LL m _ 500 _____ ---C Measurement 0 Slte z < I— 1’ o — 600 1— ____ ___ Measurement 700 D site - 800 Weir FIGURE 6,—Plan-View sketch of the study reach. One disadvantage of the fluorescent coatings prepared by this procedure was that the coatings were nonwetting. Therefore, when the fluorescent materials were placed in water, the particles had a tendency to cluster together in groups. This clustering was avoided by adding de- tergent to the fluorescent material before injection. The fluorescent materials prepared in this manner for run 2 consisted of 199 pounds of Ottawa flint quartz and 194 pounds of Ottawa crystal quartz (Ottawa Silica Co., Ottawa, 111.), 232 pounds of garnet, 288 pounds of monazite, and 83 pounds of lead shot. The specific gravities of the coated materials were 2.65, 4.08, 4.79, and 11.3 for the quartz, garnet, monazite, and lead, respectively. Median fall diameters were determined for each V2 sieve class of the fluorescent materials used in runs 1 and 2, as well as for samples of the bed material from the Rio Grande conveyance channel. Fall diameters were determined either by droppingsingle particles in a column of quiescent. distilled water or by the visual—accumulation tube method (U.S. Inter-Agency Committee on Water Resources, 1957a). The visual-accumulation tube was used to analyze the materials smaller than 0.350 mm, and the single-particle method was used for materials larger than 0.350 mm. Fall velocities obtained from the single- particle method were converted to median fall diameters by means of table 2 of U.S. Inter-Agency Committee on Water Resources (1957b). The median fall diameters are summarized in table 1. Photomicrographs of the material from two sieve classes of bed material from the Rio Grande conveyance channel, one sieve class of each of the three colors of fluorescent quartz used in run 1, and one sieve class of each of the four minerals used as tracers in run 2 are presented in figures 7, 8, and 9, respectively. The photomicrographs show that the tracer ma- terials used in run 1 were angular. Hence, the particles would tend to have a shape factor less than the 0.7 usually attributed to naturally worn quartz particles. This shape effect explains why the fall diameters for some sieve classes of tracer materials from run 1 were smaller than the lower limit of the sieve class. (See US Inter- Agency Committee on Water Resources, 1957b, fig. 7.) The effect of shape on the difference between sieve diam- eter and fall diameter increases with fall diameter. The fall diameters for the garnet, monazite, and lead tracer particles used in run 2 are larger than the sieve diameters because of the specific gravity effect. INJECTION OF THE FLUORESCENT MATERIALS The instantaneous point-source method of injection was used for both runs 1 and 2. Initially, the intent was to use a 4-inch inside diameter steel tube as an injection tube. However, the tube clogged when the material was poured rapidly into it; so in both runs 1 and 2 the fluorescent material was poured from the back of the boat as rapidly TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION FIGURE 7.—Two sieve classes of bed material from the Rio Grande conveyance channel. A. 0177-0250 mm. B, 0.2590350 mm. 17 I8 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS FIGURE 8,—Three sieve classes of fluorescent materials, run 1. A, Green quartz. 0177-0250 mm. B, Yellow quartz, 0350-0500 mm. C, Red quartz, 0.707-1.00 mm. as possible. Figure 10 is a photograph of the injection process for run 1. The injection point for run 1 was the centerline of the channel 800 feet upstream from the weir. The green fluorescent material was injected first, then the yellow fluorescent material, and then the red fluo- rescent material. The green, yellow, and red fluorescent materials required 2 minutes and 45 seconds, 2 minutes, and 2 minutes, respectively, for injection. A tendency for the large particles to migrate toward the right bank (facing downstream) was observed in run 1, and therefore the injection point for run 2 was moved 7 feet to the left of the centerline. As in run 1, the fluo- rescent material was dumped from the back of the boat as rapidly as possible. The crystal quartz was injected first, followed by the flint quartz, garnet, monazite, and lead; the materials required 1 minute, 1 minute, 1 minute and 10 seconds, 1 minute, and 35 seconds, respectively, for injection. The amounts of fluorescent material injected for each sieve class for runs 1 and 2 are summarized in table 2. The quantities shown for quartz in run 2 include both the crystal quartz and the flint quartz. The totals given in table 2 are slightly less than the total amounts of fluorescent materials prepared because of the presence of small quantities of material in the ends of the size distributions. The only significant difference is TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 19 FIGURE 9.—Four sieve classes of fluorescent materials. run 2. A, Ottawa quartz. 0.2500350 mm. B, Game-t. 0250-0350 mm. C, Monazite. 0250-0350 mm. D, Lcad, 0.177*0.250 mm. 110 FIGURE 10.—Injection of the fluorescent materials, run 1. for the monazite where there was considerable material in the 0.088- to 0.125-mm sieve class. However, particles smaller than 0.125 mm were not considered in the analysis of the samples because of the difficulty of distinguishing between actual fluorescent particles and chips or flakes of dye from large particles. TABLE 2.—Summary of the amounts of fluorescent material injected for each sieve class, runs I and 2, in pounds Quantity injected Sieve class Run 1 Run 2 (mm) (ireen Yellow Red Quartz Garnet Monazite Lead quartz quartz quartz 0.125-0.177 4.4 8.1 83.7 ............ 0.177-0.250 16.7 40.2 46.6 1.8 0250—0350 . 53.0 94.7 30.9 46.8 0350-0500 . 126.0 77.0 56.5 33.2 0500-0707 4-9.2 65.3 177.1 9.5 30.4 ............ 070771.00 131.3 14.5 > 1. 93.6 ......................................................... Total ........ 276.9 249.0 290.2 391 7 229.5 248.1 81.8 HYDRAULIC AND SEDIMENT-CONCENTRATION MEASUREMENTS Prior to and during both experimental runs. measure- ments of the hydraulic parameters water discharge, water-surface slope, and cross-section measurements were obtained. Depth-integrated samples of suspended sediment were obtained at the weir at 5-foot intervals for lateral positions from 5 feet to 70 feet from the right bank throughout both runs. About 5 minutes and 8 minutes in runs 1 and 2, respectively, were required to obtain one complete set of samples across the weir. The 5-minute schedule was maintained for about 1 hour in run 1, and the 8—minute schedule for about 2 hours in run 2. There- after, the time interval between samples was increased gradually in both runs. The results of the hydraulic measurements are sum- SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS marized in table 3, and the total-sediment-concentration measurements at the weir are summarized in tables 4 and 5 for runs 1 and 2, respectively. For run 1, the mean total-sediment-transport rate between the hours of 1313 and 1504, December 13, when most of the fluorescent tracer material passed through the study reach, was 5,490 tons per day of material larger than 0.062 mm. For run 2, the mean total—sediment-transport rate between the hours of 1006 and 1151, December 14, when most of the quartz tracer material passed through the study reach, was 4,220 tons per day of material larger than 0.062 mm. The water discharge was not as constant as desired but decreased at an approximately uniform rate throughout both runs. Figure 11 is a discharge hydrograph based on the record from the gaging station just upstream of the TABLE 3. —Summary ofthe hydraulic datafor the study reach (sis. cubic feet per second: fps. feet per second; fl/ft. feet per foot] Date Water-surface Water (Dec. Time Discharge Mean Mean Mean Slope X 10‘ temperature 1966) (cfs) width depth velocity (ft/ft) (° C) (fl) (ft) (fps) 13 0845 920 72.9 2.76 4.66 14 0840 750 72.9 2.4-8 4.05 14 1500 720 72.9 2.48 4.05 15 0815 590 72.9 2.27 3.63 TABLE 4.—Total-sediment-concentration measurements at7 the weir, run 1, December 1.3, 1966 [mg/l, milligrams per literl Concentration Concentration Time Water discharge (cfs) > 0.062 mm (mg/l) < 0.062 mm (mg/1) 1313 905 2 .280 2,920 1320 2 .060 2,900 1326 2 .290 2 ,930 1331 2 ,350 2 .920 1337 2,310 2,910 1341 2 .280 2 .880 1346 2 ,470 2 .800 1350 ......................................................... 1354 2 ,280 2 .860 1358 2,150 2,880 1404 900 2,260 2,860 1408 2,590 2,660 1422 2 ,390 2 .820 1434 2,120 2,810 1444 2,180 2,780 1453 2,330 2,780 1504 900 1 .860 2 ,080 1524 1,940 2 ,730 1542 1,960 2,590 1604 890 2,150 2.670 1624 2,500 2,640 1713 1,900 2 .580 1737 2 .440 2,590 1806 845 2 .000 2 .490 1838 1.920 2,470 1906 2,260 2,500 1930 2,010 2.420 2005 2,410 2,430 TABLE 5.—Total-sedi”Lent-concentration measurements at the weir, run 2, December 14, 1966 TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION Water discharge Concentration Concentration Time (cfs) > 0.062 mm (mg/l) < 0.062 mm (mg/l) 1006 740 2.120 2,270 1015 2 .180 2 ,200 1023 2 ,000 2 ,210 1030 2 ,080 2 ,220 1038 2 .170 2 ,210 1046 2 ,260 2 ,230 1054 2 ,150 2 ,230 1100 2 ,160 2 ,210 1109 2 .040 2 .210 1 1 17 2 ,180 2 ,200 1125 2,130 2,200 1134 1,960 2,180 1142 2,150 2,180 1151 735 2,000 2,180 1218 1,950 2,160 1414 1,690 1,940 1435 1 .860 2 ,070 1503 2 .460 2 ,040 1534 2 ,300 2,020 1604 2 .090 2 ,020 1634 2,010 2,010 1703 1,830 1,980 1738 2 .040 1,960 1904 1,820 1,950 2013 2 ,150 1 ,960 2108 2 .030 1,950 2205 2 ,060 1 ,930 2305 2 .160 1 ,890 1800 l 1 | 1 I 1 | l 1 1 | 1 1 1 1400 — 2 N a”: 5 I p—ao O 0' O l l 1 l I I l t 1 I 600 ' DISCHARGE,IN CUfiIC FEET PER SECOND FIGURE ll.—Discharge hydrograph, from the gaging station just up- 5 6 7 8 9 10 DECEMBER 1966 11 I 12 13 14 15 stream from the weir, for the period December 1—16, 1966. 16 weir for the period December 1 to December 16. Run 1 was completed in the period between 1310 and 1800 hours on December 13, and run 2 was completed in the period between 1000 and 2400 hours on December 14. The cross-section measurements obtained on December 14 at 0815 hours are shown in figure 12. These measure- ments show that the thalweg is near the right bank at cross section A and near the left bank at cross section D. A dispersion test for a water-soluble fluorescent dye was completed just prior to the start of run 1 to permit a determination of the limits of lateral dispersion for 405-770 0L - 71 — 3 111 particles of essentially zero diameter. A Rhodamine WT dye solution was injected continuously from a constant- head tank at the same irijection point that was used for the fluorescent sediment tracers in run 1. Sampling was begun after sufficient time had elapsed to insure a steady- state concentration distribution at each of the cross sec- tions. A complete set of samples across the width of the channel was obtained at cross sections A, B, and C, and two sets spaced about 7 minutes apart were obtained at cross section D. A nylon cord to which 24-ml (milliliter) screwcap vials were attached at 2-foot intervals was stretched across the channel. The cross-section samples were obtained simultaneously by dipping the vials into the channel. After the bottles filled, the cord was raised and the vials were removed from the line, capped, and labeled. The dye concentration of each sample was deter- mined with a G..K. Turner fluorometer. SAMPLING PROCEDURE Sampling was begun by three 3-man boatcrews at cross seCtion D just prior to the start of the injection of the fluorescent materials so that background samples could be obtained. These samples were used to check the bed material in the reach for naturally fluorescent materials which might be mistaken for the fluorescent tracer materials. Two men in each crew sampled while the third marked sample bags and assisted in emptying the samplers. With the exception of positions near the banks, sampling for approximately 30 seconds was sufficient to obtain 500- to BOO-gram samples. Small canvas bags were used for sample storage. Figure 13 is a photograph of the three boatcrews in the process of sampling at cross section D. In run 1, samples were collected at lateral positions 17, 23, 37, 43, 55, and 63 feet from the right bank. Unfortu- nately, no samples were obtained at position 30 until late in the experiment. Inspection of the samples indicated that the large red particles were moving toward the right bank; therefore, the crews were shifted toward the right bank, and samples were obtained at lateral positions 3, 7, and 12 feet from the right bank as well as at the other positions. The inspection of the samples also indicated that the tracer materials were moving through the study reach very rapidly; therefore, all three crews remained at cross section D for the entire experiment. After 5 hours, sampling was discontinued because inspection of the samples indicated that - essentially all the fluorescent material had passed through the study reach. In run 2, samples were collected at lateral positions 18, 24, 30, 36, 42, 48, 54, and 60 feet from the right bank at cross section D. Samples Were collected as rapidly as pos- sible for about 3 hours; then at the rate of three to four samples at each pOSition per hour for another 4 hours; EXPLANATION DEPTH, IN FEET 5 | l l SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS | | | l 5 20 30 40 50 60 7O DISTANCE FROM RIGHT BANK, IN FEET FIGURE l2.—Cross-section measurements obtained at 0815 hours. December 14-. 1966. then two samples at each position per hour for the next 3 hours; and, finally, hourly samples at each position for 4 FIGURE l3.—Three boatcrews “dustpan” sampling at cross section D. more hours. Major sampling was discontinued about 14 hours after injection of the fluorescent materials. In addition to the “dustpan” samples, a number of 6- inch core samples were obtained at various positions in the study reach about 22 hours after injection of the fluorescent materials. ANALYSIS OF THE SAMPLES Analysis of the samples consisted of sieving the sam- ples into the various size classes, counting the number of fluorescent particles of each color in each sieve class, and converting the number of fluorescent particles to concen- trations. The concentration of a fluorescent tracer is the ratio of the weight of tracer material in a given size range of the sample to the total weight of all material in that size range of the sample. All the samples were dried at room temperature. A \/§ series of 8-inch stainless steel sieves was used for the sieving, and samples were sieved on a Ro-Tap shaker for 10 minutes. After completing the sieving of each sample, the sieves were inspected under an ultraviolet light to insure that no fluorescent particles remained which might contaminate the next sample. The number of fluorescent particles of each color in each size class was determined by counting with the equipment shown in figure 14. The equipment consisted of an ultraviolet light source, a vibratory sand feeder, a FIGURE l4.-—Equipment used for determining the number of fluorescent particles in the samples. TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION variac for controlling the voltage to the sand feeder, and a hand tabulator for keeping a running count of the number of fluorescent particles of each color. The procedure consisted of placing a split of a size fraction in the sand feeder, adjusting the voltage on the variac to give the desired feed rate, and counting the fluorescent particles of each color as they fell from the end of the sand feeder into the glass dish. Sizes smaller than the 0.125 mm were not counted because of the difficulty of differentiating between actual fluorescent particles and chips or flakes of dye from the large fluorescent particles. A statistical analysis of the counting process (C. F. Nordin, Jr., written commun., 1968) has shown for tracer concentrations less than about 0.1 that the probability that the measured tracer concentration is between 0.9 and 1.1 of the true tracer concentration is 95 percent if about 400 tracer particles are counted. Thus, it was necessary only to count until 400 fluorescent particles were obtained and then weigh that part of the particular size split associated with the 400 fluorescent particles. If the size split contained large numbers of particles of several colors, then the counting process was continued until 400 fluorescent particles of the lesser of the pre- dominant colors in the size split were obtained. The entire size split was counted if the sample contained less than 400 fluorescent particles of any color. The numbers of fluorescent particles of each color in each size split were converted to concentrations with the numbers of fluorescent particles per gram of fluores- cent material. These numbers were determined for the different sieve classes of each fluorescent material. A specific number of fluorescent particles (usually 1,000) of a specific sieve class was counted and weighed. This counting and weighing process was continued until a subsequent measurement did not change the overall mean by more than 2.0 percent. The numbers of fluores- cent particles per gram of fluorescent material for the fluorescent materials used in runs 1 and 2 are given in table 6. TABLE 6.—Number5 of fluorescent particles per gram of fluorescent material for the sieve classes offluorescent tracer materials used in runs 1 and Z Particles per gram Sieve Clas’s Run 1 Run 2 (mm) Green Yellow Red Quartz Garnet Monazite Lead quartz quartz quartz 0.125v0.l77 128.000 .............................. 101,000 74,100 87,000 ............ 0177—0250 .. 45.800 33,200 38,800 13,600 0250—0350 15.800 12.600 7,520 4,910 0.350’0500 5,510 5,380 3,210 3250 0500—0707 2,540 2.760 .......... ... 0.7077100 1,170 ........... > 1.00 ........................................ 113 PRESENTATION AND DISCUSSION OF RESULTS The basic experimental data obtained in this study con- sisted of C(t), the fluorescent tracer concentration as a function of time from the “dustpan” samples obtained at the various lateral positions at cross section D; C' (t), the fluorescent tracer concentration as a function of time from the depth-integrated samples obtained at the weir; and the hydraulic and sediment-concentration measurements for the study reach at the time of the experiments. A large number of graphs of fluorescent tracer concen- tration as a function of time for the different sieve classes and specific gravities were obtained for the two runs (54 for run 1 and 105 for run 2). The C(t) data were obtained for all sieve classes of the quartz in run 1 and of the quartz, garnet, and monazite in run 2. None of the lead tracer particles in run 2 were found. The data for the 0.500- to 0.707-mm sieve class of monazite in run 2 were discarded because of the possibility of contamination from the large red quartz particles from run 1 that apparently were temporarily trapped along the right bank. Back- ground samples collected prior to the start of run 2 con- tained no fluorescent particles; however, samples ob- tained at lateral positions 18 and 24 feet about 4 hours after the start of run 2 contained some of the large red quartz particles from run 1. A small number of the graphs representative of all of the data of fluorescent tracer concentration as a function of time were selected to be included as examples. For run 1, one set of graphs of concentration as a function of time at lateral positions, 2, of 7, 17, 23, 37, 43, and 55 feet from the right bank for one sieve class of each of the three colors was selected. These sieve classes were the 0177—0250 mm for the green quartz, the 0350-0500 mm for the yellow quartz, and the 0.707-1.00 mm for the red quartz. The graphs are presented in figures 15, 16, and 17 for the green, yellow, and red quartz, respectively. For run 2, graphs of the concentration as a function of time at lateral positions, z, of 18, 24, 30, 36, 42, 48, and 54 feet for the 0.250- to 0.350-mm sieve class of quartz and the 0.177- to 0.250-mm sieve class of monazite were se- lected. These graphs are presented in figures 18 and 19. The concentrations plotted in figures 18 and 19 are rela- tive concentrations; that is, each concentration value has been divided by the total area under the curve of concen- tration as a function of time. The relative concentrations are given by C(t) _ C70) = x I C(t)dt (1) 114 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 1-5 I I I I I I 700 I I I | I I 2:7 ft 2:37 ft 1.0— _ 600— _ 2 - _ - _ < 0.5 500 a: 0 n: E 0 I I I I I I 400_ _ U) E 75 | | | | | I 300* _ ‘5 2:17 ft E § 50 _ 200— — X 0 . 100- — z 25» ~ 9 1'— ; - L I I I - I ,_ 0 Z 0 I I I I I 8 400 I I I I I I Z 8 250 I I I I I I 2:43“ 0: Lu 2:23 ft 300? ‘ U E 200— _ I- E 200» — 3 g, 150— — B'é O 100— — D d 100— _ 0 kAI I I I - 1 50- — 2.0 I I I I I I z=55ft ‘ .4 0 ‘ v Y ' I l o é—d | I | | 1300 1400 1500 1600 1700 1800 1900 2000 1300 1400 1500 1600 1700 1800 1900 2000 TIME. IN HOURS FIGURE 15.—Variation with time of the concentration of the 0.177- to 0.250-mm sieve class of green quartz at lateral positions of 7, 17, 23, 37, 4-3, and 55 feet; cross section D, run 1. TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 115 300i, #.V-__f7 ‘ ‘ I I 2500 I 1’ l l l l ‘ Z:7 ft 2:37 ft 200 “ ZOOOF I E 7 - E 100 0 1500» 1 E I o. 0 U) 3 2000“ I I I I 1000- P 0: <5 z=17 ft E "5 1500 - ‘ 500- ‘ X a L 2' 1000 , 1 c v; i r' - 4‘ ‘ -‘ 9 l; 100 l I I I I E E 500 _ ~ z=43 ft 2 O 75- “ O E 0 I | l ‘ O < E 4000 I . I I I . so» a '— 5 2:23 ft a 3000— ‘ a: 25— “ O 3 LL 2000 — A 0 I _ I I I | 1000 _ 1 2.0 I l I I I Z: 55 ft 0 v I I I 0 .x‘ I I L I_ 1300 1400 1500 1600 1700 1800 1900 2000 1300 1400 1500 1600 1700 1800 1900 2000 TIME, IN HOURS FIGURE 16.—Variation with time of the concentration of the 0.350- to 0.500-mm sieve class of yellow quartz at lateral positions of 7, 17, 23, 37, 4-3, and 55 feet; cross section D, run 1. I16 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 401000 I | I I I I 95,000 I I I I I 2:7 ft 2:23 ft 30,000 - _ 75.000 — _ 3 20,000 - "‘ 50,000 F _ K (D D: if 10.000 — _ m 25,000 — — 2 E 0 o I ~ . ‘4 . -I/' E 0 I L - I - I m’ 80,000 I I I I I I S X z=l7 ft 3000 I I I I I C _ I _ 9 70,000 2:37 f1: 2 9 2000 - — E ,1 60,000- - F- Z 1000 — - Lu 0 3 50,000- — O 0 I .I ; -I - - 4| Z I.IJ Q g 40,000- ' 2000 I I I I I ’— E 1500 ” 2:43 ft 8 30.000 - _ 1000 H 2 ‘53 500 — — 8 o 1 I I 4| : 20,000 — a 150 I I I I I 10,000 ' _ 100 I— 2:55 ft 4 50 i‘ 5 0 I l a I v I ' 0 I l I I 1300 1400 1500 1600 1700 1800 1900 2000 1300 1400 1500 1600 1700 1900 2000 FIGURE 17. — Variation with time of the concentration of the 0.707- to LOO-mm sieve class of red quartz at lateral positions of 7, 17, 23. 37, TIME, IN HOURS 43, and 55 feet; cross section D, run 1. TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION The quantity C(t) is the fluorescent tracer concentra- tion of a specific sieve class at a specific lateral position at time t. The quantity Cr(t) is the normalized, or rela- tive, concentration obtained by dividing C(t) by the total area under the concentration versus time curve. The nor- malization procedure indicated by equation 1 corrects for the differences in the quantities of the quartz and mona- zite injected and facilitates presenting the results for the two minerals on the same graphs. These particular sieve classes were chosen for presentation because they have approximately the same median fall diameters (0.289 mm for the quartz and 0.305 mm for the monazite; see table 1). Most of the results of this study depend upon the con- centrations of fluorescent tracer material in the “dustpan” samples. Concentration of fluorescent material in a sieve class of a sample is defined as the grams of fluorescent tracer per gram of total material in that sieve class. If the tracer particles of a specific sieve diameter behave exactly as the nontagged particles of the same diameter, then the efficiency of the “dustpan” sampler is not important. This should be true for the quartz tracer par- ticles if no significant shape differences exist between the tracer particles and the bed-material particles because the bed material is predominately quartz. The efficiency of the “dustpan” sampler is of concern, however, when minerals with a specific gravity different from that of quartz are used as tracers, as in run 2. Con- centrations for the garnet and monazite were expressed as the grams of garnet or monazite in the sieve class per gram of total material in that sieve class. The total material, however, was essentially all quartz; and because of the specific gravity difference between the minerals, the quartz associated with the garnet or monazite in a sieve class would have a smaller median fall diameter than the median fall diameter of the garnet or monazite. Therefore, if there were any washing of the sample during the sampling period or when the sampler was raised to the water surface, and if the effect of the washing were related to fall diameter, then the concentrations of the garnet and monazite would be affected. An analysis of the size distributions of various “dust- pan,” core, and depth-integrated samples obtained dur- ing the two runs suggested that washing of the fines from the “dustpan” samples may have occurred. On the other hand, the analysis suggested that, if washing did occur, the effect was essentially uniform with respect to time and position at cross section D. If the washing effect is uniform with respect to time and position at cross section D, then the results should not be affected significantly be- cause the data analysis involves ratios of concentration integrals. Details of the analysis of the washing effect are presented in appendix A. The experimental data from the two runs were used to determine (a) the lateral-dispersion characteristics of the 117 tracer materials between the injection point and cross section D; (b) the feasibility of applying the fluorescent tracer technique to sediment-transport-rate determina- tions; (c) the velocities of the centroids of the tracer ma- terials between the injection point and cross section D; and (d) the longitudinal-dispersion characteristics of the tracer materials between the injection point and cross section D. Each of these items is discussed in detail in the following sections. LATERAL-DISPERSION CHARACTERISTICS OF THE TRACER MATERIALS The lateral-dispersion coefficient, Kg, can be calcu- lated from the rate of change of the variance of the lateral distribution of the tracer material with distance down- stream (Sayre and Chang, 1968). In the fluorescent tracer experiments, however, meaningful data were obtained only at cross section D because of the rapid rate at which the tracer material moved through the study reach. There- fore, a true lateral dispersion coefficient could not be calculated. However, the variance, 0'5, of the area under the curves of fluorescent tracer concentration as a func- tion of time versus lateral position at cross section D can be used as a measure of lateral dispersion between the injection point and cross section D. For a valid compari- son, this procedure assumes that the initial period re- quired for the establishment of the linear variation of the variance with distance is the same for all size classes and specific gravities of tracer materials. The lateral distributions of the fluorescent tracer mate- rials at cross section D were represented by plots of the areas under the curves of concentration versus time as a function of lateral position, z, in the cross section—that is, A(z) versus 2, where A(z) =fx C(t)dt. The A(z) data 0 were normalized by dividing by the area under the A(z) B versus 2 curves, or] A(z)dz where B is the channel 0 width. Normalization facilitated the comparison of the lateral distributions for the different sieve classes and specific gravities of tracer materials. The graphs of the normalized, or relative, area, Ar(z) , as a function of: for the various sieve classes of fluorescent materials used in run 1 are presented in figure 20; and the graphs of Ar(z) versus z for the different sieve classes of quartz, garnet, and monazite tracers used in run 2 are presented in figures 21, 22, and 23, respectively. Figures 20 through 23 show, in effect, the relative amounts of each fluorescent tracer that passed through each sampling position at cross section D during the runs, if it is assumed that the sedi- ment-transport rate was constant during the run. SEDIMENT TRANSPORT [N ALLUVIAL CHANNELS 24ft Z 1800 2000 2200 2400 TIME, IN HOURS 1 600 0.6 118 N N O D e _.II M sz 22 Ana Ana an Nam Nuo m AQM MOM m m.- POI X X E E _ . _ _ _ _ 0m 4 3 2. 1 1 M M. M 0. 0 0 0 210 .ZO_.r_.r<4w~_ FIGURE 18.—Variation with time of the relative concentrations of the 0.250- to 0.350-mm sieve class of quartz and TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION RELATIVE FLUORESCENT TRACER CONCENTRATION, C,(r) 1.50 | | I I I I z=30fl ‘ EXPLANKHON o Quartz 1'25 h I Monazite 1.00 1 _ "I ’,,’ \ I 1.50 I I I I I F 2: 36 ft EXPLANATION o Quartz 1.25 — , _ ' l MonaZIte 1.00 '0 ' I 075 I 050 _ 025 _ \ /'\\ .\ ‘I~ 0 1000 1200 1400 1600 1800 TIME, IN HOURS 2200 the 0.177- to 0.250~mm sieve class of monazite at lateral positions of Z: 18, 24, 30, and 36 feet; cross section D, run 2. 405-770 0L - 71 - 4 2400 119 120' SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 2.50 I I I I I I z=42 ft 0 EXPLANATION O Quartz 2.00 - - l Monazite 1.50 — E 1.00 0.50 EXPLANATION 2'50 o Quartz I Monazite 2.00 RELATIVE FLUORESCENT TRACER CONCENTRATION, CrU) E====--h----I-—————_l" 1.00 0.50 _._3 . l 000 l 200 1400 1600 1800 2000 2200 2400 TIME, IN HOURS FIGURE l9.—Variation with time of the relative concentrations of the 0.250- to 0.350-mm sieve Class of quartz and the 0.177- to 0.250-mm sieve class of monazite at lateral positions of 2:42, 4-8, and 54 feet; cross section D, run 2. TRANSPORTAND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION I21 4.00 ‘ I | I I I 3 : EXPLANATION C I 0 Quartz Z“ I 9 I Monazite I- 3.00JI < I a: | ,_ Z I “J | 0 I Z 0 I o | I: I I6 I < 2.001 a: I I- l I- I Z | Lu 0 I (I) I I“ | n: O I 3 I -1 | L 1.00 Lu 2 I— < I —J | l“ I a: | | | o I. - 1000 1200 1400 1600 The variance of the lateral distribution at cross section D, 0-3, is given by LB zzA(z)dz .2 L8A(z)dz —z , (2) 0%: where z is the lateral position measured from the right bank of the channel, B is the channel width, A(z) is the area under the curve of concentration versus time at lateral position 2 and is given by , (3) 2:2 A(z)=f:C(t)dt and 2 is the mean lateral position of the distribution, defined as 2:]: zA(z)dz. (4) I: A (2)012 The integrals in equations 2 and 4 were determined by measuring with a planimeter the areas under the appro- 2354 ft 1800 TIME, IN HOURS priate curves. The A(z) values at the ends of the distri- bution were assumed to be zero at lateral positions displaced toward the banks from the outside sampling positions a distance equal to one-half of the interval over which the outside sampling position was assumed to apply. The distributions presented in figures 20 through 23 suggest that this assumption is valid, except perhaps for the red quartz particles in run 1. Because of the tendency for the large particles to move toward the right bank, the areas for the red quartz at Z: 7 feet were large. However, an insulficient number of samples was obtained at positions between z=7 feet and the right bank, and thus it was necessary to assume that these areas de- creased linearly from the values at z=7 feet to zero at z=2 feet. The mean lateral position values, 2, and the variances, 03, of the lateral distributions at cross section D are sum- marized in tables 7 and 8 for runs 1 and 2, respectively. The mean lateral position values are plotted as a function of the median fall diameters of the sieve classes in fig- ures 24 and 25 for runs 1 and 2, respectively. The vari- ances, 0%, are plotted as a function of the median fall diameters of the sieve classes in figures 26 and 27 for runs 1 and 2, respectively. The numbers next to each point indicate the sieve—class numbers given in tables 7 and 8. I22 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 0.08 0.06 - 0.04 - 0.02 b I I | I I EXPLANATION Red quartz (mm) I o 0.500—0.707 A O.707—1.00 I >1.00 0.08 0.06 RELATIVE AREA, A, (z) 0.02 0.04 - I I EXPLANATION Yellow quartz (mm) [A 0 0250-0350 /- ‘\_ IR A 0350-0500 /' /‘ \ I 0500-0707 .___ 0.08 0.06 0.04 0.02 I r EXPLANATION Green quartz (mm) A c 0125—0177 - /'A\ A 0177-0250 // \I, I 0250-0350 DISTANCE FROM RIGHT BANK (I), IN FEET FIGURE 20.—Variation of the area under the curve of concentration versus time with lateral position, z, at cross section D for the different sieve classes of the three colors of quartz tracer, run 1. 123 TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 0-100 I I I | I II 1" \ EXPLANATION I; I\\_ Quartz [i \ . (mm) ,7 0.075— 0 0350-0500 'i I- A 0500—0707 I, I 0.707—100 i I' 0.050» {I 0.025— 3 K Y. o——————I———F-*:' < DJ E < E F 0.100 I | | I 1 I I 5 .I. E .I \. EXPLANATION I! ‘\ Quartz I '\ ”W i I (1075‘ O 0.125-0.177 l' -\ A i 'I A 0177—0250 . \ . ./ I, \k I 0250—0350 .’ ,’ \‘x I , \ \ I o.oso~ _ 0.025» _ 0| I o 10 7o DISTANCE FROM RIGHT BANK (2). IN FEET FIGURE 21. — Variation of the area under the curve of concentration versus time with lateral position, 2, at cross section D for the different sieve classes of quartz tracer, run 2. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 124 0.150 1 I . r . EXPLANATION Garnet 0125— (mm) fi ~ 0 0350—0500 In I A 0500-0707 1' l I I I \ 0.100— 'I \‘ I I I I I I I 0.075— I I I I I I I I 0050— l I I I 3 I K I Y» 0025~ I < ' I u] I: I < N > ; < d I m 0 0.100 | I I I I I EXPLANATION 7K. Garnet . \. 0.075% (mm) _/ ‘fi — 0 0125—0177 I / .\ i ll \\ A 0177—0250 i ll \_ i \. I 0250-0350 i I] 0.050 . 0.025 0 DISTANCE FROM RIGHT BANK (2), IN FEET FIGURE 22.—Variati0n of the area under the curve of concentration versus time with lateral position, 2, at cross section D for the different sieve classes of garnet tracer, run 2. TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION I25 0.125 I I I EXPLANATION Monazite (mm) 0.100— C 0250-0350 _ A 0350—0500 0.075 - _ 0.050 I- _ ’3 ‘1 << <- 0.025 '- _ m n: ‘1 Lu 2 I- < _l L|J I m m 0 l ' I 0.075 T T I I I I *\ // \ / \ / \ EXPLANATION ll Monazite I, 0.050— (mm) / ' . 0.125—0.177 // A 0177—0250 0.025— _ 0 i 4 O 10 20 30 40 50 60 70 DISTANCE FROM RIGHT BANK (2), IN FEET FIGURE 23.—Variati0n of the area under the curve of concentration versus time with lateral position, 1., at cross section D for the different sieve classes of monazite tracer, run 2. 126 The vertical dashed lines in figures 24 to 27 represent the size limits of the sieve classes used in the analysis of the samples. In several instances, the median fall diam- eters for some sieve classes of tracer material are smaller than the lower size limit of the sieve class. As discussed previously, shape effects probably contributed to this anomaly. The photomicrographs of the fluorescent ma- terials used in run 1 (see fig. 8) indicate that this material was angular and thus had a shape factor less than the 0.7 usually attributed to naturally worn quartz particles. The median fall diameters for the different sieve classes of garnet and monazite are in general displaced to the next larger sieve class because of the effect of specific gravity. TABLE 7.—Summary of the 2 and a": values for the lateral distributions at cross section D, run I Color of Sieve class 2’ a: quartz (mm) (ft) (fig) Green (1) 0.125—0.177 33.7 69.8 (2) 0.177—0.250 34.4 63.1 (3) 0.250—0.350 33.2 62.7 Yellow (3) 0250—0350 26.7 82.3 (4) 0350—0500 22.7 61.0 (5) 0.500—0.707 18.7 34.2 Red (5) 0500—0707 19.0 33.2 (6) 0.707—1.00 17.9 50.5 (7) > 1.00 16.5 71.4 TABLE 8.—Summary of the i and a: values for the lateral distributions at cross section D, run 2 Mineral Sieve Class i 042 (mm) (f1) (fl?) Quartz (1) 0.125-0.177 45.1 78.6 (2) 0.177-0.250 44.2 38.7 (3) 0250-0350 40.3 36.6 (4) 0350-0500 37.9 26.9 (5) O.500-0.707 37.0 17.9 (6) 0.707-1.00 37.8 14.4 Garnet (1) 0.125-0.177 40.1 32.9 (2) 0177—0250 36.7 26.2 (3) 0250-0350 33.0 14.5 (4) 0350-0500 31.7 12.5 (5) 0500—0707 31.4 14.4 Monazite (1) 0.125—0.177 39.9 44.6 (2) 0.177-0.250 35.9 30.7 (3) 0.250—0.350 33.4 25.0 (4) 0350—0500 31.9 25.3 The mean lateral positions and the variances for the dye-dispersion test were calculated from summation approximations of equations 4 and 2, respectively. These approximations are BzC(z)Az Mn NI II N N (5) ll N we C(z)Az N H c SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS and (6) The approximations were assumed valid for the dye- dispersion test because samples were obtained every 2 feet across the channel width. The results of the dye-dispersion test are summarized in table 9. The variances at the different cross sections were corrected for the effect of width by the method of Fischer (1967), and the corrected variances are given in table 9. A plot of the variance as afunction of longitudinal distance from the source suggested that the second meas- urement, 0(2), at cross section D was the more correct of the two. The 0(2) values of Z and (I? for the dye-dis- persion test are shown near the ordinates of figures 24 and 26, respectively. TABLE 9,—Summary of the E, of, and 0'," (corrected) values for the dye-dispersion test Cross Width 2 a'z' tr? (corrected) section (ft) (ft) (fig) ((12 A 73.5 26.8 7.88 7.74 B 70 22.6 19.5 21.2 C 69 30.7 32.8 36.5 0(1) 79 35.2 103 87.7 D(2) 79 34.2 68.5 58.4 The mean lateral positions for the quartz tracer par- ticles ranged from 34.4 feet from the right bank for the 0.177- to 0.250-mm sieve class of green quartz to 16.5 feet for the > LOO—mm sieve class of red quartz in run 1 and from 45.1 feet from the right bank for the 0.125- to 0.177-mm sieve class to 37.0 feet for the 0.500- to 0.707-mm sieve class of quartz tracer in run 2. The tend- ency for the large tracer particles to move toward the right bank is evident from the results presented in figures 24 and 25. The difference in the magnitude of the effect for runs 1 and 2 may be attributed to the fact that the in- jection point for run 2 was moved 7 feet to the left- of the channel centerline after the behavior of the tracer par- ticles in run 1 was observed. There was little difference in the 2' values of the garnet and monazite for particles of comparable fall diameter. However, the garnet and mona- zite 2 values were displaced 2 to 6 feet toward the right bank from the 2 values for quartz particles of comparable fall diameter. A\ possible explanation for the movement of the large particles toward the right bank may be based on a consideration of the cross-section measurements obtained prior to the start of run 2. (See figs. 12 and 6.) The thalweg, or line of maximum depth, shifted from approximately TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 70 | | I I I | I | l I I Leflt bank at 79 ft I I I I I , I I | I I I E I I I I I I a so— I I I I I I ' I- I I I I ‘ I I I I I I I??? g I I I I I | of E 50 _ I I I I I iIndIcate_I O I I I I I | SIeve E I | I I I | class ,_ fll)—’I*-(2)—>I‘—(3)—-I-—(4)—-I*-(5)—-I<—(6)—>I I“ | | I “i“ 40' I I I I I I ~ I z | I I _ | (2) I I A e—Dye (1) I (3) I | Is I °’I’°\0I I I I z _ | I | I 9 30 I I I(3) I I I I I- | I - I I g I I I (4) I I I I | I 4 20- I I I I <5) IIS) 5 I — g I I I I I ( ) I <7) I I g EXIPLANATION I I I I I z 10_ I Quartz I | I I _ fi I 0 Green I I I I 2 I | | | I A Yellow I I I I I I Red | | I | 0 | | l | I I I I I I I 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0 MEDIAN FALL DIAMETER, IN MILLIMETERS FIGURE 24.-Variation with fall diameter of the mean lateral positions of the tracer distributions at cross section D, run 1. Numbers in parentheses are sieve class numbers; see tables 7 and 8. the centerline at the injection point to the right bank at cross section A and then back to the left bank at cross section D; the maximum depth was greatest at cross sec- tion A. The results of the fluorescent tracer experiments suggest that the large tracer particles, particularly in run 1, tended to follow the thalweg from the injection point to the right bank and then to move down the reach along the bank. Figures 26 and 27 show a distinct difference in the variation of 0% with fall diameter for the large quartz tracer particles in runs 1 and 2, and there are at least two factors that contribute to this difference. These factors are the movement of the red quartz particles toward the right bank and the indication that some of these particles were trapped temporarily along the right bank. The lateral distributions for the three sieve classes of red quartz, and in particular the > LOO-mm sieve class, are skewed toward the right bank (fig. 20). Temporary entrapment of some of the red quartz was indicated by the appearance of red quartz particles in samples obtained during the middle part of run 2 for positions near the right bank at cross section D, even though background samples obtained at cross section D prior to the start of run 2 indicated that all of the fluorescent material used in run 1 had passed through the study reach. Both of these 127 factors, the temporary entrapment and the displacement toward the right bank region where water velocities were less than the mean water velocity, would tend to increase 02 over the values that might be expected if the red quartz particles had moved down the center of the channel without interference. 70 I I | I | I l I I I I Leftlbank at 7'9 ft I I I I I I l I k—Size—fi I I l | I limit of I I I I | IindicatedI | x 60‘ I I I sieve | I - (2‘ I I I I class I I E I<—(1)—>I<—(2)—+I+—| (oak—I (4)-—>I<—(5)—>I<—I <6>—> I I g I I I I I I — I I I I | I ”‘ I I I I I I ' 5 I o I (1) I I I I D: I (2’ I I I I t I I I I I I I E 40. I | | I I | _ LI. I | l I 6) z I I I I‘\\. I ’. I I I kit- (3') I '3 I I I (2’ I\;;*I~-- \ (4) E 30— I I I I (3) 77:3— 5 ,: I I I I I ( I) a I I I I I I l I I | I I I .I I | I I I I < I I I I I I 5 20, I I I I I I - I- | I | I | < I I I I I '1 I I I | I I g EIXPLANATION I I I I E 10_ I O Quartz I I I | _ | A Garnet I I I I I l Monazite I I I I I I I I I I I I I I I I 0 I 1 I I l | I | I | I 0.1 0.2 0.3 0.4 0.5 0,6 0.8 1.0 MEDIAN FALL DIAMETER, IN MILLIMETERS FIGURE 25. —Variation with fall diameter of the mean lateral positions of the tracer distributions at cross section D, run 2. Numbers in paren- theses are sieve class numbers; see tables 7 and 8. The 02 values for the three sieve classes of green quartz in run 1 were approximately the same as the 0% value for the dye cloud in the dye-dispersion test. The 0% value for the 0.250- to 0.350-mm sieve class of yellow quartz exceeded the 0% value for the dye; however, the difference was small. The 0% values for garnet in general were less than the 0% values for quartz particles of comparable fall diameter. The 0% values for monazite, however, fall in line with the quartz values, with the exception of the value for the 0.350- to 0.500-mm sieve class of monazite. Thus, the lateral dispersion of the heavy minerals as represented by the variance of the lateral distribution at cross section D generally decreases with increasing particle diameter, as it does for the quartz, with the exception, however, I28 100 | I T 90 I I a 80 - I I _ I (1) | 70 2—0er k |(2) (3 ‘ 60 — | I « I I | 50 c - IL---Size—)l I limit I 40 — | of , _ indicated | sieve I | class I 30 - I I - I I | I I<—(1)—>I<—<2) +<3>—-I<—(4) —‘I‘—(5)—-I‘—(6) —- VARIANCE («5), IN SQUARE FEET I I . I I I - | EXPLANATI O N I I I I I I Quartz I | | | I 0 Green I I I I I A Yellow | I I I | | l Red | I | | 10 | l I I l I I I L I | 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0 MEDIAN FALL DIAMETER, IN MILLIMETERS FIGURE 26.-Variati0n with fall diameter of the variances of the lateral distributions of the tracer masses at cross section D, run 1. Number in parentheses are sieve class numbers; see tables 7 and 8. 100 I T I I I I I I I I I 90— k—(l)—+—(2>—,I<—(3I—>I<—(4)—»I~—(5)—>I<—(6)a 80— I (1’ I I I I I ~ 70- I L—Size—JI I I I I limit of I I I I _ indicated | I I_ 60 I I . I I In I Sleve I I I I u I I I L“ 50* I I I I I I - LIJ K I I I I I I < . 3 40— I I \_ I I I _ o I I I I I ‘0 I I I I I I z I I I I I I '1 30— I I Is _ I I a A I . I” I I I I . ) jg) V I I I I w— ----- 8 EXPLANATION I I l 12‘ 20— I 0 Quartz I \I I _ § I A Garnet I I\ I I > I . M -t I |\\ I I I °”?z' e I I If: I <6) I I I I I I I I ‘4 (4)/(5) I I I I I‘Y I I I I I I I I I I I 10 I I 1 | l I I | I l I 0.1 0.2 0.3 0.4 0.5 0.6 08 10 MEDIAN FALL DIAMETER, IN MILLIMETERS FIGURE 27.—Variation with fall diameter of the variances of the lateral distributions of the tracer masses at cross section D, run 2. Numbers in parentheses are sieve class numbers; see tables 7 and 8. that there is a slight increase in the variance for the large sizes of garnet and monazite. The results of the two fluorescent tracer experiments suggest that at least two factors may be important in SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS causing lateral mixing of sediment particles. These are the turbulence in the flow and the thalweg. In run 1, the injection point apparently was on the thalweg and the large particles tended to follow the thalweg to the right bank whereas the small particles were mixed in the lateral direction to about the same extent as the dye cloud. Thus, in run 1 the lateral mixing of the small particles was caused primarily by the turbulence in the flow, and the lateral mixing of the coarse particles was caused primarily by the thalweg. Particles with a fall diameter of about 0.5 mm were affected least by the two factors. (See fig. 26.) In run 2, the shift of the injection point apparently was sufficient to remove the fluorescent tracers from most of the influence of the thalweg and lateral mixing as indi- cated by 03 decreased with increasing fall diameter. The large and heavy particles mixed the least because they spent a greater proportion of the time resting on or rolling along the bed surface than did the small particles. APPLICATION OF FLUORESCENT TRACERS TO THE MEAS- UREMENT OF THE SEDIMENT-TRANSPORT RATE The use of fluorescent tracers for the determination of the sediment-transport rate assumes that the tracer par- ticles and the natural sediment particles behave identi- cally. Also, the quantity of tracer material injected must be small in comparison with the natural sediment-trans- port rate. Sediment-transport rate as used in this report refers to the rate of movement of the channel bed material and includes the suspended bed-material load and the bedload but does not include the fine material or “wash load.” “DUSTPAN” SAMPLES AT CROSS SECTION D The time-integration method was used to calculate the sediment-transport rate from the fluorescent tracer con- centrations of the “dustpan” samples obtained at cross section D. The time-integration equation is based on the conservation of the tracer material as expressed by W=LB I: gm, Z)C(t, 2) dt dz, (7) where W is the weight of tracer material injected, qx is the sediment-transport rate per unit of channel width, C is the fluorescent tracer concentration, and B is the channel width. The quantities qs and C are functions of lateral posi- tion, z, and time, t. If (1;, the sediment-transport rate, is steady, it is independent of time, and equation 7 becomes W=IIB q,(z) I)” ’60, 2) dt dz. (8) Because samples were obtained at various positions across the channel at cross section D throughout the pas- TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION sage of the tracer mass, the variation of the quantity ac I C(t) dt with 2 was determined. However, it is neces- 0 sary also to know how q3 varies with 2. It was assumed that (9) where qs(z) is the unit sediment-transport rate at z, (is is the mean unit sediment-transport rate for the cross sec- tion, and w(z) is the weighting factor at z. Substitution of equation 9 into equation 8 yields, after rearrangement, q =__W__ LB w(z)A(z) dz q_,(z) = (MIR), 9 (10) where A (z) is defined by equation 3. In general, the over- all size distribution of the bed material in transport will not match exactly the size distribution of the tracer ma- terial. Therefore, equation 10 must be applied to each size class and the results summed to obtain the total sediment-transport rate. The weighting factors were determined from a set of depth-integrated samples ob- tained at the weir. Details of the procedure are given in appendix B. The mean unit sediment-transport rates, (is, for the various sieve classes of quartz tracer were calculated from equation 10. The denominators of equation 10 were determined by plotting the product w(z)A(z) as a func- tion of z and measuring the areas under the curves with a planimeter. These (78 values were converted to the total sediment-transport rates, 08, by multiplying by the channel width at cross section D. The Q, values for the various sieve classes calculated from the fluorescent tracer concentrations of the “dustpan” samples at cross section D are summarized in tables 10 and 11 for runs 1 and 2, respectively. The measured Qs values determined from the depth-integrated samples obtained at the weir are presented also in tables 10 and 11. The calcula- tions of the sediment—transport rates were limited to sieve sizes larger than 0.125 mm. For sizes smaller than 0.125 mm, it was difficult to distinguish between chips of dye from large particles and actual fluorescent particles. TABLE 10.-—Summary of the calculation of the sediment-transport rate, “dustpan” samples at cross section D, run 1 Color of Sieve class 0. (calculated) 0.. (measured) 0: (calculated) quartz (mm) (tons per day) (tons per day) 05 (measured) Green 0 125—0.]77 2,109 1,515 1.39 0 177-0.250 2,336 1.191 1.96 0 25041350 1,670 922 1.81 Yellow 0250—0350 1,277 922 1.38 0.350~0.500 323 357 .88 0500—0707 55 33 1.67 Red 0.500—0.707 39 33 1.18 0.707'1.00 l6 0 ........................... > 1.00 14- 0 ........................... Total (maximum) ............. 6.523 4.018 1.62 (minimum) .............. 6,114- 4.018 1.52 129 TABLE ll.—Summary of the calculation of the sediment-transport rate, “dustpan” samples at cross section D, run 2 Quartz sieve class 0, (calculated) 0, (measured) Ox (calculated) (mm) (tons per day) (tons per day) 0, (measured) 0125-0177 859 1,194- 0.72 0.177-0.250 1,724- 937 1.84- 0.250-0.350 747 713 1.05 0350-0500 118 203 .58 0.500-0.707 36 25 1.44 0.707-1.00 6.9 0 ........................ Total ...... 3,491 3.072 1.14 1n run 1, two calculations of the sediment-transport rate were possible because of the overlap of the green and yellow 0.250- to 0.350-mm sieve classes and the yellow and red 0500- to 0.707-mm sieve classes. The maximum value given in table 10 was obtained by using the 0.250- to 0.350-mm sieve class of green quartz and the 0.500- to 0.707-mm sieve class of yellow quartz as tracers for the 0.250- to 0.350-mm and 0.500- to 0.707-mm sieve classes of bed material, respectively. The minimum value was obtained by using the 0.250- to 0.350-mm sieve class of yellow quartz and the 0.500- to 0.707-mm sieve class of red quartz as tracers for the 0.250- to 0.350-mm and 0.500- to 0.707-mm sieve classes of bed material, respec- tively. The maximum value was about 6.7 percent larger than the minimum value. The maximum and minimum calculated sediment- transport rates are 62 and 52 percent larger than the sediment-transport rate measured at the weir. The ratios of the calculated sediment-transport rates to the measured sediment-transport rates for the various sieve classes are included in table 10 and each ratio is greater than 1.0 for all size classes with the exception of the 0.350- to 0.500-mm sieve class of yellow quartz. Several factors could contribute to the fact that the calculated sediment—transport rates were almost all larger than the measured sediment-transport rates. Probably the key factor is the assumption inherent in equation 10 that all of the fluorescent tracer material injected is sampled as it passes through the measurement section. However, sampling at any cross section must be limited to a reasonable number of points with linear interpolation assumed valid between the points. A large quantity of fluorescent material could pass unsampled between two sampling positions or could pass through a sampling position while samples were being obtained at another position. These problems would be most impor- tant for high-velocity flows where the fluorescent material is moving very rapidly. In addition, a quantity of the fluorescent material may be trapped within the study reach temporarily, or sampling may be terminated before the fluorescent tracer material has passed completely through a study reach. All these factors would result in 130 low values of the areas, A(z), under the concentration as a function of time curves and, hence, high values for the calculated sediment-transport rates. In run 1 the failure to sample at 2:30 feet may have caused some reduction of the areas under the A(z) as a function of 2 curves. In the absence of data at z= 30 feet, the areas were assumed to vary linearly with z between 2:23 feet and 2:37 feet. A consideration of figure 20 suggests that the areas at 2:30 feet could be larger than these interpolated values without resulting in unusual A(z) versus 2 relations. However, it is believed that these possible errors in the areas would not be large enough to account for all of the difference between the calculated and measured sediment-transport rates in run 1. An additional factor that must be considered is the accuracy of the sediment-transport rates as measured at the weir. The basis of the weir operation is that all the sediment is suspended by the action of the baffles as the sediment passes over the weir and the sampler nozzle traverses the entire depth of flow at the weir crest. It is essential that all of the sediment be suspended and that the suspended sediment be sampled accurately. Errors in the sediment concentrations determined from the depth-integrated samples may occur if the intake velocity of the sampler differs significantly from the stream velocity. If the transit rate is too slow, overfilled sample bottles will result and the samples must be discarded. If the transit rate is too rapid, then the intake velocities are less than the stream velocities and the measured sediment concentrations are greater than the true sedi- ment concentrations. The effect of an incorrect intake velocity increases With particle diameter (US. Inter- Agency Committee on Water Resources, 1941, fig. 14) and is very important for particles in the sand-size range. In run 2, the calculated sediment-transport rate was about 14 percent larger than the measured rate. The good agreement, however, was fortuitous, as is shown by the ratios of the calculated to the measured sediment- transport rates given in table 11. Two of the ratios were less than 1.0, and this negative deviation balanced the positive deviations for the other three sieve classes. There are no apparent reasons why the ratios for the 0.125- to 0.177-mm and 0.350- to 0.500-mm sieve classes should be less than 1.0. However, when the ratio of the measured sediment-transport rate for run 1 to the meas- ured rate for run 2 was calculated for the different sieve classes, it was found that the ratio values were between 1.27 and 1.32 with the exception of the ratio for the 0.350- to 0.500-mm sieve class. This ratio was 1.76 and the large difference for the 0.350- to 0.500-mm sieve class suggests the possibility of an error in the measured sedi- ment-transport rates for this sieve class. Also note that the SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS QS (calculated)/Qs (measured) ratio for this sieve class was less than 1.0 in both runs. The mean deviations, regardless of sign, of the calcu- lated sediment-transport rates from the measured sedi- ment-transport rates for the different sieve classes were 51 and 41 percent for runs 1 and 2, respectively. DEPTH-INTEGRATED SAMPLES AT THE WEIR The calculation of the sediment-transport rate from the fluorescent tracer concentrations of the depth- integrated samples required a slightly different pro- cedure than was used for the “dustpan” samples from cross section D. Because the amount of sand in the depth- integrated samples was small and, consequently, be- cause the number of fluorescent particles in each size split would have been very small, the depth-integrated samples generally were not sieved into size classes. Because the samples were not sieved, only the total number of fluorescent particles of each color was ob- tained for each sample. The concentration of fluorescent material for these samples, therefore, was defined as the number of particles of a specific color per gram of sedi- ment in the sample. Generally the 14 samples obtained across the weir for each sample time were composited to give one sample for that particular time. In addition to requiring the modification of the defini- tion of fluorescent tracer concentration, the small size of the depth-integrated samples necessitated two as- sumptions. First, it was assumed that the fluorescent particles were sampled at the weir in the same proportion as that at which the particles were injected. Second, it was assumed that the sieve-size distribution of the depth- integrated samples at the weir did not change with time during the run. With these assumptions, it may be shown that the equation for the calculation of the sediment-transport rate of size class i from the concentrations of fluorescent tracers in the depth-integrated samples has the form =Npi AI» QSi (1 1) where 1:]: C’ (t)dt. (12) Equation 11 is similar in form to equation 10 but has the following differences. First, the weight of fluorescent tracer injected, W, has been replaced by N, the number of fluorescent particles of a specific color injected, and pi is the fraction of the total weight of sediment in the sample that is in size class i. Second, A(z) has been re- placed by A’, which was accomplished by replacing in equation 3 the concentration, C, as grams of fluorescent tracer per gram of sediment by C’, the concentration as TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION number of fluorescent particles per gram of sediment. Third, the integration across the channel width has been accomplished by the averaging effect of compositing a set of samples taken across the weir; hence the trans- port rate, 031-, is the total transport rate for size class i for the cross section, and the concentration is a mean concentration, indicated by the overbar, for the cross section. Details of the development of equation 11 and a discussion of the two assumptions are presented in appendix C. The variation with time of C" for the three colors of quartz used in run 1 and the quartz, garnet, and monazite tracers used in run 2 are presented in figures 28 and 29, respectively. The concentrations plotted in figures 28 and 29 are relative concentrations, 510); that is, each concentration for a given color or specific gravity has been divided by the area under the curve A’. Thus, C10) is equal to C—’ (t)/A' where A' is defined by equation 12. The sediment-transport rates for the different sieve classes of fluorescent quartz were calculated from equa- tion 11, and the results are summarized in tables 12 and 13 for runs 1 and 2, respectively. The N values were determined from the quantities of fluorescent materials injected (table 2) and the numbers of fluorescent particles per gram of fluorescent material (table 6). The pi values were determined from the sieve-size distributions for the TABLE l2.—Summary of the calculation of the sediment-transport rate, depth-integrated samples at the weir, run 1 Color of quartz Sieve class 0, (calculated) 0,. (measured) (mm) (tons per day) (tons per day) Green 0.125‘0. 177 2,403 1,515 0.177W0.250 1,889 1,191 0250—0350 1,463 922 Yellow 0250—0350 4-51 922 0350—0500 174- 357 0.500—0.707 16 33 Red 0500—0707 3 33 0.707—100 0 0 > 1.00 0 0 Total (maximum) ............... 5,945 4,018 (minimum) ............... 4,920 ........................ TABLE 13.—Summary 0f the calculation of the sediment- transport rate, depth-integrated samples at the weir, run 2 Quartz 0.. (calculated) 0x (measured) sieve class (tons per day) (tons per day) (mm) 0.088-0.125 ....... 890 1,013 0.125-0.177 ....... 1,050 1,194- 0177-0250 ....... 824- 937 0250-0350 ....... 627 713 0350-0500 ....... 178 203 0500—0707 ....... 22 25 0.707—1.00 ........ 0 0 Total ............... 3,591 4.085 I31 depth-integrated samples (fig. 41). The A’ values were determined for each color of fluorescent quartz tracer by plotting C" as a function of time and measuring the area under the curve with a planimeter (figs. 28 and 29). In run 1, only the three sieve classes of each of the three colors contributed a significant number of fluorescent particles to the total number of particles of each color injected. As with the calculation of the sediment-transport rate from the “dustpan” sample concentrations, two answers were possible because of the overlap of the green and yellow 0.250- to 0.350-mm sieve classes and the yellow and red 0500- to 0.707-mm sieve classes. The maximum of the two calculated results is about 48 percent larger, and the minimum is about 22 percent larger, than the sediment-transport rate measured at the weir. The big difference between the two calculated values is caused by the large difference between the sediment-transport rates predicted for the 0.250- to 0.350—mm sieve class of green quartz and the 0.250- to 0.350-mm sieve class of yellow quartz. There is some basis for selecting the minimum of the two results as the more accurate. The results presented in table I show that the median fall diameter of the 0.250- to 0.350-mm sieve class of the yellow quartz was essen- tially identical with that of the natural bed material, whereas the median diameter of the 0.250 to 0.350-mm sieve class of the green quartz was about 17 percent small- er. This suggests that the 0.250- to 0.350-mm sieve class of the yellow quartz is the better of the two “tracers” for the 0.250- to 0.350-mm sieve class of the natural bed material. Large differences exist among the median fall diameters for the 0.500- to 0.707-mm sieve classes of yellow and red quartz and the natural bed material. Of the yellow and red quartz fall diameters, the red quartz median fall diameter is nearest to the median fall diam- eter of the natural bed material. The contribution of this sieve class to the total sediment-transport rate is less than 1 percent, however. In run 2, the 0.088- to 0.125-mm sieve class contributed almost 6 percent of the total number of quartz tracer particles injected. Therefore, it was necessary to con- sider this sieve class in addition to the six sieve classes that were considered in the analysis of the “dustpan” samples. The problem of differentiating between the small particles and chips or flakes of dye from the large particles could not be eliminated but was reduced as much as possible by careful counting of the fluorescent particles in the depth-integrated samples. The calcu- lated sediment-transport rate for particles larger than 0.088 mm was about 12 percent smaller than the sedi- ment-transport rate measured at the weir. Because of the two assumptions necessary in the analysis of the fluorescent tracer concentrations of the I32 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 6.00 I T , u . v r Red quartz 4.00 — - 2.00 > _ (I) O I / r 6.00 v . , , y i . Yellow quartz 4.00 e _ 2.00 - _ RELATIVE MEAN FLUORESCENT TRACER CONCENTRATIONE Green quartz 4‘00 » 1 2.00 — ‘ r i O f 1 - _ v 1300 1400 1500 1600 1700 1800 1900 2000 TIM E, IN HOU RS FIGURE 28,—Variati0n with time of the relative mean fluorescent tracer concentrations (hfthe depth-integrated samples at the weir, run 1. I r RELATIVE MEAN FLUORESCENT TRACER CONCENTRATION, C TRANSPORT AND DISPERSION 0F FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION 133 4.00 —1 Monazite 3.00 i _ 2.00 v _ (t) 1.00— _ 2.00 | l I I l Garnet 1.00 — _ Ib |> 2.00 I I l I Quartz 1‘00 — _ I I 44* I. 1000 1100 1200 1300 1400 1500 1600 1700 TIME, IN HOURS FIGURE 29.—Variatiun with time of the relative mean fluorescent tracer concentrations of the depth-integrated samples at the weir, run 2. I34 depth-integrated samples, the ratio of the measured-to- calculated sediment-transport rates for each sieve class of a specific color of tracer was a constant. This can be shown as follows. The measured sediment-transport rate for size class i is Qsi (measured) = Qspi, (13) where OS is the total measured sediment-transport rate. The ratio for size class i is 0;, (measured) _ QsA ’ . Qs, (calculated)_ N (14) For a specific color of fluorescent tracer in a specific experiment, all the factors on the right-hand side of equation 14 are constant, and thus the ratio of Qsi (meas- ured)/Qsi (calculated) is constant for all size classes. VELOCITIES OF THE CENTROIDS OF THE TRACER MASSES The velocities of the centroids of the tracer masses were determined from the data of mean concentration, C, versus time from cross section D. The data of fluorescent tracer concentration versus time for each sieve class at the various lateral positions at cross section D were combined to give the mean con- centration, C(t). The mean concentration for a specific sieve class at time tis given by z: ”C(z, t)Az C(t) =210 f, (15) where C(z, t) is the concentration at time t at lateral position 2 where z is measured from the right bank, Az is the width increment over which C(z, t) is assumed to be the concentration, and B is the channel width. In run 1, the sampling positions were not equally spaced, and one position near the centerline was omitted through an error in sampling procedure. As a result, the sampling position was not always at the center of the Az increment. The maximum displacement of a sampling position from the center of a width increment was 2 feet for the two center sampling positions. Because the positioning of the samplers at the different sample times was subject to an error of the order of:t0.5 foot, the SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 2-foot displacement is not considered significant. Thus, equation 15 for run 1 is 10C7(t) +8C17(t) +10C23(t) + 10C37(t) 79 C(t) = + 9013“) +12C55(t) 79 (16) where 79 is the channel width, in feet, at cross section D. In run 2, the sampling locations were equally spaced at 6-foot intervals and equation 15 for run 2 has the form +6[C48(t)+C5;él)+C60(t)] (17) The mean concentrations at cross section D for the various sieve classes and specific gravities of tracer materials were calculated from equations 16 and 17 for runs 1 and 2, respectively. The mean concentration values calculated from equa-“ tions 16 and 17 were normalized by dividing by the area under the curve of mean concentration versus time to give a relative mean concentration. The relative mean concentration, CT, is defined by C(t) , CEO) = , f0 C(t)dt (18) The relative mean concentration values as a function of time for the various sieve classes of quartz tracers used in run 1 are presented in figures 30, 31, and 32. The relative mean concentration values as a function of time for the quartz, garnet, and monazite tracers used in run 2 are presented in figures 33, 34, and 35, respectively. The centroid velocities were calculated from 700 V: (i—At)3600’ (19) where I7 is the velocity of the centroid of the tracer mass, in feet ‘per second; 700 is the distance, in feet, between the injection point and cross section D; fis the mean time, in hours, or the time required for the centroid of the tracer mass to move from the injection point to cross section D; and AL is the time difference, in hours, between the start of the experiment and the mean injection time for a given sieve class or specific gravity of tracer material. TRANSPORT AND DISPERSION 0F FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION I35 200‘, 1 1 l l l r EXPLANATION Yellow quartz 0.500—0707 mm 1.00 , L 0 ‘ ‘ IQ 2.00 r , I . Z 9 I; EXPLANATION E Yellow quartz 5 0350-0500 mm 0 z O 0 1.00— I n: m O < m p— )— 2 DJ 0 8 a: 0 1 ' # O D .1 LL 2 “<1 3.00 I I | I I I E I; EXPLANATION 5 Yellow quartz .1 0250-0350 mm m c: 2400 — _ 1.00— s 0 J I j . 1300 1 400 1 500 1600 1700 1800 1900 2000 TIME, IN HOURS FIGURE 30.--Variation with time of the relative mean concentration at cross section D of the 0.250- to 0.350-mm, 0.350- to 0.500-mm, and 0.500- to 0.707-mm sieve classes of yellow quartz, run I. I36 RELATIVE MEAN FLUORESCENT TRACER CONCENTRATION, Cr(/) 3.00 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 1.00- EXPLANATION Green quartz 0.250—O.350 mm 4.00 3.00 - 2.00 > 1.00 » EXPLANATION Green quartz 0.177—O.250 mm 3.00 2.00 - 1.00» EXPLANATION Green quartz 0.125-0.177 mm 0 1300 l 400 1 500 1600 1700 TIME, IN HOURS 1 800 1900 2000 FIGURE 3l.—Variati0n with time of the relative mean concentration at cross section D of the 0.12540 0.177-mm, 0.177- to 0.250-mm, and 0.250- to 0.350-mm sieve classes of green quartz, run 1. RELATIVE MEAN FLUORESCENT TRACER CONCENTRATION, Cr (I) TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION I37 3.00 r I I I I l EXPLANATION Red quartz >1.00 mm 2.00 — _ 1.00 7 E O I I 2.00 I I I I I I EXPLANATION Red quartz 0.707—1.00 mm 1.00 — q 0 ' ‘ 4 2.00 I I I I T I EXPLANATION Red quartz 0.500-0.707 mm 1.00 > _ 0 I I I A . 1300 1400 1500 1600 1700 1800 1900 2000 TIME, IN HOURS FIGURE 32. —Variation with time of the relative mean concentration at cross section D of the 0.500- to 0.707-mm, 0.707- to 1.00 1.00-mm sieve classes of red quartz, run 1. 138 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 2.00 l I I I I I EXPLANATION Quartz 0250-0350 mm 1.00— _ o l 2.00 . . I . . . EXPLANATION ’C Quartz 2: 0177—0250 mm Io i o 1.00 d I: < (I I- Z LLJ 0 Z 0 0 1 . m 0 Lu 0 3‘: 5.00 . 1 . . . 1 '— E EXPLANATION Lu 0 Quartz 3 0125—0177 mm 0: O 3 4.00 _ LL 2 < LLI 2 LIJ 2 p. S 3.00 I IJJ I 2.00 4 1.00 — 0 . . 1 1000 1200 1400 1600 1800 2000 2200 2400 TIME, IN HOURS FIGURE 33.—Variation with time of the relative mean concentration TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION I39 EXPLANATION 4.00 - Quartz ‘ 0.707—1.00 mm 3.00 - ‘ 2.00 >- ‘ RELATIVE MEAN FLUORESCENT TRACER CONCENTRATION, CrU)‘ 1.00 r _ I I I l l I EXPLANATION 2.00 ' Quartz " 0500-0707 mm 1.00 - - A I L a 0 EX P l_A N AT I O N 2.00 - Quartz “ 0350-0500 mm 1.00 - _ 0 1000 1200 1400 1600 1800 2000 , 2200 2400 TIME, IN HOURS at cross section D of the six sieve classes of quartz tracer, run 2. I40 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 0.60 I I I I I I EXPLANATION Garnet O.177—0.250 mm 0.40— — Q 0.20 a I6 2. 9 D- < n: I- z \‘ Lu % 0 I I I O Q a: ‘63 < 0.80 I 7 I I I C: '— E EXPLANATION 5 Garnet fl 0125-0177 mm 0! O 3 L 0.60- * Z < m 2 Lu 2 p— <( .4 Lu '1 0.40 ~ 0.20 _ 0 J I 1 I I 1000 1200 1400 1600 1800 2000 2200 2400 TIME, IN HOURS FIGURE 34. —Variation with time of the relative mean concentration at cross section D of the five sieve classes of garnet tracer, run 2 (classes 3-5 on opposite page). TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION I41 0.40 I | | I I I EXPLANATION Garnet 0500—0707 mm IG 0.20 i 9 I— < m t— Z Lu 0 Z 8 o c: Lu 0 <( a: t 020 I I ' E EXPLANATION o Garnet 3 0350-0500 mm C! O D _I u. Z < 0 Lu 2 Lu 2 j— f, 0.20 I I g EXPLANATION Garnet 0250—0350 mm 0 I I I I I 1000 1200 1400 1600 ' 1800 2000 2200 2400 TIME, IN HOURS The mean time, or E values, were calculated from I: tC(t)dt =Ix ICI~(t)dt. (20) where C is the mean concentration at cross section D as calculated from equation 15. The times, t and f, are rela- tive to the time at which the experiment was begun. Mean time values were calculated from equation 20 for each sieve class and specific gravity of tracer material. The integrals were evaluated by measuring the areas under the appropriate curves with a planimeter. For the purpose of standardizing the calculations, the C(t) as a function of t curves for the different sieve classes and specific gravities were truncated at the time at which the mean concentration for a particular sieve class decreased to 1.0 percent of the maximum mean concentration for that sieve class. The initial sharp peaks in the garnet and monazite curves (figs. 34 and 35) were disregarded in the determination of the maximum mean concentrations. For the quartz tracers these times occurred within the dura- tion of both of the experimental runs. For the garnet and monazite tracers used in run 2, an extrapolation was required. The maximum extrapolation required was 2.0 hours for the 0.177- to 0.250-mm sieve class of garnet. The mean extrapolation time for the five sieve classes of garnet and the four sieve classes of monazite was 0.67 hour, or about 5 percent of the total time interval of run 2. The calculation of the centroid velocities from equation 19 requires some justification because this equation assumes that the fluorescent tracer materials were de- posited on the bed of the channel at the injection point. However, because the fluorescent tracer materials were dumped at the water surface, they were carried some distance downstream by the flow before deposition on the channel bed. Loyacano (1967) found in some quali- tative experiments that the initial fall velocity of groups of particles was four to seven times larger than the fall velocity of the single particles because of the tend- ency of the particles to fall as a group. Because of the very large injection rates used in the fluorescent tracer experiments and because of the relatively shallow depth of flow in the study reach (less than 3 feet), it was assumed on the basis of Loyacano’s work that the tracer 14.2 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 0.20 . I I I I EX PLA NATI O N Monazite 0350—0500 mm 0 I l I | I | 0.40 I r I I I I EX PLANATION Monazite 0250—0350 mm 0.20 _ | 0 | I I l 4L 0.40 | | I I | I EXPLANATION Monazite O.l77—0.25O mm 0.20 0.60 I l T I I I EXPLANATION RELATIVE MEAN FLUORESCENT TRACER CONCENTRATION, 0,0) Monazite 0.125-0. 177 mm 0.40 - _ 0.20 _ O I I L | l I 1000 1200 1400 1600 1800 2000 2200 2400 TIME, IN HOURS FIGURE 35.—Variation with time of the relative mean concentration at cross section D of the four sieve classes of monazite tracer, run 2. TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION materials fell rapidly to the bed surface. Hence, the distance traveled by the fluorescent material before deposition on the bed surface was assumed negligible with respect to the 700 feet between the injection point and cross section D. The centroid velocities calculated from equation 19 and the 5, At, and the £11,111 values are summarized in tables 14 and 15 for runs 1 and 2, respectively. The £11,111 value is the time interval required for the mean concentration at cross section D to decrease to 1.0 percent of the maximum mean concentration. The centroid velocities for the various sieve classes are plotted as a function of median fall diameters of the sieve classes in figures 36 and 37 for runs 1 and 2, respectively. The vertical dashed lines represent the size limits of the sieve class used in the analysis of the samples, and the numbers correspond to the sieve-class numbers given in the tables. TABLE 14.—Summury of the I. At. [0,01, and \7 data, run I Sieve class Median fall 10.0, i AI 17 Color (mm) diameter (hours) (hours) (hours) (fps) (mm) Green (1) 0125-0177 0.150 1.33 0.183 0.023 1.22 (2) 0177-0250 .189 1.58 .273 .023 .778 (3 ) 0230-0350 .231 1.92 .320 .023 .655 Yellow (3) 0250-0350 .271 1.53 .596 .062 .364 (4) 0350-0500 .358 2.78 .558 .062 .392 (5) 0500-0707 .452 2.63 .593 .062 .366 Red (5) 0.5000707 .539 2.65 .365 .096 .415 (6) 0.707-I.00 .613 2.67 .564 .096 .415 (7) > 1.00 .839 2.58 .546 .096 .432 TABLE 15.—Summary oflhe 1, At. [0.01, am] \7 (1am, run 2 Sieve claSs Median fall 111.111 i A! 5 Mineral (mm) diameter (hours) (hours) (hours) (fps) (mm) Quartz (1) 0125-0177 0.152 1.85 0.310 0.017 0.664 ' 0177-0250 .204 7.37 1.55 .017 .127 (3) 0250-0350 .239 7.00 .992 .017 .199 4 0350-0500 .120 5.50 .952 .017 .208 (5) 0500-0707 .541 1.97 .521 .017 .385 (6) 0707-100 .694 1.20 .401 .017 .506 Garnet (1) 0125-0177 .232 15.3 8.70 .043 .0224 (2) 0177-0250 .300 16.0 10.22 .043 .0191 (3) 0250-0350 .405 14.4 9.84- .043 .0198 (4) 0350-0500 .578 14.3 8.24 .043 .0237 (5) 0500-0707 .690 14.4 7.39 .043 .026-1- Monazite (1) 0125-0177 .235 14.4 7.20 .061 .0272 (2) 0177-0250 .305 14.6 8.35 .061 .0235 (3) 0250-0350 .481 14.4 7.52 .061 .0261 (4-) 0350-0500 .721 14.3 8 15 .061 .0240 Curves for the quartz tracer materials of runs 1 and 2 having the centroid velocity as a function of median fall diameter are similar in shape. The curves are approxi- mately U-shaped, with the maximum velocities occurring fr. the smallest particles and the minimum velocities occurring for those particles with fall diameters approxi- mately the same as or slightly larger than the fall diame- ters of the natural bed-material particles comprising 143 the largest part of the bed-material transport. The maximum centroid velocities observed were for the 0.125- to 0.177-mm sieve class of quartz tracer, and these were approximately 26 and 16 percent of the mean water velocity in runs 1 and 2, respectively. In run 1, the centroid velocities for the large particles were only slightly larger than the minimum centroid velocity. In run 2, however, the centroid velocity for the 0.707- to 1.00-mm sieve class was about four times larger than the minimum centroid velocity and was about 76 percent of the centroid velocity for the 0.125- to 0.177-mm sieve class of quartz tracer. This large increase of the centroid velocity with fall diameter for the large particles in run 2 can be'explained by the fact that the large particles project into the flow more than the small par- ticles. Other investigators (Chang, 1939; Sundborg, 1956; Meland and Norrman, 1966) have noted and discussed the tendency for the large particles to move with the largest velocity. It is expected that the particle velocity for a specific flow condition will continue to increase with particle fall diameter until the effect of increasing sur- face exposed to the flow, proportional to the square of the particle diameter, is exceeded by the effect of increasing mass, proportional to the cube of the diameter. Above this size, the velocity of the particle will decrease with increasing diameter. 1.5 1 1 1 . ‘ 1 1 I 1 I 1 1 1 1 1 o 1 1 1 1 a 1 1 1 1 l 1 1. _ A 8 o 1 1 1 1 m I 1 I 1 1 1 fi 0.8— 1 1 1 1 - D. | | 1 1 1. 1 1 1 1 “J 1 1 1 1 a 0.6» 1 1 1 1 . — 1 PSize—q 1 I 1 E 05_ 1 llimitofl 1 1 1 < r: ' 1 lindicated1 1 1 1 (7) I: 1 I sieve ) (14) MW 9 0'4- 1 1 class :(3) . (5) 1 1 _ o 1 1 1 1 1 1 E 1 1 1 1 1 1 E 0-3- 1 1 1 1 1 1 - 0 {Hm—T (2)f(3)-+1r—(4>—+—(5)—’1r—-(6)« Lu 1 I 1 1 | | I 1 f 1 1 1 1 1 1 LL _ 1 _ 0 0'2 1 1 I I 1 1 K lEXF’LANATIOI‘V 1 1 1 6 1 Quartz 1 | l | 9 l 0 Green I 1 1 1 1.1.1 1 1 1 1 I > 1 A Yellow 1 I I I 1 I Red 1 1 1 1 0.1 1 I 1 1 1 1 1 | 1 | 1 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0 MEDIAN FALL DIAMETER, IN MILLIMETERS FIGURE 36.—Variation with fall diameter of the velocities of the cen- troids of the tracer masses. run 1. Numbers in parentheses are sieve class numbers; see tables 7 and 8. 144 The observation that the centroid velocities for the large red quartz particles in run 1 were only slightly larger than the minimum centroid velocity can be ex- plained by the fact that these particles moved toward the right bank and some were trapped temporarily. This would cause the centroid velocities of the red quartz particles to be less than if these particles had moved down the center of the channel without interference. 0'80 I I fir I | | I | I I I I I I I I I I I I 0-60 - I I I I I , I I I | ) 0.50 — I I I I I — I I I I I 0-40 ‘ I I I I I ‘ I I I I | I I I I I I _ 0-30 2 I I I I I D I I | | CZ, I I I I o I I I I g | | I 0.20 ~ I I — E I I I l I I I I I; I I I I m | | | I . I I I I I I E I <2) I I I I: ' I I v 0'10 ” <— (1) <2) I (3) I <4) (5) I (6) —; 9 I I I 2 I I I I E I I I Lu r—Size—eI I 0 006_ Ilimitofl I _ Lu ‘ indicated I E sieve I 0-05 “ I class I ‘ LL I I I O | I E 0.04— I I , O I I o I I d I I I ,> 003— | ‘2' I (3) (SI 1 I I ,AL.\ A I I (1) \~ (2) -/_’ I f‘\l- I I \ (3) [/I’ (4) (4) 0.02 — I I \fiLA—A/ I I — I I I EXPLANATION I I I I O Quartz I I A Garnet I I l Monazite I I 0,01 I | I l | l I I | I 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0 MEDIAN FALL DIAMETER, IN MILLIMETERS FIGURE 37.—Variation with fall diameter of the velocities of the cen- troids of the tracer masses, run 2. Numbers in parentheses are sieve class numbers; see tables 7 and 8. Centroid velocities for the small particles were large in both runs because these particles apparently spent a greater proportion of the time moving as suspended ma- terial than did the natural bed-material particles com- posing the largest part of the bed-material transport. It is expected that the centroid velocity will continue to SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS increase for decreasing particle fall diameter until the silt and clay size ranges are reached where the particles move with the mean water velocity. The curve of centroid velocity versus fall diameter for the garnet was also U-shaped, but that of the monazite showed little relation to fall diameter. Also, the centroid velocities were about an order of magnitude less than the centroid velocities for the quartz. The concept of hy- draulic equivalence (Rubey, 1933, Rittenhouse, 1943) suggests that particles having equal fall diameters tend to be of equivalent hydraulic value. The centroid velocities in figure 37 are plotted as a function of median fall diam- eter; hence, it would appear that the concept of hydraulic equivalence was not applicable to the comparison of the centroid velocities of quartz, garnet, and monazite for the high-velocity flat—bed condition. However, if the difference between the behavior of the quartz particles and the heavy-mineral particles is attributed to the specific gravity effect, then the question may be asked as to why the denser, monazite particles moved about 20 percent faster than the garnet particles for the most of the fall-diameter range. The monazite was about 17 percent denser than the garnet, and the garnet was about 54 percent denser than the quartz. Because the difference in specific gravity between the garnet and monazite was small, the apparent anomaly may have been caused by shape differences. None of the lead tracer particles were found in any of the “dustpan” samples at cross section D. The last set of samples was obtained 22 hours after injection; hence, the centroid velocity of the lead particles was something less than 700/22X3600, or 0.0088 foot per second. However, the centroid of the 0.707- to 1.00-mm sieve class of quartz tracer particles, which has a median fall diameter only slightly smaller than the median fall diameter of the 0.177- to 0.250-mm sieve class of lead (see table 1), moved through cross section D about 0.4 hour after injection of the fluorescent materials. This corresponds to a centroid velocity of 0.506 foot per second. As before, it would appear that the con- cept of hydraulic equivalence was not applicable to the comparison of the centroid velocities of quartz and lead-tracer particles of comparable fall diameter for the high-velocity flat-bed condition. Approximately fifty 6-inch core samples were obtained over about the center third of the channel at cross sec- tions A, B, C, and 15, 40, and 65 feet downstream from the injection point. These samples were obtained about 21.5 hours after the injection of the fluorescent tracer materials in run 2 and were divided into two 3-inch seg- ments. These samples, both the top and bottom segments, contained essentially no quartz tracer particles. Two of the top- segments contained an appreciable number of TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION garnet and monazite particles, and six top segments contained a few garnet and monazite particles. All the other segments of the core samples contained very few fluorescent particles. These results indicate that there was no general tendency for either the quartz or the heavy-mineral tracer particles to be exchanged with that part of the bed material not in transport. This is in agree- ment with the observation that the bed surface below the moving layer of sediment for the flat-bed condition of alluvial-channel flow is very firm. LONGITUDINAL-DISPERSION CHARACTERISTICS OF THE TRACER MATERIALS The longitudinal-dispersion coefficient, KI, can be calculated from the rate of change of the variance of the concentration as a function of time curve with distance downstream (Sayre and Chang, 1968). In the fluorescent tracer experiments, meaningful data were obtained only at cross section D because of the rapid rate at which the tracer material moved through the study reach. There- fore, a true longitudinal-dispersion coefficient could not be calculated. However, the variance, 0%, of the mean concentration as a function of time curves for the differ- ent sieve classes and specific gravities at cross section D was used as a measure of the longitudinal dispersion between the injection point and cross section D. For a valid comparison, this procedure assumes that the initial period required for the establishment of the linear varia- tion of the variance with distance is the same for all sieve classes and specific gravities of tracer minerals. The variance, 0?, is given by I” Rama 0 — . x _,27 (21) f C(z)dt 0'5: where t is given by equation 20. The integrals were evaluated by measuring the areas under the appropriate curves with a planimeter. As in the E calculations, the tzé versus t curves were truncated at the times at which the mean concentration decreased to 1.0 percent of the maximum mean concentration. These time values, desig- nated tom, are summarized in tables 14 and 15 for runs 1 and 2, respectively. The variances of the curves of mean concentration at cross section D versus time were calculated from equa- tion 21, and the values for the various sieve classes and specific gravities are summarized in tables 16 and 17 for runs 1 and 2, respectively. The variances are plotted as a function of the median fall diameters of the sieve classes in figures 38 and 39 for runs 1 and 2, respectively. The vertical dashed lines represent the size limits of the I45 sieve classes, and the numbers correspond to the sieve- class numbers given in the tables. TABLE 16,—Summary of the of values of the mean concentration at cross section D as a function of time data, run I Color Sieve class of (hoursi) (mm) Green (1) 0.125-0.177 0.0358 (2) 0.177—0.250 .0455 (3) 0.250—0.350 .0810 Yellow (3) 0250-0350 .356 (4) 0350—0500 .200 (5) 0.500-0.707 .165 Red (5) 0.500—0.707 .149 (6) 0.707—1.00 .170 (7) > 1.00 .153 TABLE 17.—Surnmary of the o",-’ values of the mean concentration at cross section I) as afunction of time data, run 2 Mineral Sieve class of (hours?) (mm) Quartz (1) 0.125—0.177 0.120 (2) 0.177—0.250 3.35 (3) 0.250-0.350 2.23 (4) 0.350-0.500 1.70 (5) 0.500-0.707 .0762 (6) 0.707—1.00 .0423 Garnet (l) 0.125—0.177 12.9 (2) 0.177-0.250 11.6 (3) 0250—0350 8.25 (4) 0.350—0.500 7.73 (5) 0.500-0.707 8.86 Monazite (1) 0.125—0. 177 13.0 (2) 0.177-0.250 10.3 (3) 0250—0350 11.4 (4) 0.350-0.500 13.3 The variation of the variances with fall diameter should be approximately the inverse of the variation of the cen- troid velocities with fall diameter. This behavior was ex- pected because the more rapidly a slug of tracer material of a specific size moves through the study reach, the less opportunity that slug has for dispersing in the longitudinal direction. Figures 38 and 39 show that the variation of the variance, (7?, with fall diameter for the quartz tracer ma- terials in both runs was approximately the inverse of the variation of the centroid velocities with fall diameter pre- sented in figures 36 and 37. The maximum 0'? values occurred for particles with diameters approximately the same as or slightly larger than the diameters of the particles comprising the bulk of the natural bed material in transport. Minimum 0'? values occurred for the largest and smallest particles within the fall-diameter range considered. The failure of the 0% values for the 0.707- to 1.00-mm and >1.00-mm sieve classes of red quartz to continue to decrease with increas- ing particle diameter (fig. 38) may be explained by the same reasoning applied to the failure of the centroid I46 velocities for these sieve classes to increase with fall diameter. Both the displacement of the red quartz parti- cles toward the region of small velocities near the bank and the temporary entrapment of some of the red par- ticles along the bank would tend to increase the variance over that expected, had the red quartz particles moved down the center of the channel. One minor discrepancy in the inverse relation between the 0'? as a function of fall diameter and 17as a function of fall-diameter curves for the quartz tracer particles in run 2 is that the 0'? values for the 0.500- to 0.707-mm and 0.707- to LOO-mm sieve classes of the quartz tracer were less than 0'? for the 0.125- to 0.177-mm sieve class of quartz. The centroid velocity of the 0.125- to 0.177-mm sieve class of quartz exceeded the centroid velocities for the 0.500- to 0.707-mm and 0.707- to LOO-mm sieve classes of quartz, however. The variances of the garnet and monazite varied with fall diameter in the same manner as the centroid veloci- ties, as a comparison of figures 37 and 39 shows. In each 0.40 I :(3)I I | | I 0.30 - I | | I Is—Sizea ! limit of I indicated> sueve I I | | | I I | I 0.20 - I | (6) /\'\<2 I (5) : I I ' I I I I I I I I I I I I I I I I . l I Iclass | I I I I . I I I I I I _, r—(1)—-ll<—(2)—+—<3)—T~(4)—+—(5)—T—(6) 0.1m} I I I I I I I I I I I I I I l I I I I I I I I I I I I I I I I (3) 0.08 — 0.06 - I I I I I I I I I 0.05 — I | I | I | | | I | I I I l EXPLANATION_ I I | | | | | | | | I I I | | I I I | I 0.04 — (1) Quartz 0 Green 0.03 — A Yellow — I Red VARIANCE OF THE MEAN CONCENTRATION VERSUS TIME DATA (7?), IN SQUARE HOURS I | I I I I I | l | I | | | | | | I I | I I I I | I | l | | | | I I I I I | | | | I | | | I 0.01 l I I | 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0 MEDIAN FALL DIAMETER, IN MILLIMETERS FIGURE 38,—Variation with fall diameter of the variances of the mean concentration as a function of time curves at cross section D, run 1. Numbers in parentheses are sieve class numbers; see tables 7 and 3. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS instance, however, the variation of either 0'? or I7 with fall diameter was much less for the garnet and monazite than for the quartz. The centroid velocity and the variance, 0?, for the quartz tracer used in run 2 varied with fall diameter about 4-20 and 780 percent, respectively, from the minimum to the maximum value. The centroid veloc- ity and the variance for the garnet varied with fall diame- ter about 38 and 67 percent, respectively, and these 20.0 10.0 - 9° 0 I I6.0 — 4.0 — I ls-Sizesl |limit of! Indicated | sieve I l class 3.0 a I I I I I I I | I | | | | | | | | | | I I I 0.20 - (1) 0.10 - VARIANCE OF THE MEAN CONCENTRATION VERSUS TIME DATA (0?), IN SQUARE HOURS I I I I | | | | I I I | | | IK | | | I I I I I | | | I | I I I I I I I I l | | | | | | | | I | l I I I I | | I | I | I I 0.08 a I | | | I | I | I | | I I I I I I I I I | I | | I I I | I I I I I I I I I I I I I I I I | I I I I | I I I I I I I | I I I I I I I I I I 0.06 ~ - I PLANATIO I 0.05 — I Quartz o 0'04 7 A Garnet I I I I I I I I I I I <5) I EX. I I I ' I I I I (6) I I I I I I MorIIazite I I I 0.4 0.5 0.6 0.8 1.0 MEDIAN FALL DIAMETER, IN MILLIMETERS 0.03 I I 0.1 0.2 0.3 FIGURE 39.—Variation with fall diameter of the variances of the mean concentration as a function of time curves at cross section D, run 2. Numbers in parentheses are sieve class numbers; see tables 7 and 8. TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION quantities for the monazite varied with fall diameter 16 and 33 percent, respectively, from the minimum value to the maximum value. These results and the fact that the 0'? values for garnet and monazite were about an order of magnitude larger than a"? for quartz particles of com- parable fall diameter indicate a distinct difference in behavior between the quartz particles and the garnet and monazite particles. The differences in longitudinal- dispersion characteristics indicated in figure 39 are seen clearly in the relative mean concentration as a function of time plots, figures 33, 34, and 35. One additional difference between figures 37 and 39 is that the 0",: values for garnet generally fall between the values for quartz and monazite, whereas the Vvalues for monazite generally fall between the 17 values for quartz and garnet. This difference, however, probably is not significant because of the small differences between these quantities for the garnet and monazite. It is concluded that neither fall diameter nor fall diameter and specific gravity are sufficient to explain the differences in a"? for the quartz, garnet, and monazite tracers in run 2. EVALUATION OF THE FLUORESCENT TRACER TECHNIQUE With the experience gained in the planning and execu- tion of the two experiments and the analysis ofthe results, it is possible to evaluate the application of the fluorescent tracer technique to studies of sediment movement. Four basic steps are involved in the fluorescent tracer tech- nique. These are the preparation of the tracer mate- rials, the injection of the tracer materials into the study reach, the sampling of the tracer masses as they move through the study reach, and the analysis of the samples. The first step in the preparation of the tracer materials is to select the material to be coated with the fluorescent dye. At least three different sources of material may be used. The most obvious source is sediment taken from the study reach. This material has the advantage of rela- tively low cost, but it may have some significant disad- vantages. The bed material can range widely in shape and specific gravity for a given sieve size. The use of such ma- terial makes it difficult, or impossible, to determine the effect of size alone on sediment velocity or dispersion, if considerable quantities of mica or heavy minerals are present. If one could collect and dye a sample repre- senting the sieve-size distribution of the total sand in transport and then return it to the stream before the size distribution changed, then such a tracer should be excel- lent for determining sediment-transport rate. However, except under ideal circumstances, this approach is not feasible. Instead, a sample of bed material would nor- mally be used. Such bed material does not truly repre- sent the size, shape, or specific gravity distribution of the I47 sediment in transport. To some extent it represents a lag deposit. The greater the difference in characteristics of bed sediment and sediment in transport, the greater will be the error in estimating the sediment-transport rate. A second source is material from a different stream. However, such material, unless it closely matches the sediment in the stream under study, is useful mainly for reconnaissance work. Its usefulness in determining the effect of size, shape, and specific gravity on transport will depend on how uniform these characteristics are in a par- ticular sieve size. In this study, coated material from an- other stream was used for reconnaissance in run 1 because it was available from a previous investigation. A third source, and probably the best for many research studies, is a material with little variation in shape or specific gravity. Thus, one can learn how a material of known characteristics moves in a stream under particular flow conditions. Ottawa sand and other similar products are composed of clean well-rounded quartz sand with very few heavy minerals. Such sand is commercially available in large quantities at very reasonable price. In fact, total cost to buy the sand and dye can be less than 10c per pound. Because 1 pound of the fluorescent sand can “tag” 5,000 to 10,000 pounds of moving stream sand, the cost of tracer is a negligible part of the expense of a tracer experiment. The quartz sand used in the second, and main, run of this study was Ottawa silica sand of uniform shape and specific gravity. The problem of obtaining uniform material of specific gravity and (or) shape greatly different from quartz, but yet resembling the type of material that might be found in a stream, is a major one. Although heavy-mineral concen- trates and lead shot were used in this experiment, syn- thetic materials whose characteristics can be closely controlled probably should be used. The method of applying the fluorescent dye to the par- ticles developed by Kennedy and Kouba (1970), and used in the present study with slight modification, produced a good, abrasion-resistant fluorescent coating. There was apparently no difficulty with loss of the dye coating in the stream; however, sieving of the samples resulted in some chips of dye from large particles that limited the analysis of the samples to particles larger than 0.125 mm. The resultant coating was nonwetting, and this charac- teristic complicated the injection process. A detergent had to be added to the fluorescent material or the fluo- rescent material had to be injected as a slurry to which de- tergent had been added. These precautions were neces- sary to insure that the fluorescent particles did not clump together because of the surface effects of the coating. Further work toward the development of an abrasion- resistant fluorescent coating that is wettable is necessary. 148 On the other hand, there is need occasionally for fluo- rescent coatings that will decompose after a specific time interval so that a stream or river is not contaminated permanently with the fluorescent tracer particles. Pre- vious work on this type of coating as well as on other types of permanent coatings has been summarized by Ingle (1966), and Teleki (1966) has presented a detailed review of the various types of fluorescent dyes and coating proc- esses. Whatever the type of coating, however, it must be remembered that the primary requirement of any coat- ing is that the tagged particles of a specific size behave identically with the natural sediment particles of the same size. If a range of particle sizes is considered, then the size distribution within a particular size range must approximate the distribution of natural sediment parti- cles in this size range that are in transport. This does not necessarily mean, of course, that sediment from the stream must be the material used in the preparation of the tracers. The injection of the fluorescent materials into the study reach must satisfy the following conditions: 1. The location of the injection point relative to the sampling point must be known accurately. 2. If an instantaneous-slug injection is used, the time required for the injection process must be negligible compared with the time scale of the sediment motion. 3. If an intermittent-slug injection is used as an approxi- mation of the true continuous injection process, the time interval between injections should be negligi- ble compared with the time scale of the sediment motion. 4. The injection process should disturb the natural sedi- ment-transport process at the injection point as little as possible. Some difficulty was experienced with the injection tube used in the present study, but it is believed that the procedure of simply dumping the fluorescent material into the channel at as high a rate as possible reasonably approximated an instantaneous point source of fluores- cent material. However, because the tracer particles did move so rapidly for the high-velocity flat-bed condi- tion. several advantages would have been gained by the use of a continuous point-source injection. For example, a better evaluation of the lateral-dispersion characteris- tics of the tracers would have been possible, and the calculation of the sediment-transport rates would have been simplified. Similarly the possibility of failing to sample a fast-moving slug of tracer material would have been eliminated. Various types of injection procedures have been dis- cussed in the literature, and these procedures range from water-soluble containers discussed by De Vries (1966) and Lean and Crickmore (1963) to the elaborate constant-injection apparatus that was used for a period SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS of 6 weeks by Crickmore (1967). However, further work is needed in the development of injection processes. The type of sampling required in a fluorescent tracer experiment in general depends upon the bed configura- tion in the study reach. If a dune bed exists, then core samples are necessary to define the spatial distribution of fluorescent material within the study reach. In the present study, the high-velocity flat-bed condition existed. Samples of the bed material moving near the bed surface were desired because large samples could be obtained rapidly at this location and because these samples should contain some of the large bed-material particles in transport. The “dustpan” sampler described previously and used in the present study appeared to be an acceptable device for obtaining these samples. Analysis of the samples requires a determination of the number of fluorescent particles of each color in each sieve class of each sample. In the present study, the numbers of fluorescent particles were determined by a manual counting process. The manual counting process is a simple procedure, and only a minimum amount of equipment is required. Although the statistical analysis (C. F. Nordin, Jr., written commun., 1968) simplified greatly the counting process, the manual counting pro- cedure was time consumng because the length of time any one individual could spend counting particles was limited by the tedium of the process. Automatic elec- tronic devices for counting the number of fluorescent par- ticles have been described by De Vries (1967) and Teleki (1967). An electronic counter has the obvious advantage of convenience and ease of sample analysis. Disadvan- tages are the expense and the careful calibration and maintenance of the instrument that are required to ob- tain accurate concentrations. If two or more different fluorescent dyes are used, care must be taken to insure that the spectra of the dyes are displaced sufficiently so the different colors can be distinguished by the instru- ment with the use of the proper filters. The problem of differentiating between chips or flakes of dye from large particles and actual fluorescent particles for the small-diameter sieve classes was encountered in this study. Because of this problem, the smallest diam- eter sieve class considered was the 0.125- to 0.177—mm sieve class. It was impractical to attempt to distinguish visually between particles and chips in the 0.088— to J.125-mm sieve class. However, the 0.062- to 0.088~mm and 0.088- to 0.125-mm sieve classes often may be of importance, as they were in the present study because they contributed about 27 percent of the total sediment transport of particles larger than 0.062 mm. A way of eliminating the problem of chips and flakes in these sieve classes is to use one color of dye specifically for each of these two sieve classes. After the preparation of the fluorescent materials, the ma- TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES, FLAT-BED CONDITION terial for each sieve class should be carefully resieved to remove all material outside the desired sieve range. Care should be taken also in the preparation of the fluorescent materials to insure that the size distributions within each sieve class of material are approximately the same as the size distributions within that sieve class of the bed ma- terial in transport. It is concluded that the fluorescent tracer technique is a simple and sensitive experimental method for studying the movements of groups of particles either in a natural channel or in a laboratory alluvial channel. However, con- siderable improvement in technique in each of the four basic steps is still necessary. SUMMARY A fluorescent tracer technique was applied to the study of the rates of transport and dispersion of sediment particles of various sizes and specific gravities for the high-velocity flat-bed condition of alluvial—channel flow. Two runs were completed in the Rio Grande conveyance channel near Bernardo, N. Mex., and the following state— ments summarize the knowledge gained from these two experiments. 1. The centroid velocity of the 0.125- to 0.177—mm sieve class of sand was 1.2 fps in run 1 when the mean water velocity was 4.66 fps and 0.66 fps in run 2 when the mean water velocity was 4.05 fps. Thus, the fine sand moved about 16 to 26 percent of the mean water velocity. 2. The centroid velocity of the quartz tracer particles varied with particle size. In the size range from 0.125 to 1.0 mm, the minimum velocity occurred for a particle size slightly larger than the median diameter of the bed material (about 0.2 mm). Both the larger and the smaller particles moved faster. In run 1, the tendency of the large particles to follow the thalweg of the channel distorted the U-shaped velocity-diameter relation. 3. Garnet and monazite particles moved at velocities about an order of magnitude less than the velocities of quartz particles of equivalent fall diameter. Thus, the concept of hydraulic equivalence based on fall diameter is not applicable to sand-size particles under the condi- tions of this experiment. 4. At least two factors were important in producing lateral mixing of the tracer particles. These are turbulent fluctuations in the flow and the effect of the thalweg of the channel. 5. The large and heavy particles tended to follow the thalweg of the channel even though the channel was approximately straight and the flow lines at the surface appeared to follow the alinement of the channel. 6. Lateral mixing was greatest for the smallest quartz tracer particles and was approximately the same as that 149 for a water-soluble fluorescent dye. Lateral mixing de- creased with increasing size of quartz tracer in run 2 when the effect of the thalweg was minimized. The large particles mixed the least because they spent a greater proportion of the time resting on or moving along the bed surface than did the small particles. 7. Longitudinal mixing of the quartz tracer particles as related to particle size showed an approximately reciprocal relation to that observed for centroid velocity as a function of particle size; that is, the slower the sand moved, the greater was the longitudinal mixing. 8. The rapid rate of movement of the quartz tracers through the study reach made it diflicult to obtain an accurate record of the passage of the tracer mass. Failure to sample the complete tracer mass will result in calcu- lated values of the sediment-transport rate that are too large, as occurred in this study. A continuous injection of fluorescent tracer would have been preferable for the flow conditions of this study. 9. The fluorescent tracer technique has great potential as a tool for the study of movements of sediment. Further development of equipment and techniques is needed, however. LITERATURE CITED Chang, Y. L., 1939, Laboratory investigation of flume traction and transportation: Am. Soc. Civil Engineers 104, p. 1246—1313. Crickmore, M. J., 1967, Measurement of sand transport in rivers with Trans, v. special reference to tracer methods: Sedimentology, v. 8, no. 3, p. 175—228. DeVries, M., 1966, Application of luminophores in sand transport studies: Delft Hydraulics Lab. Pub. 39, 86 p., Delft, Netherlands. 1967, Photometric counter for fluorescent tracers: La Houille Blanche, no. 7, p. 717—722. Fischer, H. B., 1967, Transverse mixing in a sand-bed channel, in Geological Survey research, 1967: U.S. Geol. Survey Prof. Paper 575-D, p. D267—D272. Gonzalez, D. D.. Scott, C. H., and Culbertson, J. K., 1969, Stage- discharge characteristics of a weir in a sand-channel stream: U.S. Geol. Survey Water~Supply Paper 1898-A, 29 p. Guy, H. P., and Norman, V. W., 1970, Field methods for measurement of fluvial sediment: U.S. Geol. Survey Techniques Water-Resources Inv., Book 3, Chap. C2, 59 p. Harris, D. D., and Richardson. E. V., 1964, Stream gaging control structure for the Rio Grande conveyance channel near Bernardo. New Mexico: U.S. Geol. Survey Water-Supply Paper 1369—E, p. 123—154. Hubbell, D. W., 1964, Apparatus and techniques for measuring bed- load: U.S. Geol. Survey Water-Supply Paper 1748, 74 p. Ingle, J. C., Jr., 1966, The movement of beach sand: New York,Elsevier Pub. Co., 221 p. Kennedy, V. C., 1968, Fluorescent sand as a tracer of fluvial sediment movement: Geol. Soc. America Spec. Paper 101, p. 108-109. Kennedy, V. C., and Kouba, D. L., 1970, Fluorescent sand as a tracer of fluvial sediment: U.S. Geol. Survey Prof. Paper 562—15, 13 p. Lean, G. H., and Crickmore, M. J., 1963, Methods for measuring sand transport using radioactive tracers, in Symposium on the appli- 150 cation of radioisotopes in hydrology: Tokyo, Internat. Atomic Energy Agency, p. 111—131. 1966, Dilution methods of measuring transport of sand from a point source: Jour. Geophys. Research, v. 71, no. 24, p. 5843-5855. Loyacano, J. N., 1967, Fall velocity of sand particles in turbulent f‘lume How: Fort Collins, Colo., Colorado State Univ. Dept. Civil Eng. unp'ib. M.S. thesis. Meland, N., and Norrman, J. 0., 1966, Transport velocities of single particles in bed-load motion: Geog. Annaler, v. 48, ser. A, p. 165—182. Rittenhouse, G., 194-3, Transportation and deposition of heavy minerals: Geol. Soc. America Bull. v. 54. p. 1725-1780. Rubey, W. W., 1933, The size-distribution of heavy minerals within a water-laid sandstone: Jour. Sed. Petrology, v. 3, no. 1, p. 3—29. Sayre, W. W., and Chang, F. M., 1968, A laboratory investigation of open-channel dispersion processes for dissolved, suspended, and floating dispersants: U.S. Geol. Survey Prof. Paper 4-33—E, 71 p. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS Sundborg, Ake, 1956, The river Klaralven—a study of fluvial processes: Geog. Annaler, v. 38, p. 127-316. Teleki, P. G., 1966, Fluorescent sand tracers: Jour. Sed. Petrology, v. 36, no. 2, p. 468—485. 1967, Automatic analysis of tracer sand: Jour. Sed. Petrology, v. 37, no. 3, p. 749-759. U.S. Inter-Agency Committee on Water Resources, 1941, Laboratory investigations of suspended sediment samplers, in A study of meth- ods used in measurement and analysis of sediment loads in streams: Washington, U.S. Govt. Printing Office, Rept. 5, 99 p. 1957a, The development and calibration of the visual-accumula- tion tube, in A study of methods used in measurement and analysis of sediment loads in streams: Washington, US. Govt. Printing Office, Rept. 11, 109 p. 1957b, Some fundamentals of particle size analysis, in A study of methods used in measurement and analysis of sediment loads in streams: Washington, US. Govt. Printing Office, Rept. 12. 55 p. APPENDIXES 152 SEDIMENT 'I'RANSPORT IN ALLUVIAI. CHANNELS APPENDIX A—DISCUSSION OF THE WASHING EFFECT Because of the flow'through the “dustpan” sampler dur- ing thecollection of the sample, some of the fines may have been preferentially washed from the sample. This effect is not of concern if the tracer particles of a specific sieve diameter behave exactly as nontagged particles of the same diameter, as is assumed to be true for the quartz tracer particles. For the garnet and monazite, however, the natural bed material in a specific sieve class would be of a smaller median fall diameter than that of the garnet or monazite in the same sieve class because of the specific gravity difference. Thus, if the washing effect were re- lated to fall diameter, the concentrations of the garnet and monazite would be affected. The purpose of this appendix is to discuss briefly some observations concerning the washing effect. These observations are based primarily on the size distributions of various types of samples collected in runs 1 and 2. The median diameter, dso, and the gradation, 0',ifor the size distributions of various types of samples obtained in runs 1 and 2 are presented in table 18. The median diam- eter, dso, is defined as the diameter for which 50 percent TABLE 18.—Comparison of the median diameters and the gradations of the size distributions of selected “tlustpan,” core, and depth- integraled samples Method Lateral position Type of of Cross (feet from 11'5“ sample Run Time analysis section right bank) (mm) (1' Depth-integrated ............ l 1326 Sieve Weir (1) 0.168 1.60 .. 2 1015 ..... do ..... ,. ..... do ...... ('1 .164 1.57 .. 1 154-2 VA tube ..... (lo ...... (‘1 .176 1.54- .. 2 1604 ..... do ........... do ...... ('1 .170 1.48 . 2 1655 Sic-V0 B 35 .185 1.46 . 2 1701 d 35 .251 1.28 . 2 1638 35 .245 1.27 2 1552 35 .258 1.27 6-inch t'ore .................... 2 1620 37 .172 1.45 "1)ustpan”.. . 2 1605 36 .270 133 Do ...... . 2 1623 36 .280 1.34 Do ...... . 2 1634 36 .233 1.36\ (Sore. top 3 in ..... . 2 ‘1 0830 36 .193 1.44- Core. bottom 3 in... . 2 .doa ........ do ........... do ...... 36 .201 1.4-6 Core. top 3 in ........ . 2 " 0815 35 .208 1.38 (lore. bottom 3 in... . 2 ..... do i‘ ....... do ............ do ...... 35 .202 1.52 Core. top 3 in ........ . 2 “084-5 ..... do.. C 35 .206 1.4-7 (Lore. bottom 3 in ........... 2 ..... do" ....... do ........... do ....... 35 .184- 1.51 xComposite over channel width. 350 feet upstream of D. 3Doc. 15. of the sediment by weight is finer. The gradation, 0', is de- fined as 1/2(d84/d50+d50/d16), where d34 and (116 are, re- spectively, the diameters for which 84 and 16 percent of the sediment by weight are finer. At the centerline of cross section B, the median sieve diameter of a 6-inch core sample was 0.185 mm and the t gradation, (r, was 1.46. The mean median diameter of three “dustpan” samples obtained at the same point at about the same time was 0.251 mm, and the mean grada- tion was 1.27. Similar results were obtained at cross sec- tion D. A comparison of the median diameters off—the “dustpan” samples with the median diameters of the depth-integrated samples and the top and bottom 3-inch segments of the core samples showed that the median diameters of the “dustpan” samples were about 25 to 40 percent larger than the median diameters of the other samples. Also the gradations of the “dustpan” samples were less than the gradations of the other samples, indi- cating more uniform size distributions. These observa- tions would be expected if some of the fine material had been washed from the “dustpan” samples. However, other factors could contribute to the observa- tion that the “dustpan” samples contained coarser mate- rial than did the other types of samples. As was dis- cussed previously, it was found in the fluorescent tracer experiments that particles larger than the median size of material in the bed moved faster than the median-size particles did. Thus, the material in the “dustpan” would tend to become enriched with the larger particles. Also, the fact that the “dustpan” samples were obtained on the bed surface emphasized the coarser material. The results presented in table 18 show that the median diameters and gradations for “dustpan” samples obtained at different times at the same position are essentially identical. However, there is a slight difference between the results at cross sections B and D. Because the calculations, described previously, of the quantities 17, t, 0'}, z, and 0'22 involve ratios of concentration integrals, the effect of the washing depends on how much the wash- ing varies with time and position at cross section D. The dls, dso, dg4, and a values for sieve-size distribu- tions for “dustpan” samples obtained at cross section D at lateral positions of 18, 30, 42, and 54 feet for times near the beginning, the middle, and the end of run 2 are tabulated in table 19 to show the variation of the size distributions with time and position. The results presented in table 19 show that dls varies little with either time or position, dso shows increased variation, and dg4 shows the greatest variation with time , and position. The mean values of dg4 and 0' for cross sec- tion D vary little with time; however, these quantities at a specific position do vary appreciably with time. Also, the d84 values for the sampling positions in the right—hand TRANSPORT AND DISPERSION OF FLUORESCENT TRACER PARTICLES. FLAT-BED CONDITION part of the channel (2: 18 and 2:30) are, with one ex- ception, larger than the d.“ values for 2:42 and z=54. This means that the samples from the right-hand part of the channel contained more coarse material than the samples from the left-hand part of the channel. This ob- servation is in agreement, as was discussed previously, with the observed behavior of the large quartz tracer particles. To summarize this discussion of the washing effect, the results in table 18 show that the median diameters of the “dustpan” samples are larger than the median diameters of other types of samples. This could be the result of washing of the fines from the “dustpan” sampler or the several factors that tend to increase the numbers of large particles in the “dustpan” samples. The results in table 19 suggest that if washing of the fines is occurring, then the effect is essentially uniform with respect to time and posi- tion at cross section D. 153 TABLE I9.—Comparison of the d15, (150, dH-I, and 0' values for selected “dustpan” samples at cross section D, run 2 Approximate Particle Diameter (mm) or gradation at time diameter 2:18 2:30 2:42 2:54 Mean 1015 dlfi 0.225 0.214 0.210 0.220 0.217 .0 .311 .300 .291 .283 .296 dm .424 .441 .407 .352 .406 0' 1.37 1.44 1.39 1.26 1.36 1700 due .199 .213 .190 .223 .206 dso .281 .307 .253 .304 .286 d3; .450 .467 .327 .418 .416 (T 1.50 1.48 1.31 1.36 1.41 2400 dlfi .212 .223 .201 .240 .219 also .289 .329 .262 .323 .301 d“ .393 .498 .323 .422 .409 0' 1.36 1.50 1.26 1.33 1.36 Mean d... .212 .217 .200 .228 duo .294 .312 .269 .303 din .422 .469 .352 .397 0' 1.41 1.47 1.32 1.32 APPENDIX B—DETERMINATION OF THE WEIGHTING FACTORS The weighting factors, w(z), defined by equation 9 were determined from a set of depth-integrated samples obtained at the weir. A set of samples obtained near the beginning of each run was used in the determination of the w(z) values because most of the quartz tracer moved through the measurement section during the early part of each run. Both the water discharge and the sediment con- centration at each vertical were necessary in the computa- tion of the weighting factors. The procedure was as follows. The sediment concentration, C* (2), for 5-f00t intervals from z=5 feet to z=70 feet was determined from the depth-integrated samples. The asterisk is added to dif— ferentiate the standard sediment concentration, expressed as milligrams of sediment per liter of water-sediment mixture, from the fluorescent tracer concentration. The sampling transit rate was relatively uniform at all verti- cals; therefore, the distribution of water weights in the samples across the weir was the same as the distribution of water discharge across the weir. The water-discharge distribution was represented by T; where _net weight at vertical z z—————.——~ (B-l) sum of the net weights The weight of the sand was not subtracted from the net weights of the depth-integrated samples because the sand weight was less than 0.5 percent of the total weight at each vertical. The incremental water discharge at each vertical, q(z), was calculated from (1(2) = TzQ, (13—2) where Q is the measured total water discharge. The incremental sediment-transport rate. (1,.(2). was calculated from am=%mmmt 06 (13—3) where y is the specific weight of the water-sediment mixture. The mean unit sediment-transport rate, q.(z), was obtained from __kmlqwcm _ aM—zfiw 14. ea z=5 where 14 is the total number of verticals at 5-foot inter- vals between z=5 feet and 2:70 feet. The weighting factor, w(z). is given by %m -fiwmm (7s _Z=7" <1_)q(Z)C*(Z)=q(Z)C*(Z). z=5 106 14 4(Z)C*(Z) w(z) = (345) 154 Two additional assumptions were necessary in the appli- cation of the weighting factors obtained from equation B—5 to data obtained at cross section D. First, it was assumed that the variation of the weighting factor with lateral position was the same at cross section D as at the weir; second, it was assumed that the weighting factor at a given lateral position applied to all size classes of material. The shift of the large particles toward the right bank suggests that the second assumption was not exactly true for all sizes; however, the contribution of the large sizes to the total sediment-transport rate was insignificant. The weighting factors obtained from the depth-inte- grated samples for runs 1 and 2 are presented in figure 40. The distribution of the weighting factors across the channel was similar for the two runs. APPENDIX C — CALCULATION SEDIMEN'I‘ TRANSPORT lN ALLUVIAI. CHANNELS 3.00 | l EXPLANATION o Runl / 2.50 ~ 2.00 - 1.50- 1.00 , WEIGHTI NG FACTOR, w(z) DISTANCE FROM RIGHT BANK (1), IN FEET FIGURE 40.—Variation with lateral position of the sediment-transport weighting factors, run': I and 2. OF THE SEDIMENT-TRANSPORT RATES FROM THE DEPTH- INTEGRATED SAMPLES AT THE WEIR Because the depth-integrated samples from the weir were small, the samples generally were not sieved into size classes; and because. these samples were not sieved, only the total number of fluorescent particles of each color was obtained for each sample. Thus, two assump- tions were necessary to permit the calculation of the sediment-transport rates from the numbers of fluores- cent particles in the depth-integrated samples. These as- sumptions and the development of the equation for the calculation of the sediment-transport rate are discussed in the following paragraphs. First, it was assumed that the fluorescent particles were sampled at the weir in the same proportion at which the particles were injected. For example, in run 1 the num- ber of green quartz particles injected was 23.0 X 103, 27.9X 10", and 12.0 X 108 for the 0.125- to 0.177-mm, 0.177- to 0.250-mm, and 0.250- to 0.350-mm sieve classes, respectively. Therefore, it was assumed that 36.6 percent of the green particles in any sample were from the 0.125- to 0.177-mm sieve class, 44.3 percent were from the 0.177- to 0.250-mm sieve class, and 19.1 percent were from the 0.250- to 0.350-mm sieve class. This assumption should be valid if all of the sediment is suspended by the weir and if the depth-integrated sampler functions properly; that is, each size of sediment is sampled in direct proportion to the amount of that size in transport. A problem exists with the fluorescent tracers, however, because the instantane- ous type of injection was used. The fastest-moving parti- cles would be sampled first, and the slowest would be sampled last. This problem was not too great in run 1, where, as was discussed previously, the variation of cen- troid velocity for the sieve classes within a specific color of tracer was not large. In run 2, however, quartz particles of all sizes were coated one color, and, as was discussed pre- viously, the fastest moving particles were the largest and the smallest particles. Thus, it is expected that the quartz tracer particles sampled first were predominately the large and the small particles and that those sampled last were the medium-sized quartz tracer particles. As a re— sult, some deviations from this assumption might occur in run 2. Second, it was assumed that the sieve-size distribution of the depth-integrated samples at the weir did not change with time. If this assumption is valid, then size distribu- tions determined for one sample in each run could be used for all of the depth-integrated samples. Figure 41 shows the sieve-size distributions of two depth-integrated samples, one from each run, obtained at the weir; and figure 42 shows the visual-accumulation-tube size distri- butions of two other depth-integrated samples, one from each run, obtained at the weir. The sieve-size distributions of the two depth-integrated samples presented in figure 41 are essentially identical, even though the time interval between the samples was about 21 hours. Also, the visual- accumulation-tube size distributions presented in figure 42 are similar for two other samples obtained about 24 hours apart. These distributions differ slightly from the sieve-size distributions, particularly at the large diameter TRANSPORT AND DISPERSIOV OF FLUORESCENT TRACER PARTICLES. FLAT-BED CONDITION end of the distributions. This difference was not con- sidered significant, however. On the basis of these size distributions, therefore, the second assumption was con- sidered to be valid. The sieve-size distributions presented in figure 4-1 were used in the calculations in preference to the visual-accumulation-tube distributions presented in figure 42 because the size distributions of the fluorescent tracer materials were determined by sieve analysis. If the sediment-transport rate is assumed to be inde- pendent of time, then the equation for the calculation of the sediment-transport rate from the fluorescent tracer concentrations of the depth-integrated samples has the form a 99.9 , . 99.8 — 99.0 - 98~ 95— 60— 50— EXPLANATION Run Sample time (hr) — 1 1326 20 10 A 2 1015 — PERCENTAGE OF PARTICLES FINER THAN INDICATED SIZE | | I I I I 0.06 0.1 0.2 0.3 0.4 0.6 1.0 DIAM ETER, IN MILLIM ETERS FIGURE 4I.—Sieve-size distributions of two depth-integrated samples obtained at the weir. 155 99.9 | u I I 99.8— 99.5 - 99.0 - 98- 95— 80' 70- 60- 4o— EXPLANATION 10 Run Sample time — (hr) 1542 PERCENTAGE OF PARTICLES FINER THAN INDICATED SIZE 1 504 l I | 0.06 0.1 0.2 0.3 0.4 0.5 DIAM ETER, IN MILLIM ETERS FIGURE 42. —Visual-accumulation-tube size distributions of two depth-integrated samples obtained at the weir. tracer injected. W, has been replaced by N, the number of fluorescent particles of a specific color injected, second, the concentration, C, as grams of fluorescent material per gram of sediment, has been replaced by C', the concentration as number of fluorescent particles per gram of sediment; third, the integration across the channel width has been accomplished by the averaging effect of compositing a set of samples taken across the weir; hence, the transport rate, 03, is the total transport rate for the cross section, and the concentration is a mean concentration, indicated by the overbar, for the cross section. If n(t) is the total number of fluorescent particles of a specific color in a sample at time t and if W(t) is the 156 total weight of sediment in the sample, then A', the inte- gral in equation C—l, can be written ,_ °° n(t) A ‘lu WW1“ With the two assumptions discussed previously, equation C—Z can be written for a specific size class i, or (C—2) ”(0% A.'= __ d , _ ' 0 Wm ‘ (C 3) where p; is the fraction of the total weight of sediment in the sample that is in size Class i, and N,- is the total number of fluorescent particles of size class 1' of a spe- cific color injected at the beginning of the experiment. The quantity Ni/N is a constant for a specific experi- ment, and p,- is independent of time because of the second assumption. Therefore Ni °° ”(5) Arz— dz. 1 Npi 0 W0) (C—4) By comparing equations C—4 and C-2, it follows that SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS Ni , A.’=—A. (C—5) 1 Npi If equation C-l is written for size class i, the result is Ni=Qs1AL (C-6) where AI=L 5§(t)dt. (C—7) By combining equations C-6 and C-5 and rearranging, it follows that _@ 05‘1- _ A/ ' (C_8) Equation C-8 is equation 11, which was used to calcu— late the sediment-transport rates for the different sieve classes from the numbers of fluorescent particles of each color in the depth-integrated samples. Because of the two assumptions, only one integral evaluation was necessary for each color of tracer particle. U. S. GOVERNMENT PRINTING OFFICE : 1971 0L - 405-770 7 DfikY Summary of Alluvial-Channel Data From Rio Grande Conveyance Channel, New Mexico, 1965-69 GEOLOGICAL SURVEY PROFESSIONAL PAPER 562—] Summary of Alluvial—Channel Data From Rio Grande Conveyance Channel, New Mexico, 1965—69 By J. K. CULBERTSON, C. H. SCOTT, and J P. BENNETT SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS GEOLOGICAL SURVEY PROFESSIONAL PAPER 562—] Summary of basic hydraulic and sediment data obtained from a field stream UNITED STATES GOVERNMENT PRINTING OFFICE, VVASHINGTON:1972 UNITED STATES DEPARTMENT OF THE INTERIOR ROGERS C. B. MORTON, Secretary GEOLOGICAL SURVEY V. E. McKelvey, Director Library of Congress catalog—card No. 72-600155 For sale by the Superintendent of Documents, US. Government Printing Oflice Washington, D.C. 20402 — Price 70 cents (paper cover) Stock Number 2401—2184 CONTENTS Page Page Abstract ..................................................................................... J1 Data—collection methods and equipment — Continued Introduction ................................. 1 Vertical velocity profiles ................................................ J5 Description Of study reaches. ------------ 2 Suspended-sediment samples .................... 6 Channel near Bernardo... -------------- 2 Point-integrated sediment samples. 6 Channel near San Marc1al """"""""""" " 3 Depth-integrated samples ..... . .............. 7 Channel near Nogal Canyon ............................. 3 B . . . ed material ....................................... '7 Data-collection methods and equipment ......... 4 Section data 8 Water discharge .............................................................. 4 """""""""""""""""""" Water temperature ......................................................... 4 Reach data """""""""""""""""""" 10 Bed configuration ________ 4 References ................................................................. 11 Cross-sectional areas ....................................................... 4 Appendix 1. Descriptions of observation conditions ....... 14 Water-surface slope ........................................................ 5 Appendix 2. Basic data ......................................................... 26 ILLUSTRATIONS Page FIGURE 1. Location map, channel near Bernardo ............................................................................................................................ J2 2—5. Photographs: 2. Typical views of channel near Bernardo ............................................................................................................ 3 3. Control weir, channel near Bernardo ................................................................................................................ 3 4. Boat with sounder equipment .............................................................................................................................. 4 5. Meter stack and digital-counter box used for obtaining vertical profiles of point velocities... 5 6 Typical velocity profiles over dunes, channel near Bernardo, February 4 and May 12, 1965 ......................... 6 7. Photograph showing U.S. DH—48 sampler modified for point-integrated sampling .............................................. 7 8. Photographs showing bed-material sampling equipment ............................................................................................. 8 9 Hydrographs of water discharge and sediment concentration at the weir (section 194), channel near Ber- nardo .................................................................................................................................................................................. 9 10. Sketch showing plan view of channel near Bernardo ..................................................... 10 11. Graph showing water-surface elevations, channel near Bernardo, February 3, 1965 ......................................... 14 12—14. Longitudinal profiles, channel near Bernardo: 12. May 12, 1965 ............................................................................................................................................................ 15 13. June 2, 1965 ............................................................................. 16 14. June 3, 1965 .............................................................................................................................................................. 16 15. Typical cross section for flat bed form, channel near Bernardo, (section 245), November 30, 1965... 17 16. Longitudinal profile, channel near Bernardo, May 4, 1966 ....................................................................................... 18 17—22. Cross sections, channel near Bernardo: 17. May 4, 1966 .............................................................................................................................................................. 19 18. November 23, 1966 ......................................................................................................... 20 19. February 14—15, 1967... ............... 21 20. May 21, 1968 ........................................................................................................................... 23 21. May 29, 1968 ............................................................................................................................................................ 24 22. June 11, 1969 ............................................................................................................ 24 III IV TABLE CONTENTS TABLES Page Summary of available data ................................................................................................................................................. J26 Measured velocity at indicated heights above riverbed ................................................... 27 Summary of size analyses and related data for point-integrated sediment samples ............................................. 36 Summary of size analyses and related data for depth-integrated sediment samples ............................................. 38 Summary of size analyses of bed material ........................................................................... 40 Cross- sectional data for channel near Bernardo ........................ 42 Summary of average values for streamflow and sediment data for channel near Bernardo ............................. 49 Summary of measured suspended- sediment analyses, May 27— 28, 1965, for channel near Bernardo ............... 49 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS SUMMARY OF ALLUVIAL CHANNEL DATA FROM RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965-69 By J. K. CULBERTSON, C. H. SCOTT, and J. P. BENNETT ABSTRACT The Rio Grande conveyance channel near Bernardo, N. Mex., was the site for a field study of mechanics of flow and sediment transport. During the period of study, the channel bed consisted of sands with median diameters rang- ing from 0.15 to 0.35 millimeters, and the bed form varied from dunes to flat. A few data were obtained at two other locations in the channel system. The report summarizes the basic hydraulic and sediment data obtained during the study. Brief descriptions of equip- ment and procedures of sampling are followed by descriptions of two sets of data. The first set, consisting of a series of measurements taken at individual cross sections, is intended to be descriptive of conditions at successive points along the reach. The second set consists of a series of measurements characterizing the entire length of the Bernardo reach of the channel system. The data described, which include water discharge, cross- sectional area, channel width, slope, point velocity, point- integrated sediment concentration, depth-integrated sediment concentration, and bed material, are summarized in eight tables. Data were obtained for water discharges ranging from 560 to 1,860 cubic feet per second and'slopes ranging from 0.00041 to 0.0011. Also observed were cross-sectional area variations from 143 to 425 square feet and suspended-sedi- ment concentration, of materials in all sizes, ranging from 1,240 to 7,700 milligrams per liter. INTRODUCTION As part of the research program of the Water Resources Division of the US. Geological Survey, a field study of the mechanics of water and sediment movement in alluvial channels was started in July 1964. The study site was the Rio Grande conveyance channel near Bernardo, N. Mex. This site was selected because (1) the channel had a sand bed, (2) bed forms ranging from dunes to flat bed and standing wave had been observed in the channel, (3) a concrete weir across the channel acted as a con- trol for accurate water-discharge measurement and as a sampling point for the total-sediment concentra- tion, and (4) water discharge could be controlled by means of a gated headwork. A few sets 0f data obtained at two other channel sites, near San Mar- cial, N. Mex., and near Nogal Canyon, N. Mex., are included in this report. The primary objective of this study was to collect field data that describe the interrelations among hydraulic and sediment-transport variables over the range of bed forms in sand channels. The secondary objective was to obtain data On the resistance to flow resulting from different bed forms in sand-bed channels. This report is a compilation of the hydrau- lic and sediment data from the Rio Grande convey- ance channel reaches at Bernardo, San Marcia], and Nogal Canyon during the period 1965 to 1969. The data are divided into two sets: those describing the conditions at individual cross-sections and those characterizing the entire length of a particular reach. A brief general description of the channel reaches in which the measurements were made is followed by a description of data-collection methods and equipment and by a discussion of the two sets of data. Appendix 1 is a general description of the conditions prevailing in the study reach when each set of data was collected, and appendix 2 consists of the tables of data collected. Some data presented in this report have been mentioned in earlier interpretative reports. These reports include discussions by Scott and Culbertson (1967) and Scott, Norman, and Fields (1969) on flow-measurement techniques which use fluorescent tracers. Scott (1968) and Scott and Culbertson (1971) reported on resistance to flow in flat-bed alluvial channels, and Culbertson and Scott (1970) discussed sand-bar development and movement in alluvial channels. Other data from this report were used by Fischer (1967 ) in a discussion of transverse mixing in alluvial channels. The project, was started under the general super- vision of Luna B. Leopold, chief hydrologist, Water J1 J2 RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965—69 106°51’ 106°47'30” 34° 25' FIGURE 1.——Location of channel near Bernardo, N. Mex. Numbers along channel designate every 20th sampling sec- tion. Sampling sections are between stations at 100-foot increments on each side of the channel. Resources Division, and continued under Ernest L. Hendricks, chief hydrologist, Water Resources Di- vision. Technical guidance was given by P. C. Benedict, R. W. Carter, Tom Maddock, Jr., D. B. Simons, and others from the Geological Survey. The principal investigators were J. K. Culbertson and C. H. Scott, who were assisted by C. F. Nordin, Jr., E. V. Richardson, W. F. Curtis, V. W. Norman, J. D. Dewey, and others. DESCRIPTION OF STUDY REACHES CHANNEL NEAR BERNARDO The part of the channel near Bernardo, N. Mex. is approximately 6.8 miles long from the gated head- work to the point at which it returns to the Rio Grande floodway channel (fig. 1). The channel was originally a riverside drain. In 1948, the river broke through the drain at the location of the present headwork. The Bureau of Reclamation installed the headwork and straightened the channel, creating the first segment of the present channel. The capac- ity of the headwork is nominally 2,000 cfs (cubic feet per second) ; however, the discharge in the channel usually is limited to less than 1,600 cfs. The channel banks are composed of a sandy clay and are fairly well stabilized by salt cedar and range grass. Where bank erosion has occurred, the banks have been stabilized with rock and gravel. A few hundred feet of Kelner jetties also have been placed along some short reaches for bank stabilization. The channel bed consists of sands with median diameters ranging from 0.15 to 0.35 mm (millimeters). Figure 2 shows the channel during typical low-flow and high-flow situations. In 1964, prior to this study, a concrete control structure was constructed 19,800 feet downstream of the headwork. This structure, referred to as a weir in this report, acts as a control for the gaging station installed at the site. Because baffles placed on the upstream apron of the weir force all sedi- ment into suspension, suspended-sediment samples obtained at a sill on the downstream apron of the weir represent total sediment in transport. The sill is designed so that the nozzle of a US. DH—48 suspended-sediment sampler (discussed later in this report) can be lowered through the entire depth of flow at the weir section. At the bottom of the sam— pler’s descent, its nozzle rests directly on the sill of the weir, which means that the sample represents all of the suspended material and, therefore, all the sediment moving through the section. Gonzalez, Scott, and Culbertson (1969) described the construc- tion of the weir and evaluated its effectiveness as a control structure. Figure 3A shows the sampling sill and the orifice of a bubbler gage installed at the weir. Figure 3B shows the entire weir, baffles, sampling sill, and footbridge; and figure 30 shows a US. DH—48 sampler being lowered to the sampling sill along specially prepared guides which are posi- tioned from the footbridge. SEDIMENT TRANSPORT FIGURE 2.——-Typical views of channel near Bernardo. A, Typical low—discharge situation. B, Typical high-discharge situation. CHANNEL NEAR SAN MARCIAL The San Marcial reach of the channel is between the San Acacia diversion dam and Elephant Butte Reservoir. Data given in this report were collected at a location near San Marcial which is about 41.7 miles downstream of the headwork at San Acacia and about 59.8 miles downstream of the headwork at Bernardo. The channel near San Marcial is a dug channel with a capacity of about 2,000 cfs. The channel bed in this reach consists of sand having a median diameter of about 0.18 mm. The channel banks are sand and gravel. CHANNEL NEAR NOGAL CANYON The Nogal Canyon reach is about 18.8 miles down- stream of the San Marcial reach. This reach has a FIGURE 3.——Control weir, channel near Bernardo. A, Sam- pling sill and bubbler—gage orifice. B, Weir, baffles, sam— pling sill, and footbridge. C, U.S. DH—48 sampler in use from footbridge. IN ALLUVIAL CHANNELS J3 J4 RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965—69 sand bed consisting of material having a median diameter of about 0.18 mm. The channel banks in this reach are unstabilized sand and clay. At the time the data of this study were collected, the banks were deteriorating under high-flow conditions. DATA-COLLECTION METHODS AND EQUIPMENT WATER DISCHARGE Water discharge was obtained either from the record of stage and the stage-discharge relation for the gaging station at the weir at station 194 or from water-discharge measurements. Gonzalez, Scott, and Culbertson (1969) discussed the stage-discharge relation for the gaging station at the weir. The water-discharge measurements were made at the cableway of US. Geological Survey gage 08—33199, at station 180, 100 feet upstream of the US. 60 highway bridge. The measurements were made by current meter using standard US. Geological Survey methods as described by Buchanan and Somers (1969). The discharges reported in the tables of basic data are the means for the periods unless the discharge varied considerably, and then the discharge at the time of observation is reported. WATER TEMPERATURE Water temperatures were determined several times during each observation period. Temperatures are reported to the nearest degree Celsius in the tables of basic data. The range in temperature usually was not more than 2° or 3° Celsius during any period of observation. BED CONFIGURATION Profiles of the streambed were obtained with an ultrasonic sounder (Richardson and others, 1961). The sounder was mounted in a boat, with the trans- ducer in a well near the center of the boat (fig. 4). The bed-form classification used herein conforms to that presented by the Task Force on Bed Forms in Alluvial Channels (1966). Longitudinal profiles of the bed form were obtained for those data-collection periods when the bed form was transition or dunes. The profiles generally were obtained at the ap— proximate quarter points of the channel width. Be- cause the speed of the boat varied somewhat through the length of the reach, marks at 50-foot intervals of boat movement, as indicated by stationing on the bank, were placed on the chart of the sounder pro- file. Variations in length of chart per unit distance traveled by the boat usually were not large, and an average scale value was computed and applied to each separate longitudinal profile. The average length of dunes was computed by FIGURE 4.— Boat with sounder equipment. dividing a distance by the number of dunes occurring in that distance, and the average height of dunes was computed as the sum of heights, measured from crest to downstream trough, divided by the number of heights measured on the profile. This method of determining average length and height of dune is subjective because different persons may not agree as to what should be called a dune on the profile, particularly when smaller dunes appear to be super- imposed on larger dunes. The classification of the bed form as dunes, transition, or flat is based on the observer’s best judgment and is also, therefore, somewhat subjective. CROSS-SECTIONAL AREAS Cross—sectional areas were determined either from cross-section profiles obtained with the ultrasonic sounder or from depths obtained with a sounding rod. To determine profiles with the ultrasonic sounder, the transducer was placed a known distance below the water surface in the well in the boat. A cable was stretched tightly across the section, and the boat was hooked to the cable by means of a crossarm. The boat was pulled across the channel at about one- half foot per second by means of a second cable and a constant-speed-drive motor. Reference marks at 2-foot intervals of distance traversed in the cross section were marked automatically on the sounder chart of the profile. The depths at verticals near the banks were determined with a wading rod. Cross- sectional profiles usually were determined with the ultrasonic sounder when there were dunes because of the softness of the bed and the relatively large changes in bed elevation in the cross section. The cross-sectional area was determined by planimeter- ing the cross-section profile, taking into account SEDIMENT TRANSPORT the distance of the transducer face below the water surface. Cross sections usually were obtained with a sound- ing rod when the bed was hard and had relatively constant elevation; it was possible to determine depth to the nearest 0.1 foot with the sounding rod. It was assumed that the depth at a given vertical applied to half the distance between adjacent verti- cals, and the cross-sectional area was computed as the sum of subareas. WATER-SURFACE SLOPE Water-surface slopes were determined from water- surface elevation taken near the banks either with a level and rod or from staff—gage readings. Water-surface elevations generally were obtained twice a day at 100-foot intervals over reaches 1,000 to 1,200 feet in length. The water-surface elevations were plotted, and a mean slope was determined graphically. Because the readings were taken near the banks, local conditions could have affected water-surface elevation. For example, a dune near the bank could affect the water-surface elevation. However, water- surface slopes determined by this method generally were consistent for any given day. VERTICAL VELOCITY PROFILES Vertical velocity profiles were obtained with stand- ard Price current meters equipped with magnetic heads which produced two impulses per revolution of the current-meter bucket wheel. Five current meters were mounted on a sounding rod, and the impulses from the meters were recorded by digital counters (fig. 5) which were started and stopped together by single switch. Point velocity was com- puted from counts produced by the current meter for a 1-minute period. The average of the five indi- vidual meter ratings was used for converting meter counts per unit time to stream velocity. For a given meter count per unit time, the maximum difference between the average rating and any of the individual . ratings was about 1 percent. The results of extensive tests of meters indicate that an average rating for meters can be used (Smoot and Carter, 1968). Ratings taken from meters all mounted on one rod were checked in a towing tank and did not depart from the individual ratings when meter spacing was as close as 0.5 foot (R. W. Carter, written commun.). Because the velocity at as many as five points in the vertical could be obtained at one time, it was possible to obtain 10—12 vertical velocity profiles at a cross section in 20—30 minutes. Usually the bottom four meters were set at fixed depths, and only the position of the top meter was changed when a large 472-032 0 - 72 — 2 IN ALLUVIAL CHANNELS J5 change in depth of flow occurred from one vertical to another. The depth of flow at the vertical was measured on the rod on which the meters were mounted, and the meters were assumed to be the same distance above the bed as they were above the base plate of the rod. At some verticals the rod would settle because of the weight of the rod and meters and the softness of the bed. When this hap- pened, the indicated depth of the rod was noted, and the actual depth was measured with another sound- ing rod. The indicated distances above the bed at which the velocities were obtained were adjusted accordingly. Velocity profiles for the flat bed form, when plot- ted as loglo y versus velocity, Where y is the eleva- tion above the streambed, generally were consistent except at verticals near the banks. Near the banks, the slopes (the difference in velocity at y and 102/ distances above the bed) and intercepts (the velocity 1.0 ft above the bed) of the profiles varied because of the roughness of the banks. Velocity profiles for dune bed forms generally were less consistent than profiles for flat bed forms. FIGURE 5.—Meter stack and digital-counter box used for obtaining vertical profiles of point velocities. J6 The slopes and intercepts of the velocity profiles varied across the channel. The value of the slope and of the intercept of the profile depended on the location of the vertical with respect to a dune. Figure 6 shows typical velocity profiles obtained down- stream of points near the middle of the channel on February 4 and May 12, 1965. Near the crests of the dunes, the velocities were high and nearly equal at all points in the verticals. This is a result of ac- celeration of the flow caused by the decrease in depth toward the crest of the dune. In the trough between dunes, the velocity 1 foot from the bed was relatively low and increased considerably from near the bed to near the surface in the vertical. This is a result of deceleration of the flow as the depth increases rapidly from the crest to the trough. Immediately downstream of the crest of the dune, flow near the RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965-69 attempt was made to determine the direction of flow in the troughs between dunes, and some velocities obtained near the bed in troughs may actually have been negative, even though they were recorded as positive. Velocity profiles were especially difficult to obtain in the troughs because sand stopped the lower meters before sufficient counting time had elapsed. SUSPENDED-SEDIMENT SAMPLES POINT-INTEGRATED SAMPLES Point-integrated samples of suspended sediment were obtained at five points in each of three to five verticals in a cross section. The samples at each point were analyzed for concentration and for size distri- bution of sediment coarser than 0.062 mm. The analysis was performed using a visual-accumulation tube according to the methods described by Guy bed may have been in an upstream direction. No (1969) and by the US. Inter-Agency Committee on E m _ LI. .2. / ' d ... - In I l I : m - < _ E Q ~ 0 3 5 7 9 12 15 17 21 24 27 30 33 39 ‘ “J I 01 I l I I I l 41 J I I '12323 234 234 254 34 34 0123412323234343434234 ._ fl VELOCITY, IN FEET PER SECOND IE 3 E FEBJI. 1965 E I. 4 ._ a 5 I I I I I 1 | I I ‘3 o 5 10 15 20 25 30 35 4o DISTANCE DOWNSTREAM. m FEET 7.o_ ,_ _ W a E _ Z - I— d |.|J m 1.0: w c > _ o _ fl : E / g » o 5 I0 15 20 25 so 35 4o 45 50 55 so 65 I 0.1 | I l I I I I I | I I J l I I 345345341234123423423412341234234345234 45 45 ._ 4 _ VELOCITY, IN FEET PER SECOND 5 MAV12,1965 u. 5 —- E. 6 ~ 0 8 —I I l I I I I I I I I I I I o 5 10 15 20 25 so 35 40 45 so 55 so 65 DISTANCE DOWNSTREAM, IN FEET FIGURE 6. ——Typical velocity profiles over dunes, channel near Bernardo, February 4 and May 12, 1965. Values in rectangles are distances downstream, in feet. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS J7 Water Resources (1957). None of the point samples were analyzed for size distribution of sediment finer than 0.062 mm. The samples were taken with a US. DH—48 sampler modified for point sampling (fig. 7). The modified sampler was equipped with a pres- sure-equalization chamber that was connected to the sample chamber and vented to the outside. Water- tight covers sealed the water-inlet nozzle and the air-outlet port. The covers could be opened and closed together by means of a pull cable. The length of sampling time varied inversely with stream velocity, from 5 to 6 seconds for high-velocity flows to 12 to 15 seconds for low-velocity flows. Because the local flow conditions could change with time at a given vertical, particularly where the bed form was dunes, it was desirable to obtain samples at all points in the vertical as quickly as possible. Therefore, only one to three samples were obtained at a given depth in each vertical, and because of the short sampling time involved, some variability in the concentration sampled at a given depth probably was introduced because short-term fluctuations of concentration were not adequately averaged. FIGURE 7.—U.S. DH—48 sampler modified for point-inte- grated sampling. DEPTH-INTEGRATED SAMPLES Depth-integrated samples of suspended sediment at a cross section were obtained with a US. DH—48 sampler. In the sampling method used, the Equal-- Transit Rate (ETR) method, the sampler is moved at the same transit rate for each one of a set of equally spaced verticals in the cross section. The sediment concentration of the composite of all samples collected from the cross section is the aver- age concentration of the suspended material moving in the sampled zone (Guy and Norman, 1970; Task Committee on Preparation of Sedimentation Manual, 1969). Samples were collected at verticals 5 feet apart, and the composited samples for each cross section were analyzed for concentration and for size distribution of sediment coarser than 0.062 mm. The size distribution of sediment coarser than 0.062 mm was determined by the visual-accumulation-tube method (U.S. Inter-Agency Committee on Water Resources, 1957; Guy, 1969). In addition, the size distribution of sediment finer than 0.062 mm was determined for a few samples by the pipette method (U.S. Inter-Agency Committee on Water Resources, 1941; Guy, 1969). Depth-integrated samples of suspended sediment were obtained by the ETR method with a US DH— 48 sampler at verticals spaced at 5-foot intervals across the weir (section 194). A sampling lip with a guide slot allowed the nozzle of the DH—48 sam- pler, which was mounted on a guide frame, to tra- verse the full depth of flow. In this way, samples represented essentially the total material passing the weir. Each set of samples was composited and ana- lyzed for concentration and for size distribution of sediment coarser than 0.062 mm. Size distribution of sediment finer than 0.062 mm was determined for a few samples. In this report, samples obtained by the ETR method at the sampling section on the weir (section 194) will be referred to as total-sediment samples, and samples obtained by the ETR method at any other sampling section will be referred to as mea- sured suspended-sediment samples. BED MATERIAL Samples of bed material were obtained usually at 10-foot intervals across cross sections in the study reach. Analyses of samples from the individual points in cross sections for two flow conditions in- dicated no great variation in size distribution of bed material from point to point in the cross sec- tions, and therefore, all other bed-material samples were composited into a single sample for a cross section. The samples were analyzed for size distribu— tion by the Visual-accumulation-tube method in the laboratory. The values of dm, d50, and d8, were scaled from the original curve on the visual-accumulation- tube chart. The value of the gradation coefficient, 0', was computed from the equation dso ds4 a—V2( (116+ d...)' (1) .For flow depths greater than 3 feet, most samples of bed material were obtained with a hand-held clam- shell-type sampler (fig. 8A). The sampler was J8 RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965—69 equipped with a seal to prevent loss of fine material from the bucket as the sampler was raised to the surface. The bucket sampled to a depth of about 0.1 foot. For flow depths less than 3 feet, samples were obtained either with the clamshell sampler or with the U.S. BMH—53 piston-type (fig. SB) sampler Committee on Water Resources, (Inter-Agency B FIGURE 8.—Bed-material sampling equipment. A, Hand— held clamshell-type sampler. B, U.S. BMH—53 piston-type sampler. Rule is 6 inches long. 1959). The core barrel of the piston sampler is 8 inches long, but only the top 0.1 foot of the core was retained for analysis. SECTION DATA The data collected for the description of flow conditions at individual cross sections in the Ber- nardo, San Marcial, and Nogal Canyon reaches of the Rio Grande conveyance channel are summarized in tables 1 through 5 of appendix 2. Given in ap— pendix 1 are detailed descriptions of the flow and channel characteristics prevailing in the reaches prior to and during the data-collection periods. The authors strongly recommend that, before using ap- pendix 2, one study the pertinent sections of appen- dix 1 to become aware of the prevailing conditions when measurements were made. Table 1 summarizes available section data, in chronological order, for the Bernardo, San Marcial, and N ogal Canyon sites. The term “section,” as used in this report, refers to the cross section’s location. The number in column 2 assigned to a section for the Bernardo observations is the distance, in hun— dreds of feet, downstream of the first cross section downstream of the headwork. The first cross section, section 0, is 400 feet downstream of the headwork. Section 20 is 2,000 feet downstream of the first cross section and is therefore 2,400 feet downstream of the headwork. The number in column 2 assigned to a section for the San Marcial and Nogal Canyon ob- servations is the distance, in hundreds of feet, up- stream of Elephant Butte Dam. For example, section 2261+00 in the San Marcial reach is 226,100 feet upstream of Elephant Butte Dam. In table 1, water discharge, cross-sectional area, water—surface width and slope, and bed form were determined as discussed earlier in this report; any special conditions are discussed in appendix 1. In column 2 of this table, the notation “Reach” indicates that the data listed were averaged from the partic- ular cross sections listed in the remarks column. Figure 9 shows daily—mean water discharge and daily-mean sediment concentrations for 10-day peri- ods prior to the day on which data were collected for each of the observation periods. This informa- tion should be considered in interpreting data shown in the tables of basic data. Table 2 gives measured velocities at five points in the vertical in some of the cross sections listed in table 1. The velocities were measured using a rack of five Price current meters over a counting period of 60 seconds. Typical velocity profiles over a dune bed are plotted in figure 6. Table 3 gives the size analyses and related data for the point—integrated sediment samples. The SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS samples were collected with a modified U.S. DH—48 sampler and were analyzed by means of the visual- accumulation-tube method. At sampled verticals in the cross section, size analyses are given for each point in each vertical. The analyses data are given both as the percent finer than a given reference size and as the concentration, in milligrams per liter, in a given size class. Related parameters reported are water discharge, water temperature, and total depth of flow at the point in the cross section where the samples were collected. 'Table 4 gives the size analyses and related data for the depth-integrated sediment samples. The sedi- ment samples were collected with a US. DH—48 sampler and the ETR collection procedures; they were analyzed by means of the visual-accumulation- tube method for the material coarser than 0.0625 J9 mm and the pipet method for material finer than 0.0625 mm. The weir at section 194 is designed so that all sediment moving in a vertical can be sampled by means of a US. DH—48 sampler. There— fore, the sediment sampled at the weir represents the total-sediment load at that section. The analyses for a composite of the samples collected in the cross section at a particular time are listed both in terms of percent finer than a given reference size and as concentration, in milligrams per liter, in a given size range. Related parameters listed are water dis- charge, water temperature, median particle diam- eter, and gradation coefficient. The water discharge listed is that at the time the sediment samples were collected. Table 5 summarizes size analyses of bed material. The material, obtained from the upper 0.1 foot of 1000 3000 1800 — a 4000 2200 — - 9000 JAN 24-FEB 51965 300 2000 1600 _ APR 24—MAv 6, 1966 _ 3000 2000 _ MAY 11_23, 1968 _ 8000 \ _\ I\ 600 1000 1400 — W — 2000 1800 7000 \ _ 1 400 o 1200 — — 1000 1600 6000 1000 1 | 1 | 1 | 1 l 1 l L | 1 0 1400 5000 24 26 23 30 2 4 6 E 1200 4000 1400 6000 180° ‘ ‘ 9000 1000 3000 1600 NOV 13-25. 1966 8000 5000 — ‘ 1: 1200 MAY 2-14,1965 800 2000 'E’ g 1000 4000 1400 7000 1: Q 1.14 w 1200 6000 L m 800 3000 1400 — — 6000 g E w 1000 5000 < ,°_' 60° 2000 1200 — 5000 5 DJ .J m =1 Z 1000 — — 6000 1000 4000 2 E1 JAN 23-FEB 4. 1967 E 3 1300 7000 800 — - 5000 800 3000 g- z W _ — _ / r f _ 1 I 1 l 1 1 1 1 1 1 1 1 1 2000 V— 131“ 150° 5°00 50° - \ / V \’ \ 400° 60° 19 21 23 25 27 29 31 E 1: Z < 400 1 I 1 1 1 1 1 1 1 1 l 1 3000 L 11.1 g ”0“ 5°00 23 25 27 29 31 2 4 g ‘3 1200 4000 G 8 2 1900 1‘ 7000 ’2 H1! 1- 1000 3000 1000 — — 5000 \ 1g ‘3‘ FEB 4—16. 1967 1700 MAY 31-JUNE 12, 1969 II \ 6000 E 00 — \ — 300 2000 8 4 400° 1500 '\ 5000 m 600 \jf" \ 7 — 3000 V \ / \ \ 1300 4000 400 1 l 1 I 1 l 1 I 1 I 1 l 1 2000 4 6 s 10 12 14 16 1100 3000 1600 7000 H NOV 19-DEC 1, 1965 900 200° 1400 5000 1000 - — 5000 JAN 22-FEB 3, 1968 700 1000 1200 5000 600 — / ,‘ — 4000 31 2 4 6 8 1° 12 M M \ 1000 4000 600 - /\\/\/ — 3000 EXPLANATION f _‘ / 800 3000 400 1 I 1 | 1 l 1 » | 1 I 1 l 1 2000 - 19 21 23 25 27 29 1 22 24 26 28 3 1 3 W:te:d:s_c}jr€e D J Sediment concentration FIGURE 9. —- Hydrographs of water discharge and sediment concentration at the weir (section 194), channel near Bernardo. J10 the bed, was collected with either a clamshell-type sampler or a US. BMH—53. The samples analyzed were actually composites of samples from several points (usually at 10-ft intervals) in the cross sec- tion. Listed in addition to percent finer than a given reference size are median diameter, gradation co— efficient, water discharge and temperature, and bed form. REACH DATA Hydraulic data collected at each section in the Bernardo reach are shown in table 6. Generally, data were collected at sections 2,000 feet apart; however, 4,000-foot intervals were used for some observations. The data from table 6 were used to compile the average values shown in table 7. The weir divided the channel into two reaches. Channel widths up- stream of the weir were greater and more variable than the relatively uniform channel widths down- stream of the weir (fig. 10). Some of the observa- tions were completed in 1 day; others, over 2 days. Table 7 was developed from table 6. Water dis- charge is the mean discharge at the weir for the period of observation. Reach length is the length, in feet, between the two end sections. Mean water- surface width is the average width of all sections within the reach length. Mean depth of flow is the average of the areas of each section within the reach length divided by the average width. Mean velocity is the mean discharge during the period divided by the average area within the reach length. Water- surface slope is the mean slope of a graph of ob- served water-surface elevations versus distance. Water temperature is the average during the period of observation. Median diameter of bed material is the average of the (150 at each section within the reach length. Fall velocity and gradation are for the d50 shown. The dominant bed form listed in table 7 is based , on the qualitative field observations. If the majority 100 FEET O Headwork | I I I I I I 80 100 120 140 160 RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965—69 of the sections were classified as dune, the reach length was classified as dune. For some observations, bed form varied from section to section, and no specific bed form was considered to be dominant; therefore, the reach was classified as transition. No practical method for the classification of discrete bed forms in an alluvial channel has been de- termined; therefore, the classification of bed form remains qualitative, based entirely on the authors’ observations and judgments. In cases where the longitudinal variation of bed form was considered to be excessive, not all sections listed in table 6 were used in determining the reach data of table 7. In table 7, the values of suspended-sediment con- centration for all observations prior to September 30, 1965, are daily mean concentrations. They were determined from suspended-sediment samples col- lected usually at section 180. Beginning October 1, 1965, the suspended—sediment concentrations shown are total-sediment concentrations determined from samples collected at the weir, section 194. In table 7, Manning’s n was computed for each reach observation from the relation ”:1.49 D”3 S”2 V ’ where D is mean depth of flow, in feet, S is average water-surface slope, and V is mean velocity, in feet per second. The range in values of Manning’s n for the reach data was approximately twofold. The n values for flat bed forms generally were from 0.015 to 0.017 for dune bed forms, from 0.023 to 0.033; and for transition bed forms, from 0.019 to 0.024. The flow conductance coefficient, C/ V57, was computed from the relation V C/ VIE—W, where D is mean depth of flow, in feet, S is average water-surface slope, V is mean velocity, in feet per (2) (3) To floodway —.—_. | I l | | | l l | 180 200 220 240 260 280 300 320 340 SECTION NUMBER FIGURE 10. -— Plan view of channel near Bernardo. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS second, and g is the gravitational constant, 32.2 feet per second. The range in values of C/Vg for these data was from about 21 for the flat bed form to 11 for the dune bed form. For flat bed forms, values of C/Vg generally ranged between 18 and 21; for dune bed forms, values ranged between 10 and 13. Transition reach values of C/\/g generally were between 13 and 18. Measured suspended-sediment samples for May 27—28, 1965, were collected at all sections in the reach. These observations (table 6) illustrate the unsteady sediment transport from section to section through the length of the conveyance channel. Table 8 gives the particle-size distributions and size-class concentrations of these samples. The format of table 8 is essentially the same as that of table 4. REFERENCES Buchanan, J., and Somers, P., 1969, Discharge measurement at gaging stations: U.S. Geol. Survey Techniques Water- Resources Inv., book 3, chap. A8, 65 p. Culbertson, J. K., and Scott, C. H., 1970, Sandbar develop- ment and movement in an alluvial channel, Rio Grande near Bernardo, New Mexico, in Geological Survey Re— search 1970: U.S. Geol. Survey Prof. Paper 700—B, p. B237—B241. Fischer, H. B., 1967, Transverse mixing in a sand-bed chan- nel, in Geological Survey Research 1967: U.S. Geol. Survey Prof. Paper 575—D, p. D267—D272. Gonzalez, D. D., Scott, C. H., and Culbertson, J. K., 1969, Stage-discharge characteristics of a weir in a sand- channel stream: U.S. Geol. Survey Water-Supply Paper 1898—A, 29 p. Guy, Harold P., 1969, Laboratory theory and methods for sediment analysis: U.S. Geol. Survey Techniques Water- Resources Inv., book 5, chap. Cl, 58 p. J11 Guy, Harold P., and Norman, W., 1970, Field methods for measurement of fluvial sediment: U.S. Geol. Survey Techniques Water-Resources Inv., book 3, chap. CZ, 59 p. Richardson, E. V., Simons, D. B., and Posakony, G. J., 1961, Sonic depth sounder for laboratory and field use: U.S. Geol. Survey Circ. 450, 7 p. Scott, C. H., 1968, Flow resistance in plane-bed alluvial chan— nel: Fort Collins, Colorado State Univ., M.S. thesis. Scott, C. H., and Culbertson, J. K., 1967, Discussion of “Flow measurements with fluorescent tracers”: Am. Soc. Civil Engineers Proc., Jour. Hydraulics Div., v. 93, no. HY3, p. 211—216. 1971, Resistance to flow in flat-bed sand channels, in Geological Survey Research 1971: U.S. Geol. Survey Prof. Paper 750—B, p. B254—B258. Scott, C. H., Norman, V. W., and Fields, F. K., 1969, Reduction of fluorescence of two tracer dyes by contact with a fine sediment, in Geological Survey Research 1969: U.S. Geol. Survey Prof. Paper 650—B, p. 3164— B168. Smoot, G. F., and Carter, R. W., 1968, Are individual cur— rent-meter ratings necessary?: Am. Soc. Civil Engineers Proc., Jour. Hydraulics Div., v. 94, no. HY2, p. 391—397. Task Force on Bed Forms in Alluvial Channels, 1966, Nomenclature for bed forms in alluvial channels: Am. Soc. Civil Engineers Proc., Jour. Hydraulics Div., v. 92, no. HY3, p. 51—65. Task Committee on Preparation of Sedimentation Manual, 1969, Fluvial sediment, part A of Sediment measure- ment techniques: Am. Soc. Civil Engineers Proc., Jour. Hydraulics Div., v. 95, no. HY5, p. 1477—1515. U.S. Inter-Agency Committee on Water Resources, Sub— committee on Sedimentation, 1941, Methods of analyz- ing sediment samples, Report 4 of A study of methods used in measurement and analysis of sediment loads in streams: Washington, U.S. Govt. Printing Office, 203 p. ___1957, The development and calibration of the visual- accumulation tube, Report 11 of A study of methods used in measurement and analysis of sediment loads in streams: Washington, U.S. Govt. Printing Office, 109 p. 1959, Federal Inter-Agency sedimentation instru- ments and reports, Report AA of A study of methods used in measurement and analysis of sediment loads in streams: Washington, U.S. Govt. Printing Office, 38 p. APPENDIXES J14 APPENDIX 1. DESCRIPTIONS OF OBSERVATION CONDITIONS FEBRUARY 3—4, 1965 Water discharge in the channel was relatively constant for 10 days prior to January 24. From January 24 to January 30, the discharge decreased from about 600 to 500 cfs. The discharge then began to increase slowly (fig. 9A). Four water-discharge measurements obtained on February 3 averaged 560 cfs, and on February 4 five measurements averaged 575 cfs. The daily—mean sediment concentration varied between 1,000 and 2,000 mg/l (milligrams per liter) during the period January 24 to February 1 (fig. 9A). Water temperature varied from 6°C at 0800 hours to 1100 at 1600 hours on both days. Bed forms in the channel were observed period- ically by means of a sonic sounder beginning on January 14. On January 14 the bed form throughout the channel was flat. By January 20, however, an 850-foot reach of dunes had developed, beginning at a point 850 feet upstream of section 220. Down- stream of section 220 the bed remained flat. By January 29, the dune reach had lengthened to 1,650 feet, beginning 700 feet farther downstream than on January 20. On January 31, the dune reach was 1,850 feet long; the beginning point had moved downstream another 300 feet, and the downstream point of the dune reach was at section 240. On February 3, the downstream end of the dune reach. was at section 246.5, and on February 4 it had reached section 247. The dune bed form was three dimensional throughout the dune reach. Crest-to- crest length of the dunes was 20 to 25 feet, and dune heights were from 1.5 to 2.5 feet. Profiles of the channel cross section were obtained with the ultrasonic sounder on February 3 at sec- tions 236, 238, and 240 in the dune-bed reach and at sections 250 and 255 in the flat-bed reach. The profile at section 252 in the flat-bed reach was ob- tained with a sounding rod. The average cross- sectional areas and widths for the three sections in the dune-bed reach and for the three sections in the flat-bed reach are shown in table 1. Water-surface elevations were determined once for the reach from section 223 to 257 and once for the reach from section 234 to 246 on February 4. Elevations of water surface were determined along the left bank at 100-foot intervals; where bed form changed from dunes to flat, 25-foot intervals were used. Figure 11 shows the water-surface elevations through the 3,200—foot reach from section 223 to 255, including the dune-bed reach and the flat-bed reach, for one of the observations on February 3. Vertical velocity profiles in the cross section were RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965-69 obtained on February 3 at section 252 (flat bed form), and at section 240 (dune bed form) on February 4. Profiles were obtained at 5-foot intervals. Total-sediment samples were collected at the weir (section 194) on February 3 and 4; measured sus- pended—sediment samples were collected at sections 236 and 255 on February 3 and at section 255 on February 4. Samples of bed-material were collected on Febru- ary 4 in the dune—bed reach at section 238 and in the flat-bed reach at section 255. The analyses shown in the tables of basic data are for composite samples at each cross section. Individual samples were taken at nine points in the cross section at section 238 (5-ft intervals) and at six points in the cross section at section 255 (5-ft intervals). The median diameter of bed material for the samples at section 238 (dune bed form) varied from 0.22 to 0.27 mm, and the average value was 0.24 mm. The median diameter at section 255 (flat bed form) varied from 0.17 to 0.22 mm, and the average value was 0.19 mm. MAY 12—13, 1965 Water discharge fluctuated between about 700 and 1,000 cfs during the 10-day period prior to these observations. Daily-mean sediment concentrations varied between 2,800 and 4,300 mg/l. Both water discharge and sediment concentration remained rela- tively constant during May 12-13 (fig. 98). Water temperature varied from 14°C to 17°C on May 12 and from 15°C to 160C on May 13. Bed form was three—dimensional dunes prior to and during these observations. Figure 12 shows the longitudinal profile for the reach between sections 245 and 255, at the approximate centerline of the channel. Sketches of three cross sections, 245, 250, 4723 lllllllllllllllllll , Slope = 0.00053 010,9 bed 4722 — 4721 '- WATER-SURFACE ELEVATION, IN FEET ABOVE MEAN SEA LEVEL 4720 | l l l l l l l | | l l l l l | l | l 220 230 240 250 260 SECTION NUMBER FIGURE 11.—Water—surface elevations, channel near Ber- nardo, February 3, 1965. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS and 255, also are shown to illustrate the three-di— mensional bed form. The average height and length of dunes, as determined from the longitudinal pro- file along the centerline of the channel from section 240 to 260, were 2.6 feet and 47 feet, respectively. Cross-sectional profiles were obtained with the ultrasonic sounder at 14 sections on May 12 and 13. The profiles were obtained at 100—foot intervals from section 243 to 255. A profile also was obtained at section 260. The cross-sectional areas (A) ranged from 238 to 350 square feet and averaged 300 sq ft on May 12, and they ranged from 264 to 368 sq ft and averaged 300 sq ft on May 13. Water—surface elevations were determined four times each day over the 1,200-foot reach from section 243 to 255. Elevations of the water surface were determined at 100-foot intervals along both banks. The individual determinations of slope of the water surface ranged from 0.00060 to 0.00069 on May 12 and from 0.00063 to 0.00067 on May 13. The average slope for each day, as shown in table 1, was 0.00065. Vertical velocity profiles were obtained at 5-foot intervals at sections 249 and 250 on May 12 and at section 250 on May 13. The average concentrations of total sands, or ma- terial coarser than 0.062 mm, determined from samples collected at the weir were 920 mg/l on May 12 and 910 mg/l on May 13. Concentrations of fine material (finer than 0.062 mm) averaged 2,430 mg/l on May 12 and 2,150 mg/l on May 13. Samples ob- tained at the weir and at section 240 were collected at 1- to 2—hour intervals each day. Samples of bed material were collected at 15 cross sections on May 12 and at three cross sections on May 13. JUNE 2—3, 1965 Daily-mean water discharge averaged about 900 cfs from the time the observations were made on J15 May 12 and 13 until May 24. The large dune bed configurations present on May 12 and 13 remained during this period. Beginning May 24, the discharge in the channel was increased by about 100 cfs per day by opening the headgates. This was done to ob- serve changes in bed form resulting from the in- crease in discharge. Large transverse bars were formed as a result. Culbertson and Scott (1970) described the development and movement of these transverse bars during the period May 24—29. The discharge was reduced from the high of about 1,450 cfs on May 29 to about 1,200 cfs on June 2 (fig. 90), at which time the observations in this report were made. Daily-mean sediment concentrations de- creased from an average of about 5,300 mg/l on May 25 to an average of about 3,200 mg/l for the period May 27 to June 4 (fig. 90). The values given for water discharge in table 4 were determined from the stage-discharge relation for the stages at the weir for the times shown. On June 2, data were obtained at section 250 in a dune reach. Figure 13 shows the longitudinal pro- file of the reach between sections 244 and 256. Cross- sectional profiles of sections 245, 250, and 255 also are shown with mean depths and mean velocities indicated. Observations were made June 3 at section 322 over one of the large transverse bars that had formed during the period May 24—30. Figure 14 shows the longitudinal profile of the reach between sections 316 and 327. The bed was Virtually flat for about 650 feet and varied little in depth across the channel. Cross-sectional profiles were obtained with the ultrasonic sounder at 15 sections on June 2. The up- stream profile was at section 240, and the next was at section 243. The remainder of the profiles were obtained at 100—foot intervals to section 255 and at section 260. The average width and average area WIDTH, IN FEET WIDTH, IN FEET WIDTH, IN FEET 0 10 20 30 40 50 60 >70 80 90 o 10 20 30 4o 50 60 70 80 o 10 20 30 4o 50 60 7o '_ IIIIIIII IIIIIITI IIIIIII a A:350 “2 2 2 A2338 “2 2 2 [1:278 “2 u_ 1 _ D=4.55 ft D=4.51 ft D=4.08ft E V=2.60 fps 4 4 V=2.69 fps 4 4 V:3.27 fps n: o 2 — 5 e 6 s —l < E Section 245 Section 250 m Section 255 3 3 - K DJ ’2 4 _ g _ a S 5 — _ W on I E s — _ Ian! D 7 1 I l l I I I I I I I 244 245 246 247 248 249 250 251 252 253 254 255 256 SECTION NUMBER FIGURE 12.—Longitudinal profile, channel near Bernardo, May 12, 1965. J16 for the 15 cross sections are given in table 1. The widths ranged from 66 to 77 feet, and areas ranged from 209 to 365 sq ft for the 15 cross sections. Slopes were determined from water-surface eleva- tions obtained at 100-foot intervals twice on June 2 from section 243 to 255 and twice on June 3 from section 320 to 325. Average slope through the dune reach (1,200 ft) was 0.00073, and average slope through the flat-bed reach (500 ft) was 0.00052. Vertical-velocity-profile data collected at sections 250 and 322 at 5-foot intervals are given in table 2. The average sand concentrations at the weir were 1,400 and 1,440 mg/l, respectively, for June 2 and 3. Fine-material concentration increased from an aver- age of 1,430 mg/l on June 2 to an average of 2,010 mg/l on June 3. Samples of bed material were collected twice at WIDTH, IN FEET RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965—69 section 250 on June 2. The first set of samples was obtained at 1100 hours, apparently on or near the crest of the large dune form seen on the sounder chart (fig. 13) ; the d50 of the composite sample was 0.20 mm. The second set of samples was obtained 4 hours later, at 1500 hours. The crest of the dune had moved downstream 30 to 50 feet, so that the d50 of 0.24 mm was representative of the material closer to the trough upstream of the dune. The composite of samples collected at section 322 on the back of the large transverse bar had a d50 of 0.18 mm. NOVEMBER 29430, 1965 Water discharge decreased from about 1,400 cfs on November 19 to 1,000 cfs on November 28 (fig. 90). The headgates were cleaned and opened farther on the morning of the 29th, and the discharge in- creased to about 1,250 cfs. It then remained fairly WIDTH, IN FEET 0 20 40 60 80 0 20 40 60 80 WIDTH, IN FEET 0 20 40 60 80 | I I D:4.75 ft V=3.58 fps To floodway Section 245 Section 250 DEPTH BELOW WATER SURFACE, 0 I | I . i I I 1 _ D=3.21ft V=4.82 fps 2 2E 0:234 ft V=5.48 fps 12 2 2 — 4 4 4 4 3 6 _ E E Section 255 u.4 _ 6 — _ 7 I- _ 8 I I I I I I I 244 245 246 247 248 249 250 251 252 253 254 255 256 SECTION NUMBER FIGURE 13.—Longitudina1 profile, channel near Bernardo, June 2, 1965. WIDTH, IN FEET 0 20 40 60 80 100 0 I I I I I 2% A=262 n2 0:2.91 ft V=4.92 fps 2 _ 4 4 ‘ 1 Section 322 ._ LLI E To floodway 52 — _ u.i O < E :> 3 — .4 U! 1 [LI r— < 34 — _ 3 o .1 LU m —. :r: 5 _ ._ 0. Lu D 6 _ _ 7 I I I I I I I L I 1 316 317 318 319 320 321 322 323 324 325 326 327 SECTION NUMBER FIGURE 14.—Longitudinal profile, channel near Bernardo, June 3, 1965. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS steady during the period of these observations. Daily- mean sediment concentration increased during the period November 19 to November 29 from about 3,500 mg/l to about 5,500 mg/l (fig. 9D). Water temperature varied from about 3°C to 6°C during the day for each observation. Bed form prior to and during these observations was flat. The median diameter of bed material, 0.18 mm, was consistent throughout the period. Figure 15 shows a typical cross section for the observation reach. Cross-sectional profiles were obtained with the ultrasonic sounder at 15 sections on November 29. The first profile was at section 240, and the second, at section 243; from section 243 to 255, the profiles were obtained at 100-foot intervals, and the last profile was at section 260. Water—surface widths ranged from 64 to 74 feet, and the areas, from 234 to 269 sq ft. The average width and area for the reach are shown in table 1. Water-surface elevations were obtained at 100- foot intervals from section 243 to 255 twice each day. The average slope from two determinations was 0.00066 on November 29 and 0.00059 on Novem- ber 30. Vertical-velocity-profile data were obtained on November 30 at section 252 at 5-foot intervals and are given in table 2. Point-integrated sediment samples were obtained by means of the modified DH—48 sampler with a 14- inch nozzle at section 255 on both days. Particle-size analyses and concentrations in each size class are given in table 3. Total-sand concentrations of sam- ples collected at the weir averaged 2,700 mg/l on November 29 and 2,870 mg/l on November 30. Fine- sediment concentrations averaged 1,790 mg/l on November 29 and 1,530 mg/l on November 30. J17 Bed-material samples were obtained at 5-foot in- tervals at section 245 on November 29 and 30. The sample from each vertical was analyzed separately in the laboratory; the median particle size ranged from 0.16 to 0.21 mm on November 29 and from 0.17 to 0.19 mm on November 30. The averages of the 10 analyses across the section for each day are given in table 5. MAY 4, 1966 Water discharge was relatively steady from April 28 through May 4, the day of observations. Daily- mean sediment concentrations varied from 2,500 to about 1,200 mg/l during this period (fig. 9E). Water temperature varied from 16°C to 210C during the day of observations, May 4. The 1,000-foot reach chosen for this set of ob- servations, section 245 to 255, was classified as transition upstream of section 250 because the bed form was irregular dunes between sections 240 and 250; it was classified as flat downstream of section 250. Figure 16 shows the bed profile between sections 240 and 260. Cross-sectional profiles were obtained by means of a sounding rod at seven sections on May 4. Profiles were obtained once at sections 245 and 255 and twice at sections 246, 248, 250, 252, and 254. The average areas and widths of sections in the transition-bed reach (section 245 to 250) and the flat-bed reach (section 252 to 255) are given in table 1. Sketches of cross-sectional profiles obtained from 1300 to 1440 hours are shown in figure 17., Water-surface slope was determined from obser- vations obtained at 100-foot intervals between sec- tions 243 and 255, twice on May 4 and once on May 5, and was consistent at 0.0011. This was the greatest slope observed for any of the observations presented in this report. However, inspection of the bed pro- O I A :269 ft2 D=3.64 ft V=4.64 fps DEPTH BELOW WATER SURFACE. IN FEET 20 3O WIDTH, l I l l I 40 50 6O 70 80 IN FEET FIGURE 15. — Typical cross section for flat bed form, channel near Bernardo (section 245), November 30, 1965. J18 file obtained with the ultrasonic sounder (fig. 16) indicates that the mean depth was decreasing from about section 242 to 252. The water-surface eleva- tions were obtained in the reach where bed form was changing from rough to smooth. The water- surface slope would tend to be greater through this reach than in reaches upstream or downstream. That a relatively steep slope can exist in a reach where bed roughness is changing from rough to smooth is well illustrated in figure 11. The flow would be accelerating through the reach shown in figure 16 and, therefore, would be considered as un— steady. Vertical velocity profiles and point-integrated sedi- ment samples were collected at section 245 in the transition-bed reach and at section 255 in the flat- bed reach. Depth-integrated samples were collected at 30- minute intervals throughout the day at the weir (section 194). Total-sand concentration averaged 2,300 mg/l, varying between 1,820 and 2,870 mg/l. Fine-material concentration averaged 905 mg/l during the period of observations. Measured suspend- ed-sediment samples also were collected at section 240 in the transition-bed reach and at section 260 in the flat-bed reach. Average measured sand con- centrations were 840 mg/l at section 240 and 1,010 mg/l at section 260. Fine—material concentrations were 902 mg/l at both sections. Bed-material samples were collected at verticals at 10-foot intervals at each of five sections, and the samples from each section were composited for analysis in the laboratory. Median diameters of these samples are indicated in figure 16 for the sections sampled to illustrate the decrease in size of material as the bed form changes from transition to flat. NOVEMBER 23, 1966 Water discharge varied widely prior to and during these observations. Daily-mean sediment concentra- tions remained relatively steady, however, through the period November 13—25 (fig. 9F). Water dis— RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965—69 charges, measured at five sections spaced at 500-foot intervals from section 240 to 260, are given in the tables of data. Water temperature was 8°C during the period of observations. Bed form was flat for the period prior to and during these observations. Longitudinal profiles showed the bed was flat near the center of the chan- nel, but that long, low-amplitude waves were present near both banks. Cross-sectional profiles were obtained by means of a sounding rod at five sections on November 23. Depth soundings were made at 5-f00t intervals at each section. The profiles were obtained at the‘same sections and at the same times as the point velocities. Water-surface slope was determined from water- surface observations made at 100—foot intervals through the 1,200 foot reach, section 243 to 255. Slopes during these observations were 0.00062. Vertical-velocity-profile data, measured suspended- sediment samples, and bed material samples were collected at five sections. Figure 18 shows sketches of the five cross sections, lines of equal velocity, and hydraulic data and serves to illustrate the typical flow conditions for the flat bed form in the channel near Bernardo. The average measured suspended-sand concentra- tion during the observations was 1,880 mg/l, and the average fine-sediment concentration was 2,520 mg/l. The concentration of fine material increased during the observation period from 2,070 mg/l to 2,980 mg/l, whereas the concentration of sand re- mained constant. Median diameter of bed material was virtually the same at all sections. FEBRUARY 2, 1967 Water discharge and daily-mean sediment con- centration were relatively steady for the period January 23 to February 4 (fig. 9G). Water tempera- ture varied from 6°C to 8°C during the day of the observations. Bed form was flat prior to and during the period of observations. 0 2 To floodway l 4 6 8 lilllllllll 10 DEPTH BELOW WATER SURFACE IN FEET d50 =0.33 mm d50 =0.27 mm d 50:0.21 mm 1 d50:0.20 mm dso :02] mm |l||||l|J_l 240 245 250 260 SECTION NUMBER FIGURE 16.—Longitudina1 profile, channel near Bernardo, May 4, 1966. DEPTH BELOW WATER SURFACE, IN FEET J: | FIGURE SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS J19 A=290 ftz D=3.86 ft V=4.41 fps Section 245 A=345 ftz D=4.93 ft V=3.7l fps Section 246 A=285 ftz D=3.80 ft V=4.49 fps Section 248 A=235 n2 0:335 ft V:5.45 fps Section 250 A:230 ftz 0:3.49 ft V=5.57 fps Section 252 A2231 ftz 0:3.72 ft V:5.54 fps Section 254 A=244 n2 0:3.54 ft V: 5.25 fps Section 255 WIDTH, IN FEET 17.—Cross sections, channel near Ber- nardo, May 4, 1966. Cross-sectional profiles were determined by means of a sounding rod at five sections spaced at 500-foot intervals from section 240 to 260. Soundings were obtained at 5-foot intervals except near the banks, where a smaller interval was used. The profiles were typical of those for flat bed form. Depths, which were uniform across most of the channel, were greater near the banks. Water-surface elevations were obtained at 100-foot intervals through the 1,200-foot reach from section 243 to 255 once on February 2. The water-surface slope determined from water-surface elevations was 0.00052. Vertical velocity profiles, suspended-sediment samples, and bed-material samples were collected at five sections in the 2,000-foot reach from section 240 to 260. Samples at each cross section were com- posited in the laboratory. Bed-material samples were obtained at 10-foot intervals, and the samples for each section were composited in the field. No total- sediment samples were collected at the weir during these observations. The average measured suspended- sand concentration for the five cross sections was 1,100 mg/ 1, and the average fine-material concentra— tion was 833 mg/l. Median diameter of the bed- material samples was virtually identical at all five sections, d50:0.19 mm. FEBRUARY 14—15, 1967 These observations were obtained in conjunction with a special study on lateral dispersion. A 6,000- foot reach from section 220 to- 280 was used, which was much longer than the reaches used for any of the other observations. Water discharge prior to and during these obser- vations was relatively steady. Daily-mean sediment concentration decreased from about 4,000 mg/l on February 4 to about 2,800 mg/l on February 14 (fig. 9H). Water temperature varied between 6°C and 9°C during the 2 days. Bed form had alternated between transition and flat prior to this set of observations. During the observation period, the bed remained flat over the center part of the channel. Long, low-amplitude sand waves were near both banks. The bed form was classified as flat for these observations. Cross-sectional profiles were obtained with a sounding rod at nine cross sections on February 14 and at 10 cross sections on February 15. Depth soundings were taken at 5-foot intervals at each section. The cross-sectional profiles were typical of those for flat bed forms except that the depths near the banks at some sections were relatively large (fig. 19). J20 RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965—69 O 4 _ Section 240 A2242 n2 D=3.6l fl: 6 _ V:5.25 fps 0 4 Section 245 A=262 ft2 023.45 ft 6 _ V:5.08 fps *- Lu Lu LL 2 o uJ 2 u. 2 _ n: D (I) 5 4 — '; Section 250 A2269 ft2 3 D:3.75 ft 3 6 - _ O V_5.48 fps 4 ‘5’ o I E Lu 0 2 _ 4 __ Section 255 A=265 n2 D:3.84 ft 6 ‘ V:5.66 fps 0 : \J A2284 ftz D=4.18 ft V:5.53 fps Section 260 I_ l | | l l | | l l | l l | | | O 10 20 30 40 50 60 7O WIDTH, IN FEET EXPLANATION —6.0 Line of equal velocity, in feet per second FIGURE 18. — Cross sections, showing lines of equal velocity and hydraulic data, channel near Bernardo, November 23, 1966. Water-surface elevations were obtained at 1,000- section 240 to 260, on both days. The maximum foot intervals from section 220 to 240 and from sec- deviation of any individual elevation from the mean tion 260 to 280, and at 500-foot intervals from line used to determine slope was 0.08 foot. Vertical- DEPTH BELOW WATER SURFACE, iN FEET (”ND-‘0 UNI-'0 éwNHO wNHO tht-‘O wNHO #OJNt-‘O wNHO whit—o SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS J21 FEBRUARY 14, 1967 | l | T | | l D=2.36 ft V:4.17 fps Section 220 D2248 ft V:3.96 fps — Section 225 D3231 ft V=4.06 fDS Section 230 D: 2.24 ft V=4.17 fps Section 235 D=2.36 ft V=4.03 fps Section 240 D=2.34 ft V=4.0l fps Section 250 o D=2.37 ft _ V:3.96 fps Section 260 D=2.38 ft _ V=4.20 fps Section 270 D=2.4O ft V:3.91 fps Section 280 I; J l l l I l | 0 10 20 30 4O 50 60 70 WIDTH. IN FEET DEPTH BELOW WATER SURFACE, IN FEET FEBRUARY 15. 1967 F l I | I | I I 0' 1 D: 2.44 ft = . 3f 2 V 4 0 ps 3 ' Section 220 0 1 _ D=2.52 ft 2 _ V:3.91 fps 3 _ Section 225 (1’ _ 0:253 ft 2 _ V=3,77 fps 3 ” Section 230 4 >— 5 L 0 l 2 3 Section 235 4 _ 0 1 D:2.35 ft 2 V=4.06 fps 3 — Section 240 o _ 1 _ 0:227 ft 2 _ V=3.75 fps 3 T Section 245 O l D: 2.34 ft V=4.01 f 2 ps 3 Section 250 o .— 1 _ 0:2.31 ft 2 _ V=4.06 fps 3 _ Section 260 o _ 1 _ D=2.54 ft 2 — V:3.94 fps 3 — . Section 270 4 _ O _ l _ D=2.45 ft 2 _ V=3.34 fps 3 5 Section 280 L l | l | J | I l O 10 20 30 40 50 60 70 80 WIDTH, IN FEEI' FIGURE 19.——Cross sections, channel near Bernardo, February 14—15, 1967. J22 velocity-profile data were collected at nine sections on February 14 and at 10 sections on February 15. The vertical velocity profiles were obtained at verti— cals spaced at 5—foot intervals. No total-sediment samples were collected at the weir during these observations. Suspended-sediment samples were obtained at two sections on February 14 and at four sections on February 15. Suspended— sand concentration averaged 880 mg/l on both days. Fine—material concentrations were 760 mg/l on February 14 and 840 mg/l on February 15. Bed—material samples were collected at seven sections on February 14 and at four sections on February 15. The samples at each section were taken at 10—foot intervals and composited in the field. FEBRUARY 1, 1968 Water discharge increased rather uniformly dur— ing the period January 22 to February 1, from about 620 cfs to an average of 750 cfs during the observa- tions on February 1. Daily—mean sediment con- centration increased from 2,400 to 3,800 mg/l during this period (fig. 9J) . Water temperature varied from 50C to 80C during the period of observations. Five sections upstream from the weir were used for these observations. The bed form was flat at all sections. Sections 99, 100, and 101 were in a rela- tively narrow reach, and sections 159 and 160 were in a wide reach. Cross-sectional profiles were obtained with a wad— ing rod at the five cross sections. Depths were sound— ed at 5-foot intervals except near the banks, where a smaller interval was used. Water-surface elevations were obtained at 50-foot intervals from section 97 to 103 and from section 157 to 163. The water—surface slopes in these 600- foot reaches were 0.00041 and 0.00045, respectively. These were the least slopes for any of the observa- tions listed in this report. Vertical-velocity-profile data, measured suspended— sediment samples, and bed-material samples were collected at all sections. The suspended-sand con- centration averaged about 1,000 mg/l for all sec- tions. Fine-material concentration averaged 1,250 mg/l for all sections. No total—sediment samples were collected at the weir during these observations. Samples of bed material were obtained at 10-foot intervals in each cross section. The samples at each cross section were composited in the field. Median diameter of composite bed-material samples aver- aged about 0.20 mm at all sections. MAY 21, 1968 Water discharge fluctuated rather widely prior to these observations. The discharge dropped from a high of 1,910 cfs on May 12 to about 900 cfs on May RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965—69 17, where it remained relatively steady through the period of observations on May 21. Daily-mean sedi- ment concentration also fluctuated during the period prior to the observations (fig. 9K). The water dis- charge shown in the tables of basic data is the average of seven measurements made between 1235 and 1520 hours on May 21. Water temperature ranged between 180C and 21°C during the period of observations on May 21. Bed form was dunes prior to and during the period of observation. Profiles were obtained with the ultrasonic sounder from section 220 to 235. The average height and length of dunes, as deter— mined from measurements of 45 dunes on the profile at the center line of the channel, were 2.7 and 30 feet, respectively. Cross-sectional profiles were obtained with a sounding rod at five cross sections spaced at 200— foot intervals from section 225 to 233. Depths were sounded at 25—foot intervals in each cross section. The cross-sectional profiles are shown in figure 20. Water-surface elevations were obtained at 500- foot intervals from section 240 to 260. The water- surface slope through the 2,000-foot reach was 0.00063. Relatively few water—surface elevations were obtained for this set of observations. However, all the elevations were within 0.1 foot of the mean line; therefore, the water—surface slope is probably within an acceptable limit of error. Vertical velocity profiles were obtained at 5-foot intervals at each of the cross sections. Velocities at five points are shown in table 2 for most of the verticals; however, the meter nearest the bed failed to function properly at a few verticals located just downstream of the crest of a dune, and at those verticals only four-point velocities are shown. Suspended—sediment samples were obtained at each of the five cross sections, and total—sediment samples were collected at the weir (section 194). Bed-material samples were obtained at 10-foot intervals at each of the five cross sections in the study reach. The samples at each cross section were composited in the field. The median diameter of the composite samples for the individual cross sections varied from 0.22 to 0.32 mm and averaged 0.27 mm for the reach. MAY 29, 1968 Water discharge prior to the day of observations, May 29, ranged between 760 and 1,190 cfs; however, discharge was steady during the observations made on May 29. Daily-mean sediment concentratlon varied from 2,800 mg/l to a high of about 4,900 mg/l. Concentrations during the period of observation were relatively steady (fig. 9L). The water dis- DEPTH BELOW WATER SURFACE, IN FEET SEDIMENT TRANSPORT A=281 n2 D:4.32 ft V=3.06 fps Section 225 A=289 n2 D:4.3l ft V=2.97 fps Section 227 A=227 n2 D:4.32 ft V:3.10 fps 6 — Section 229 A=285 ft2 D:4.32 ft V2302 fps Section 231 A=299 ft2 D:4.10 ft V2288 fps Section 233 L I I I I I I I I 0 10 20 30 4O 50 60 7O 80 WIDTH, IN FEET FIGURE 20.——Cross sections, channel near Bernardo, May 21, 1968. IN ALLUVIAL CHANNELS J23 charge shown in the tables of data is the average of five measurements made during the observation period. The measurements for this set of observa- tions were taken at the same cross sections that were used for the measurements obtained on May 21, 1968. Water temperature was 21°C to 22°C during the day on May 29. Bed form was dunes prior to and during the period of observations. Longitudinal profiles were obtained with the ultrasonic sounder from section 220 to 235. The average height and length of the dunes, as determined from measurements of about 30 dunes on the sounder profile, were 4.2 and 44 feet, respectively. Cross—sectional profiles were obtained with a sounding rod at five cross sections spaced at 200- foot intervals. Depths were sounded at 2.5-foot intervals. The cross-sectional profiles are shown in figure 21. Water—surface elevations were obtained at 30-foot intervals from section 225 to 235. The mean water- surface slope through the 1,000-foot reach was 0.00056. Vertical-velocity-profile data, measured suspend- ed-sediment samples, and bed-material samples were collected at all five sections. No total-sediment samples were collected at the weir during these observations. The median diameter of the composite samples of bed material varied from 0.23 to 0.26 mm for the individual cross sections, and the average for the reach was 0.24 mm. JUNE 11, 1969 Water discharge generally increased for several days prior to these observations (fig. 9M). On June 10, the discharge peaked at 1,720 cfs, and on June 11, another peak at 1,600 cfs occurred at 0800 hours. The discharge was decreasing as the measurements on this date were obtained. A single discharge measurement was made on June 11, and the dis- charges reported in the tables of basic data are based on the stage-discharge relationship and the stages at the weir at the times shown. Temperatures ranged from 18°C to 19°C during the period of observations. Bed form was dunes prior to and during these observations. Cross-sectional profiles were obtained with a sounding rod. Depths were sounded at 2.5-foot intervals at each section. Profiles of each cross section are shown in figure 22. Water-surface elevations were obtained at 100- foot intervals from section 243 to 257. The water- surface slope for the 1,400-foot reach was 0.00069. J24 RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965-69 o o A=425 «2 2 2 D=5.38 ft V=3.48 fps 4 4 6 6 Section 225 8 . 8 Section 245 1- Lu 0 — Ed 0 r A=349 ft2 _2_ A=373 ft2 2 _ D=4.91 ft :3 2 D=4.85 ft < _ V=2.29 fps 5; V=3.72 fps 3 4 — m 4 D: __ DJ |— I- E6 _ g 6 Section 250 z _ Section 227 3 ._ 0 Lu‘ 3 — d 2 m it I 0 3 E A=371 ft2 m 0 — Lu 5 _ A=280 ft2 0 2 — D=5.08ft F. E2 _ D=4.25 ft — V2359 fps ; _ V=3.61 fps 4 — 0 d 4 — _ Section 255 m 5 _ I _ E 6 _ _ Lu Section 229 Q 8 _ o _ _ — A2303 ftz 1° — l | | l l | l l | l 2 ‘ D2427 ft 0 , 10 20 30 4o 50 60 7o 80 90 - V=3.34 fps WIDTH, IN FEET 4— FIGURE 22.——Cross sections, channel near Bernardo, June t 11, 1969. 6 Section 231 ° ” Vertical velocity profiles were obtained at 5-foot ‘ A2328 n2 intervals at three cross sections spaced at 500-foot 2 — 0:437 ft intervals. At some verticals, the bottom meter failed — V_3 08 fps to operate because the vertical was located immedi- 4 — ately downstream of a dune crest. >— Suspended-sediment samples were obtained at 6 L Section 233 three cross sections, and total-sediment samples at the welr were obtalned tw1ce during the observa- | 1 L J 1 1 I I I 1 tion period. 0 1° 2° 3° 40 50 60 70 80 90 Bed-material samples were obtained at three cross WIDTHv 'N FEET sections at verticals spaced 10 feet apart. The sam- FIGURE 21.—Cross sections, channel near Bernardo, May p195 at eaCh cross seetion were comDOSited in the 29, 1968. field for analysis in the laboratory. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS DECEMBER 21—22, 1965 The water discharge at the San Marcia] gaging station remained relatively constant near 1,900 cfs from December 11 to 15. The discharge increased to 1,950 cfs on December 18 and then decreased to 1,860 cfs on December 21, when the data in the San Marcia] reach were obtained. The discharge was about 1,750 cfs on December 22, when the data in the Nogal Canyon reach were obtained. The dis- charges for the San Marcia] and Nogal Canyon reaches reported in the tables of basic data are the daily-mean discharges at San Marcial. The bed form was flat in both reaches during the observations. Standing waves were present near the center of the channel in both reaches but were most pronounced in the Nogal Canyon reach. The stand- ing waves tended to build up with some regularity and to dissipate before reaching the anti—dune stage in both reaches. Cross-sectional areas were computed on the basis of depth soundings obtained in conjunction with point velocities. The depths were uniform across the channel at all sections. Water-surface elevations were obtained at ap- proximately 500-foot intervals one time only in each of the reaches. At San Marcia], the elevations were obtained in the 2,900-foot reach from section 2261+00 to 2232+00; at Nogal Canyon, in the 2,800- foot reach from section 1323+00 to 1295—1—00. Point velocities in the vertical were obtained at verticals spaced at 10—foot intervals except at section 1300+00 in the Nogal Canyon reach, where a 20- foot spacing of verticals was used. The pres- ence of large standing waves at section 1300+00 J25 created somewhat difficult and hazardous working conditions. Point-integrated samples were obtained With a modified DH—48 sampler at five points in three verticals at each section. In the San Marcia] reach, the verticals were spaced at 10-foot intervals. No point-integrated samples were obtained at section 1300+00 because of the standing waves. Suspended-sediment samples were obtained by the equal-transit-rate method at verticals spaced at 10-foot intervals with a DH—48 sampler at sections in both reaches. Because of standing waves at sec- tion 1300+00 in the Nogal Canyon reach, the sus- pended-sediment samples were obtained at section 1306+00. Bed—material samples were obtained at verticals spaced at 10-foot intervals. The samples at each cross section were composited in the field for anal- ysis in the laboratory. In addition to the data obtained in the reaches at San Marcia] and Nogal Canyon, bed-material samples were obtained at approximately 5,000-foot intervals from section 4400—1—00, just below San Acacia diversion dam, to section 1200+00, just above Elephant Butte Reservoir, a distance of more than 60 miles. The size distributions of these samples are not given in the tables of basic data; however, the median diameters ranged from 0.17 to 0.20 mm at 33 of the 64 sections. At two sections, the median diameter was 0.16 mm, and at the remainder of the sections, the median diameters were fairly evenly distributed in the range of 0.21 to 0.29 mm. There was no indication that the bed material became finer in the downstream direction. J26 RH)GRANDECONVEYANCECHANNEL,NE“7MEXKD, APPENDIX 2. BASIC DATA TABLE 1. —- Summary of available data Water Cross Water Water Data Available Sampling Discharge Section Surface Surface ' “““ '——“"17 ~W Date Section Q Area Width Slope Bed Point Point Suspended— Bed (ft3 per A B 5 Form Veloc— Sediment Sediment Material second) (ftz) (ft) (x10“) ities Analyses Analyses Analyses] 1965—69 Remarks Rio Grande conveyance channel near Bernardo, N. Mex. 1965 2/ Feb. 3- 194 560 —— —- —— —— x Reach 560 212 69 5 3 Dune. 236 560 212 70 5.3 Do. x 252 560 143 64 5.3 Flat. x 255 560 159 67 5 3 Do. x Reach 560 149 66 5 3 Do. Feb. 43/ 194 575 —- —— —— —— x 238 575 —— 70 5.3 Dune. x 240 575 -— 68 5.3 Do. x 255 575 —- 67 5 3 Flat. x x May 123/ 194 910 —— —— —— —— x Reach 910 300 71 6.5 Dune. X 240 910 —— —- 6.5 Do. x x 249 910 298 70 6.5 Do. x x 250 910 338 75 6 5 Do. x x May 133/ 194 890 —- —— —- —— x Reach 890 300 71 6 5 Dune. 240 890 -— —- 6.5 Do. x x 250 890 368 75 6.5 Do. x x 260 890 270 66 6 5 Do. x 2/ June 2‘ 194 1,190 —- -- -— -— X Reach 1,190 267 71 7.3 Transition, 250 1,190 217 74 7.3 Ba. x x x June 3 3/ 194 1,290 —- —— —— -_ x 322 1,290 262 90 5.2 Flat- x x x Nov. 292/ 194 1,250 —— —- —— —— x Reach 1,250 251 68 6.6 Flat. 245 1,250 266 74 6.6 Do. x x 255 1,250 254 67 6 6 Do. x Nov. 303/ 194 1,250 -- -— —— —— x 245 1,250 269 74 5.9 Flat. x x 252 1,250 242 65 5.9 Do. x x 1966 May 4 Z/ 194 —— —- —- ~— —- x Reach 1,280 289 73 11.1 “ransition. 240 1,280 —— —— 11.1 Do_ x 245 1,280 290 75 11.1 Do. x x x 250 1,280 235 70 11.1 Do_ x Reach 1,280 233 66 11.1 Flat. 255 1,280 244 69 11.1 Do. x x 260 1,280 -- —- 11.1 Do. x Nov. 23 240 1,270 242 67 6.2 Flat. x x x 245 1,330 262 74 6.2 Do. x x 250 1,430 270 72 6.2 Do. x x x 255 1,500 265 69 6.2 Do. x x x 260 1,570 284 68 6.2 Do. x x x 1967 Feb. 2 3/ 240 650 157 66 5.2 Flat. x x x 245 650 172 72 5.2 Do. x x x. 250 650 152 67 5.2 Do. x x x 255 650 155 66 5.2 Do. x x x 260 650 160 66 5.2 Do. x x x Feb. 143/ 220 630 151 64 5.4 Flat. x x 225 630 159 64 5.4 Do. x 230 630 155 67 5.4 Do. x x 235 630 151 68 5.4 Do. x 240 630 156 66 5.4 Do. x x 250 630 157 67 5.4 Do. x x 260 630 159 67 5.4 Do. x x x 270 630 150 63 5.4 Do. x x 280 630 161 67 5.4 Do. x x x Feb. 153/ 220 630 156 64 5.6 Flat. x x x 225 630 161 64 5.6 Do. x 230 630 167 66 5.6 Do. x x 235 630 169 68 5.6 Do. x 240 630 155 66 5.6 Do. x x 3 cross sections in dune-bed reach. 3 cross sections in flat—bed reach. 14 cross sections, bed material at 15 cross sections. 14 cross sections. 15 cross sections. 15 cross sections. 4 cross sections. 3 cross sections. SEDIMENT TRANSPORT 1N ALLUVIAL CHANNELS TABLE 1. —— Summary of available data — Continued J27 Water Cross Water Water DAEE’ZQAiiéale A Sampling Discharge Section Surface Surface “ 1/ a Date Section 0 Area Width Slope Bed Point Point Suspended— Bed (ft3 per A B S Form veloc- Sediment Sediment Material Remarks second) (ftz) (ft) (xlok) ities Analyses Analyses Analyses 1967--Continued Feb. 15 2/ 245 630 168 74 5.6 Do. X "Con, 250 630 157 67 5.6 Do. x 260 630 155 67 5.6 Do. X X X 270 630 160 63 5.6 Do. X 280 630 164 67 5.6 Do. X X X 1968 Feb. 1 99 750 175 62 4.1 Flat. X X X 100 750 163 57 4.1 Do. X X X 101 750 174 66 4.1 Do. X X X 159 750 197 87 4.5 Do. X X X 160 750 186 85 4.5 Do. X X X 2/ May 21 — 194 860 -— -— —— —— X 225 860 281 65 6.3 Dune. X X X 227 860 289 67 6.3 Do. X X X 229 860 277 64 6.3 Do. X X X 231 860 285 66 6.3 Do. X X X 233 860 299 73 6.3 Do. X X X May 29 225 1,010 336 67 5.6 Dune. X X X 227 1,010 349 71 5.6 Do. X X X 229 1,010 280 66 5.6 Do. X X X 231 1,010 303 71 5.6 Do. X X X 233 1,010 328 75 5.6 Do. X X 1969 June 11 245 1,480 425 79 6.9 Dune. X X X 250 1,390 373 77 6.9 Do. X X X 255 1,370 371 73 6.9 Do. X X X Rio Grande conveyance channel near San Marcial, N. Mex. 1965 Dec. 21 2249+93 1,860 305 70 5.9 Flat. X X X X 2243+62 1,860 308 67 5.9 Do. X X X X Rio Grande conveyance channel near Nogal Canyon, N. Mex. Dec. 22 1318+00 1,750 352 80 5.5 Flat. X X X X 1300+00 1,750 337 110 5.5 Do. X X X 1-/The suspended sediment measured at the weir (station 194) represents total sediment moving through that cross—section. 3IWater discharge measured at the cableway, station 184. TABLE 2.—Measured velocity at indicated heights above riverbed [Velocity, V, in feet per second. Height above riverbed, y, in feet] Rio Grande conveyance channel near Bernardo, N. Mex. February 3, 1965, Section 252, Right bank station 4, Left bank station 68 Sta. lO Sta. 15 Sta. 20 Sta. 25 Sta. 30 Sta. 35 Sta. 4O Sta. 45 Sta. 50 Sta. 57 D=2.7 ft. D=2.5 ft. D=2.4 ft. D=2.6 ft. D=2.5 ft. D=2.4 ft. D=2.3 ft. D=2.4 ft. D=2.4 ft. D=3.1 ft. V y V y V y V y V y V y V y V y V y V 2.2 3.10 2.2 4.24 2.2 4.91 2.2 4.99 2.2 5.15 2.2 4.94 2.2 4.78 2.2 4.78 2.2 4.37 2.2 2.99 1.7 3.20 1.7 4.14 1.7 4.76 1.7 4.81 1.7 4.96 1.7 4.81 1.7 4.72 1.7 4.77 1.7 4.30 1.7 2.77 1.2 3.01 1.2 3.94 1.2 4.62 1.2 4.60 1.2 4.80 1.2 4.59 1.2 4.57 1.2 4.62 1.2 4.12 1.2 2.42 .7 2.77 .7 3.82 .7 4.40 7 4.37 .7 4.54 .7 4.34 .7 4.37 .7 4.44 .7 3.92 .7 2.16 .2 1.84 .2 3.18 .2 3.39 2 3.36 .2 3.36 .2 3.32 .2 3.45 .2 3.50 .2 3.19 .2 1.58 February 4, 1965, Section 240, Right bank station 4, Left bank station 72 Sta. 10 Sta. 15 Sta. 20 Sta. 25 Sta. 30 Sta. 35 Sta. 40 Sta. 45 Sta. 50 Sta. 55 Sta. 60 Sta. 65 D=3.2 ft. D=3.6 ft. D=3.2 ft. D=3.3 ft. D=3.1 ft. D=3.6 ft. D=3.2 ft. D=2.7 ft. D=2.7 ft. D=3.9 ft. D=4.5 ft. D=3.0 ft. y V y V y V y V y V y V y V y V y V y V y V y V 2.9 2.58 3.2 3.25 2.9 3.25 2.9 3.45 2.8 2.65 3.2 2.67 2.9 3.19 2.4 3.30 2.4 2.85 3.4 3.07 4.0 2.80 2.6 2.60 2.3 2.64 2.5 3.16 2.3 3.31 2.3 3.33 2.3 2.64 2.5 2.64 2.3 3.17 2.0 3.42 2.0 2.79 2.5 2.86 2.9 2.73 2.0 2.33 1.7 2.70 1.7 3.07 1.7 3.18 1.7 3.29 1.7 2.56 1.7 2.65 1.7 3.20 1.5 3.49 1.5 2.64 1.7 2.82 1.7 2.71 1.5 2.18 1.0 2.68 1.0 2.91 1.0 2.86 1.0 3.19 1.0 2.46 1.0 2.64 1.0 3.22 1.0 3.62 1.0 2.64 1.0 2.84 1.0 2.62 1.0 2.02 .5 2.40 .5 2.36 .5 2.76 .5 3.10 .5 2.30 '.5 2.43 .5 1.70 .5 3.45 .5 2.54 .5 2.56 .5 1.41 .5 2.08 65 D=A.5 ft. Sta. Sta. 60 D-3.9 ft. Sta. 55 3.6 ft. D Sta. 50 D=4.5 ft. Sta. 45 4.0 ft. D Sta. 40 D=3.0 ft. 35 D=4.4 ft. Sta. Sta. 30 D 3.9 ft. May 12, 1965, Section 249, Right bank station 8, Left bank station 82 3.7 ft. Sta. 25 D RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965—69 3.8 ft. Sta. 20 TABLE 2.—Measured velocity at indicated heights above riverbed—Continued D Sta. l7 =3.9 ft. D 4.1 ft. Sta. 14 D J28 14 14 no no 14 4u :4 n7 :4 :4 14 14 14 14 14 4a :4 :4 no 14 14 14 1; :4 14 :4 14 1I :4 :4 14 14 R 14 14 14 14 14 Au 41 :4 no 14 14 14 1; 14 no 14 14 nu Lu :0 :u :4 1; 14 14 14 14 14 14 I4 :4 no 14 14 14 1; I1 1I 04 1I 14 no 1I :4 1; 1; 14 14 14 14 14 14 Id :4 no 14 14 14 1L nu 14 14 14 14 14 «4 I4 1; 4o :4 I4 :4 I4 14 14 Im :4 nu 14 14 «4 1L 1; 1I ,0 :4 14 on 04 :4 1I :4 14 14 14 14 14 14 I4 :4 av 14 14 14 1; 14 n7 :4 n7 14 (D :4 14 14 1; 14 14 14 14 14 14 :4 :4 oo 14 14 14 1; nu .4 14 14 :4 cu no :4 :4 04 14 14 14 14 14 14 :4 :4 oo 14 14 14 1; nu A: no nu 10 cu 1I 14 :4 14 14 14 14 14 14 14 I“ :4 ho 14 14 14 1L 14 nu 4u 1; nu 1I 1I cu 41 14 14 14 14 14 1L 14 I4 :4 no 14 14 14 1L 1I ,0 n9 1I .4 14 I1 1; 1; 04 14 14 14 14 14 14 I4 :4 no 14 14 14 1L :4 14 41 I4 1; :u a4 04 1I 14 14 14 14 14 14 14 :4 :4 no 14 14 14 1L Sta. 76 D=3.8 ft. 3.7 ft. Sta. D Sta. 70 D=3.7 ft. oz 14 4U nu no ,0 1; oz 1; 1; 1; :4 :4 :4 no 14 14 14 1; 04 no 10 n: nu 4u Av 04 (D 14 14 14 14 14 14 I4 :4 :4 no 14 14 14 1; nu 04 I4 :9 nu nu 14 I4 04 04 14 14 14 14 1; I1 :4 :4 no 14 14 14 1; 66 5.3 ft. V Sta. D 5.4 ft. Sta. 60 D Sta. 54 D 6.2 ft. Sta. 49 D=6.2 ft. 5.4 ft. Sta. 47 D Sta. 42 D 6.1 ft. 6.5 ft. Sta. 36 May 12, 1965, Section 250, Right bank station 6, Left bank station 77 D Sta. 30 D=6.5 ft. 24 5.6 ft. Sta. E 3.8 ft. Sta. 17 D 04 14 a4 41 04 :4 r0 1; 11 n: 14 14 14 14 1; (D :1 :4 Ho 14 14 14 1; cu 1I 1; 40 14 A~ :4 (0 :1 1I 14 14 14 14 14 0/4583 .4 14 1; [41809 :4 In 14 1; 14 333L2 0 4 5 8 3 4 2 1 0784.0 14 no :4 14 1; 14 1; 1; 14 14 nu I4 :4 nu 14 :4 14 1; 54/906 :4 :4 4n n: 41 & 7.1.1 1 O 4.5 8 3 L.2 l 14 pa nu :4 :4 :4 n4 1; 14 nu L 142 l 1 44 1I u: :4 10 1I :4 14 14 14 .4 14 nu I4 :4 no 14 41 14 1; Sta. 70 D=2.9 ft. V Sta. 65 5.2 ft. V D Sta. 60 D-4.3 ft. Sta. 55 D 4.0 ft. Sta. 50 D 4.5 ft. 4.7 ft. Sta. 45 D Sta. 40 D=4.8 ft. Sta. 35 =4.5 ft. May 13, 1965, Section 250, Right bank station 7, Left bank station 80 D Sta. 30 D=4.3 ft. 25 D=S.8 ft. Sta. 6.5 ft. Sta. 20 D 15 7 ft. Sta. D=5. Av 40 :4 14 1; 1; 14 14 14 14 1; 1; 0/4583 I4 14 1; Au :4 14 :4 14 1; Au n7 I4 no 14 14 14 14 1L nu I4 :4 no 14 I1 14 1; 1; nu 14 :o (D 04 :u I4 14 1; 14 14 14 14 1L 1I I1 :4 no 14 14 14 1L 04 1I n4 a; nu 1I 1I :4 14 14 14 14 14 14 14 1/ I4 :4 on 14 14 14 1; 1; 1; 14 :4 no ,0 ,0 :4 14 14 14 14 14 14 14 Au La :4 oo 14 41 14 1; ‘u 4v :4 14 no 1; n7 no 00 1I 14 14 14 14 14 nu I4 :4 no 14 .4 14 1; 14 nu 1I 4u 1; :4 14 1; 04 1I 14 14 14 14 14 nu I4 :4 cu 14 I4 14 1L 14 nu 1I nu nu (D 14 nu 04 on 14 14 14 14 14 0/4583 I1 14 1; 1I 1I 14 1; 1I nu 04 :u .4 nu I4 14 14 14 14 nu I4 :4 nu 14 L» 14 1; 1; nu :4 (0 n3 14 14 1; no 14 I1 I4 I4 14 14 nu I4 :4 no 14 I9 14 1; 04 n: no 1; 8760 14 14 14 1; nu I4 :4 no 14 [$21 09520 :4 :4 :4 14 nu 14 14 14 14 14 AU :4 :4 no 14 41 14 1; Sta. 75 D=4.3 ft. V Ste. 70 D 4.0 ft. Sta. 65 D=4.2 ft. Sta. 60 4.0 ft. D 4.4 ft. Sta. 55 D Sta. 50 D=5.0 ft. Sta. 45 6.0 ft. D D=6.8 ft. June 2, 1965, Section 250, Right bank station 14, Left bank station 88 Sta. 40 Sta. 35 D=6.5 ft. Sta. 30 D=6.6 ft. 4.3 ft. Sta. 25 D 4.2 ft. Sta. 20 D 1I :4 no 1; 1; (o 14 14 1; 3.84 :4 :4 1/ 14 3.7 2 1 14 n7 14 I» sl :4 [433 :4 :4 1/ 14 3.7 3.97 04 1: o; n) 14 14 I4 :4 14 :4 1I 14 3.7 4.92 2.5 14 1I 04 1; I4 14 :4 I» 14 3.7 4.99 1I :4 I4 14 7: 14 I1 44 14 1; 1I :4 :4 1I 14 14 74 1; no 1I :4 1I I» IN I4 14 14 1L 1I :4 :4 1I 14 14 14 1; 1I I4 :4 nu :4 In 14 no :4 14 In :4 14 1; 1; 1I :4 :4 1I 14 14 14 1; nu 1; :4 14 1I I4 4U 1I 14 14 1; 1I :4 :4 1/ 14 14 14 1; 1I 14 00 Du 14 1/ 7: Lu 14 nu 14 14 14 14 14 1I :4 :4 1/ 14 14 14 1L 14 Ru 0» 41 1I I4 41 14 1I 14 14 14 14 14 :4 1I :4 :4 1I 14 14 14 1; 2.7 ft. V Sta. 80 D Sta. 75 3.0 ft. D Sta. 70 D=3.2 ft. Sta. 65 D=3.6 ft. Sta. 60 D=3.4 ft. Sta. 55 D=3.3 ft. 50 3.2 ft. Sta. I Sta. 45 =3.3 ft. June 3, 1965, Section 322, Right bank station 20, Left bank station 110 D Sta. 40 D=3.2 ft. Sta. 35 D 3.2 ft. Sta. 30 D=3.0 ft. 3.3 ft. Sta. 25 D co 1; nu .4 n7 14 nu 10 n7 nu ,0 Lu :4 :4 I“ 14 1I 14 :u 14 14 1; 1L :4 no :4 41 1I 1I :4 14 :4 1I :4 :4 :4 I» 14 14 1I 14 4o 14 14 1L 1L 88/41 8633 :4 :4 :4 I4 14 1I 14 ,0 14 14 1L 1L :4 :4 1; 41 4m 14 00 1I :4 :4 Im 14 14 1I 14 ,0 14 14 1L 1L 14 14 :4 14 1I nu ,0 14 I1 14 :4 :4 :4 I4 14 14 1I 14 (D 14 14 1; 1; 14 no :u o4 no Au :4 :4 :4 :4 :4 14 {4 7I 14 Av 14 14 1L 1L 14 14 no Au Au 0/ 1I 14 :4 co :4 :4 :4 I1 14 :4 1I 14 ,0 14 14 1L 1L 14 14 nu 1I n7 00 Au 14 I1 1I 555/43 :4 1I 14 4o 14 14 1L 1L a; nu 14 04 1; 14 Au Au 1I 1; ,0 (D :4 I4 :4 :4 1: 14 (D 14 14 1; 1; nu 1I no nu 04 no (u 14 4v nu :4 :4 :4 I4 I4 :4 11 14 ,0 14 14 1L 1L 1I 04 14 I4 .4 14 4o 14 4m :4 14 14 :4 1I 14 40 :4 14 1L 1L Au 1/ 04 1; :4 (o nu 1; :4 I4 14 14 14 14 14 _S_1I 14 :u 14 14 1; 1; Sta. 105 D=3.2 ft. v 100 D=2.8 ft. Sta. D=2.6 ft. Sta. Sta. 90 D=2.6 ft. 2.6 ft. Sta. 85 D 1; 14 (O :4 14 Au 14 14 1I 1; 14 14 14 14 14 :4 04 14 :u 14 14 1; 1; no :4 au 14 14 nu 04 14 1I 14 :4 I1 I4 14 «4 :4 n7 14 (O 14 14 1; 1L 0/ 1I ,0 14 1I [441/47 :4 :4 :4 I1 14 14 1I 14 ,0 14 14 1L 1L [48751 1I :4 14 I4 04 :4 :4 :4 I4 14 14 1: 14 ’0 14 14 1L 1L 42155 14 :4 14 Lu n7 :4 :4 :4 :4 14 14 1I 14 ,0 14 14 1L 1L Sta. 55 D=4.0 ft. V Sta. 50 D=3.9 ft. 4.3 ft. Sta. 45 D Sta. 40 D=4.A ft. November 30, 1965, Station 252, Right bank station 4, Left bank station 69 35 D=4.5 ft. Sta. 4.4 ft. Sta. D= Sta. 25 D=4.4 ft. Sta. 20 D=4.2 ft. :4 14 nu 1; 14 :u I» no ,0 I4 .4 La 14 14 14 :4 11,04 nu :4 14 14 1; 1; 14 14 11 (D 14 :4 14 n7 :4 14 :4 :4 I» :4 I» :4 1I n7 nu :4 14 14 1; 1; 68783 :4 14 no on 14 4o 40 :4 In I» :4 7: a) nu :4 14 14 1; 1; 08610 nu 1I 14 14 Lu 1I ,0 ,0 :4 I1 :4 1I n7 nu :4 14 14 1; 1; 0207 :4 14 (D (o nu 1I 1I :u :4 :4 :4 7: A? nu :4 3211 :4 7: :4 1; :4 14 nu :4 ,0 14 1I «I 40 :4 :4 :4 1/ n: nu :4 14 14 1; 1L nu nu 14 I1 10 no :4 nu 14 «I ,0 r0 ,0 :4 I4 :4 1i 1: nu :4 14 14 1L 1L :4 14 :4 14 :4 00 1I co co :4 :4 :4 I4 :4 I4 :4 1I n7 Au :4 14 14 1; 1; J29 Sta. 65 D=4.5 ft. y V 60 D=4.4 ft. v Sta. Y Sta. 55 D=4.4 ft. y V 50 D=4.4 ft. V Sta. Y -4.4 ft. V Sta. 45 Y D ‘4.4 ft. V Sta. 40 Y D Sta. 35 D=4.1 ft. y V D=4.0 ft. y V May 4, 1966, Section 245, Right bank station 3, Left bank station 78 Sta. 30 Sta. 25 D=3.9 ft. v V SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS Sta. 20 D 4.1 ft. V TABLE 2.——Measured velocity at indicated heights above riverbed—Continued Y Sta. 15 -4.1 ft. V Y D 12 D-4.1 ft. V Sta. Y . t . . 1.9 2 5 3 t 8 1 8 5 2 . 9,9 5 2 1 ..... AJJJJ onv 73132 mfv 21222 onv 9.162 41v .3332 ouv 01153 L» 74 La 15 a; (0 <5 05 a5 65 52 11 :5 Lu 1. 74 74 I» 25 a. . :u (u :5 74 o3 a; n2 2; . 84 20483 u: . a 3 2 0 4.8 3 . . . . a.fi 7 m J m M Y 2 0 4 8 3 R M Y L L L . . m fl Y 2 0.4 8 3 R m Y 2.2 1 u % Y 1 D A 8 J 3 2 1 1 S D 3 2 1 S D 3 2 l S D 3 2 l . 8 4.5 6 7 . 1.3 5.8 6 2 4 8 2 8 . 6 4.9 3 7 t 7.3 l 6 2 . 6 2 2 5 7 t 1.7.4 0 7 . 6 l 5 9 53163 snv 97417 62v 1441. nv 77432 mfv 54441 suv 13.13 ..... 5 . . . . . 4 4.4.4.3 5 l 4.4 4.4 3 4 5 1 5 5 5 4 4 .3 5 2 5 4 4 3 . . a 4. 2 0 4 8 3 . . . . a 3 2 0 4.8 3 . . ..... 3£JAJ may 20483 kwy 3LL may 20483 hwy 321 may JfiAfiJ 1.2 1 1 S D 1.2 1 S D 1.7.1 S D 1.2 1 . 6 5 6 2 8 . 1.3 5 8 8 . 6 4 4 3 0 . 8 M H w M t 6 3 8 9 5 . 4.8 7 6 5 t 3 9 7 3 8 . O 6 4 7 3 §.fi V fl J J 3 J t % w M w 5 . . m f V i 5 4.1 L 0 H V 9 5 2 7 l m f V L L L L l 0 H V 8 2 7 8 4 5 6 5 5 4 4 0 f V . . _ . 4 4.4 3 3 0 5 0 5 5 5 4 4 4 5 l 6 6 5 4 2 .3 5 3 5 5 4 4 . . . . 3 a 4 7.0 4.8 3 8 . . 2 a 4 0 1 3 5 1 _/ . . 8 a 3 2 0 4 8 3 3 . . . . 5.2.26.1. . 7 “my 3.2... a 3.7 202:. 7 3.7 12.1... 7 37 202.3 7 8...: 321 5 37 2.12.13. 1.2 l n n S D 2.2 l n n S D 1.2 l m m S D 1.2 l m m m m 1 1 . t . 5 9 7 7 2 t t . 1.4 2 1 5 t t . 1.9 1 7 7 t . 3 M M B H a t 0 7 4 6 7 a . 5 9 9 5 6 a t 8 7 5 8 0 a . 6 6 8 9 6 m 0 H V 0 J J A 0 u t W m U n . . . t 5 f V . . . t t 5 1 7 2 5 t 5 f V ..... t t 3 6 4 6 7 s 5 7 6 6 5 4 s 5 f V . _ . l l 3 3 3 s 5 6 5 5 4 3 s 5 f V . . s 5 5 5 5.4.4 5 5 f V . . 3 4 6 6 5 5 9 4 6 6 5 5.4 7 4 7 6.6 S 4 k . . k 4 fl & L 1 2 4 6 2 fl . 3 W m L 0 0 4.8 3 m .J n a 4. 2 0 4.8 3 n . . 7 4 5 8 3 a t = Y ..... a a 4 2 0 4 8 3 ..... a t = Y . . . . . a a 3 2 O 4 8 3 a t = Y . . . . . a a 4 2 0 4.8 3 b S D 3 2 1 b t = Y . . . . . 3 2 1 b S D 1.2 1 b t = Y ..... b S D 1.2 1 b t = Y . . S D 2.2 l S D 3 2 1 S D 3 2 l t t fi fi H R f f e . 5 5 5 8 2 e e . 8 8 2 6 3 e e . 4.5 2 5 7 e B W M M u L t 6 4 1 3 8 L . 7 1 8 0 1 L t 2 0 7 0 0 L . 3 O 9 5 9 L 5 R V J J J J J L L B % fl % ..... m f V 6 6 8 5 4 7 0 R V 0 J 2 4 8 E f V 6 6 L 5.4 0 h V 0.2 6 6 5 7 4 7 6.6 5 4 7 0 f V . ._ .. 4.4.4.4 4 3 8 O 4 9 7.6 6 5 4 4 8 1. 4.1 7 7 6 5 3 4. .3 0 4 4. 7 6 S 3 . . . . n a 4. 2 O 4 8 3 n . . n a 3 1.2 4 6 2 n . . n a 3 0 0 4.8 3 n . . . . 7 A J 8 3 o t = Y . . . . o a 3 2 O 4.8 3 o t = Y ..... o a 4. 2 0 4 8 3 m h M Y 3 2 l .m m # v. J m A 8 J 21 .1 SD 37.1 .1 ray .. .1 SD 321 .1 t=Y ... t .1. SD 321 3 t t S D 1.2 l t t S D 1.2 l a a m m m .... t c s - 42767 S s . 7 5 6 6 6 s s . 6 7.1.6 3 s . nmumn r. 07237 . 75666 t 95234 . 7699 k OfiV 0.3300. k t ”M w . . . fl M.t V L & 3 5 4 fl 5 H V 4 0 6 9 1 fl 6 f V & 3 S i L fl 5 fl V O l 6 6 . n 4 8 7.6 6 5 n 5 f V . . _ . 5 5 5 4 4 a 8 a 3 7 7 6 5 5 a 8 a 3 8 7 6 5 M .3 M 3 5 7 7 5 b m L 0 1.3 5 1 b . 3 b a L 0 0 4.8 3 b .J t m % Y J £.A 3 J t L L 2 0 4 8 J J.J 9 4 M k W Y 1.L L m M Q Y 9.0 4 8 3 m R % Y qu L m m % Y 2 0 4.8 3 h S D 2.2 1 h t = Y . . . .3 3 2 1 8 8 S D 2.2 l 8 S S D 1.2 l .m .¥ S D 3 2 1 1 i i i R R R . 4.0 2 3 9 R R . 0.5 8 5 R 7 L M M % Mym 7 . 1 0 7 5 B W w M w 7 t 2 0 6 4 9 7 . 9 0 7 9 8 7 t 0 5 0 2 7 . 6 4.8 5 5 5 5 f V ..... 0 t 1 2 8 4 . . E M f V 7 7 8 5 4 W 0 H V 5 2 7 0.1 H W f V 7 6 fl 5 _ w 0 R V 9 3 9 1 6 5 3 8 7 6 6 4 6 O f V ._ . 4 3 3 3 3 7. 8 2 3 8 7 7 6 5 5 2 8 2 3 7.7 6 6 4 7. .J 2 3 5 8 7 5.4 . . . . 2 n a 4 2 0 4.8 3 n . . n a 3 l 2 4 6 2 n . . n a 3 0 0 4 8 3 n . . ..... 1.3.1.7.... n :7 12.1.2... 37 20.83 n “my 3.21. m 3.7 202.3 .m “my 321 m .37 2.04.23 3 2 1 t t S D 3 2 1 t t S D 3 2.1 a a S D 3 2 l a a a a e e S . 3 2 4 2 2 S S . 2 5 9 6 7 S S . 5 3 8 4 S m 3 N 2 % t 3 0 5 5 8 . 0 3 8 1 9 t 4.9 4.5 . 2 6 6 9 9 7 0 fi V 3 J 3 J A 7 L H H w M 8 5 i. 5 f V 7 7 h i A Ln 5 H V 5 l 7 0 9 ,% % f V 7.& 3 5 . .M h V 8 l 6 7 5 6 3 777.6 5.4 6 5 f V _ 1 0 I uuuuu S I- t 4.4 4.4 3 6 8 % 2 8 7.7.6 6 4. 6 0 % 2 l 7 7 6 5 3 % .3 % 2 6 8 7 6 5 9 . . 9 . . . 4 5 8 3 1. a 3 1 2 4 6 2 1 . . 1. a 4 0 0 4 8 3 1 . . 1. m fl Y J fi.A 3 J 1 a 4 2 0 4 8 3 2. . . .. $7 12.1. 3.7 207.83 3.7 121. 37 20.83 . 57 321 , :7 ..... 321 4 3 SD 321 3 3 SD 321 B B SD 321 2 2 2 Y r . 6 O 0 7.8 r a . 4.3 4 5 7 r r . 6 6 9 0 r 3 H H w M M t 0 7 2 2 6 e . 4.8 2 5 2 e t 1 6 7.7 e . 4 1 5 1 6 m 5 H V J 1 fi J J w L H N m U 4 . . m f V L 6 a i L m 0 R V 3 1.8 1.2 m m f V . 7 S i 3 m 0 H V 8 5 1 6 9 m 2 7.7.6 6 6 m 0 f V . .. 4 4.4.4 4 8 e 2 7 7 6 6 5 e 0 e 2 6 6 6 5 4 w .3 W 2 5 7 7 6 5 L L 1.2 4 6 2 W . J W m L 0 O 4.8 3 W . J M m % v. J 0 A J J M L L 2 0 4 8 3 7.0.0 3 8 t M Y QwL L . . N m fl Y 0.0 4 8 3 N R % Y QLL L . . N m fl Y 2 O 4 8 3 S D 1.2 l t = Y .. a .... s uuuuu ‘30.: uuu 3 7.2 1 S D 3 2 l S D 3 2 l S D 3 2 l . 7.1 7 5 1 I 72774 v 54165 4 4.9 5 c 0 6 1 2 7 . 5 7 7 4 8 t O 4.0 3.4 . 0 3 2 2 3 0 R V J J 8 J A b M B M M J J J 9 . 5 f V 7 & & i k 5 h V 1 1 8 2 3 E f V L m & i A 5 R V 9 0 7 2 8 2 6 6 5 5 4 5 f V . . 4.4.4 3 7 1 8 6 6 5 5.4 l 1.1 4.6 5 5 2 .3 1.4 6 6 5.4 . . . . a 4. 2 0 4 8 3 . . a 3 0 1 3 5 1 . a 4 O O 4 8 3 . . ..... 0 2 3 6 1 t w v. L L L m fl v. 2 0 4.8 3 R m v. L L L . . m fl v. 2 O 4 8 3 R M v. 3 2 l m % v. J 0 4 8 3 n :::: S nnnnn sunnl u:- 3 2 1 S D 3 2 l S D 3 2 l S D 3 2 l . . 0.7.6 4.1 9 1.2 7 7 . 9 l 4.6 2 4 6 9.6 w t 5 4 9 9 4 . §.7.3 6 9 t 1.4.9 3 7 . 4 9 1 8 4 5 fl V A A J J J L H W % % 9 9 7 5 0 f V . . . . t 6 9 6 1 7 0 f V ..... t 2 2 9 2 7 l 5 5 5 4.4 0 f V _ . . . . . . 2 6 6 5 4 4 0 f V ..... 2 6 6 5 5 4 0 f V . . . . . 3 1 5 4 3 3 4.4.4.4 4 7 1 7 4 4 4 4 3 1 1 4.4.3 3 2 . . S . . . 2 a 4 2 0 4.8 3 . . a 3 0 1 3 5 1 . . a 4 0 0 4.8 3 . . ..... 5 7 8 1 6 t M v. 1 L L . . m fl v. 2 0 4 8 3 h M V. l L L . . 3 % v. 2 0 4 8 3 R M v. 3 2 1 m M v. 2 O 4 8 3 . .... S ... . . . . . . . 2.9.1 1 S D 1.2 l S D 1.2 1 S D 3 2 l . 7.6 8 1 9 . 7.8 3 . 1 2 3 9 1 . 2 6 8 6 0 . 0 9 6 8 0 . 0 2 8 3 9 n w H N M L M m E W 3 5 H V 5 2 l 2 9 R V 5 8 6 2 6 5 H V 6 6 3 9 5 H V 6 1 9 6 1 0 H V J 3 J 5 J & V J J _ J . . . 0 f V . . . . . l L i L m L 5 3 3 l 3 L 1 L A L l L 6 L L L L L 1 2 2 2 2 2 5 3 3 l 4.4 4.4 4. 7 2 2.1.3 3 2 7 7 2 5 J .3 5 7 8 1.6 a L 7 7 8 1 6 m fl v. 2 3 5 7 3 m fl v. 2 0 4 8 3 m % v. 0 0 4 8 3 m 6 v. 2 0 4.8 3 m fl v. J D A 8 3 m fl v. J 0 A 8 3 lLLL. M%Y LLLL. SD 321 SD 321 SD 321 SD 321 SD 321 SD 321 Sta. 60 D=3.l ft. 3.3 ft. Sta. 55 D Sta. 50 D=2.4 ft. 2.4 ft. Sta. 45 D 2.4 ft. Sta. 40 D Sta. 35 D—2.3 ft. 2.3 ft. Sta. D: Sta. 25 =2.3 ft. February 2, 1967, Section 240, Right bank station 1, Left bank station 67 D 2.4 ft. Sta. 20 D RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965—69 Sta. 15 =2.4 ft. TABLE 2,—Measured velocity at indicated heights above riverbed—Continued D 2.6 ft. Sta. D Sta. 5 D—2.8 ft. J30 9 0 0 5 1 9 9 8 3 8 2 2 2 2 l 6 0 4.8 3 2 2 1 7 9 0 3 2 1 9 8 2 5 3 2 2 2 1 6 0 4.8 3 2 2 l 7 1 2 O 9 9 5 l 3 3 3 3 0 4.8 3 2 1 6 9 4 5 5 4 0 5 4.4 4 3 0 4 8 3 2 l 4 3 6 5 2.1 5 9 5 5 4.3 0 4 8 3 2 1 9 9 0 4 6 4 9 2 5 5 4.4 0/483 2 1 8 2 7 9 7 5 9 2 5 5 4 4 9 3 7 2 1 l 4.0 1 6 9 7 1 3 5 5 5 4 9 3 7 2 1 l 9 l 0 0 6 5 9 2 5 5 4.4 0 4 8 3 2 l 4 9 l 7 3 0 6 9 554.3 9 3 7 2 l 1 3 8 0 9 4.1 7 1 4.4.3 3 9 3 7 2 l l 1.4 4 7 5 6 3 3 8 3 2 3 3 2 2 6 0 4.8 3 7.2 1 3.2 ft. V Sta.60 D 55 D=2.0 ft. Sta. 2.2 ft. Sta. 50 D 2.2 ft. Sta. 45 D Sta. 4O D=2.2 ft. Sta. 35 D 2.3 ft. Sta. 30 D=2.3 ft. Sta. 25 D=2.4 ft. February 2, 1967, Section 245, Right bank station 0, Left bank station 72 20 2.5 ft. Sta. D: 2.6 ft. Sta. D= Sta. 10 D=2.6 ft. Sta. 5 D=3.3 ft. 4.7.3 2 7 7 6 4 7 0 2 2 2 1 1 60483 2 2 1 6 2 8 6 16/41 3333 0 4.8 3 2 1 l 8 4.5 9 9 6 2 3 3 3 3 0 4.8 3 21 4 0 5 6 9 9 4 8 4 4.4 3 0 4 8 3 2 1 9 5 9 7 2160 5 5 4.4 9 4 8 3 1 l 3 l 9 3 6 5 9 3 5 5 4.4 0.4 8 3 1 l 6 6 7 8 7 5 0 3 5 5 5 4 9 4.8 3 l l 7.1 9 5 6 5 9 2 5 5 4 4 8 3 7 2 l l 8 8 2 4 3 1 7 0 5 5 4.4 9 4 8 3 1.1 1 0 3 0 8 7 3 8 4.4.4 3 9 4.8 3 l l 0 4 7 6 6 8 O 9 6 2 1.A.& & 1 5 9 4 8 3 7.1 1 2 0 8 8 5 7 6 2 4 0 2 2 2 1 l 5 9 4 8 3 2 l 1 Sta. 60 D=3.4 ft. v Sta. 55 D=2.8 ft. Sta. 50 2.5 ft. D Sta. 45 D=2.4 ft. 2.4 ft. Sta. 40 D Sta. 35 D 2.4 ft. Sta. 30 D=2.4 ft. Sta. 25 D=2.3 ft. February 2, 1967, Section 250, Right bank station 0, Left bank station 67 20 2.3 ft. Sta. D: 2.3 ft. Sta. D= Sta. 10 D=2.4 ft. 2.6 ft. Sta. D l 4 3 9 1 0 9 0 8 0 3 2 3 2 2 59/483 2 1 1 84.300 8 8 9 8 l 2.3 3 3 3 4 8 3 7 l 2 1 l 8 7 9 4 5 9 9 7 4 2 3 3 3 3 3 4.3 3 7 2 2 l 1 9 0 7 6 7 7.2 6 4 4.4 3 8 3 7 2 1 l 8 4.8 7 1.7.7 0 5 5 4 4 8 3 7 2 l 1 6 2 4 2 5 4 9 2 5 5 4 4 8 3 7 2 l 1 2 8 3 7 7.5 0 2 S.5 5 4 8 3 7 2 1 1 5 1 9 7 6 5 9 2 5 5 4.4 8372 5764. 6 4 9 2 5 5 4.4 8 3 7 2 ll 5 3 7 7 2 l 6 0 5 5 4 4 8 3 7 2 2 2 6 1 5 4 0 6 4.4.4 3 9 4 8 3 4.5 6 2 6 5 l 6 3 3 3 2 8 3 7 2 Sta. 6O D=2.8 ft. V 2.8 ft. Sta. 55 D Sta. 50 D 2.6 ft. 2.5 ft. Sta. 45 D Sta. 40 D=2.4 ft. Sta. 35 D=2.4 ft. Sta. 30 D=2.4 ft. 25 2.4 ft. Sta. D February 2, 1967, Section 255, Right bank station 0, Left bank station 66 2.4 ft. D 2.4 ft. D Sta. 10 0-2.4 ft. 5 .6 ft. Sta. =2 D 5 2 4 l 2 3 l 9 5 l 3 3 2 2 2 4 8 3 7 2 7.1 l 0 8 2 2 1 5 6 6 3 8 3 3 3 3 2 7 l 6 0 5 2 2 l l 2 Z 4 8 0 5 4 3 9 5 4.4.4 3 3 5 9 4 8 3 2 l 1 5 2 5 6 8 7 2 6 4.4.4 3 0.4 8 3 0 2 0 6 4.2 7 0 5 5 4 4 8 3 7 2 1 l 0 2 6 8 7 5 9 1 5 5 4 4 8 3 7 2 l 1 3 7 5 6 8 6 l 3 5 5 5 4 8 1.7 2 l l 6 l 9 3 7.6 0 3 5 5 5 4 8 3 7 2 1.1 9 6 2 7 4.3 9 2 5 5 4 4 8 3 7 2 1 9 2 8 0 0.6 6 3 2 2 1 0.4.8 3 1.1 V Sta. 65 D=2.9 ft. Sta. 60 D=2.3 ft. 2.3 ft. Sta. 55 D Sta. 50 D 2.4 ft. 2.4 ft. Sta. 45 D Sta. 40 D=2.5 ft. Sta. 35 D=2.5 ft. Sta. 30 D=2.5 ft. February 2, 1967, Section 260, Right bank station 4, Left bank station 70 25 2.5 ft. Sta. D Sta. 20 D=2.5 ft. 2.5 ft. D 2.8 ft. D 6 7 1 5 0 0.8 7 2 9 2 2 2 2 l 5 9 4.8 3 7.1 2 5 5 7 5 0 3 3 3 3 9 4 8 3 l l 8306 8 9 7.2 3 3 3 3 9 4 8 3 1 1 9 l 7 l 7.6 2 7 4.4.4 3 9 4.8 3 l 1 4 5 6 7 1.2 7 0 5 5 4.4 0.4.8 3 1.1 3 9 6 8 6 4.9 l 5 5 4.4 9 4 8 3 1 l 8 3 3 1 7.6 l 3 5 5 5 4 0.4.8 3 1 l l 1 3.8 8 6 0 1 5 5 5.4 8 3 7 2 1 1 9 O 9 4 4.4 7 0 5 5 4 4 8 3 7 2 l 1 6 1 l 7 1 0 6 9 5 5 4 3 9 4 8 3 1.1 4 O 8 4 2 2 8 3 4.4.3 3 9 4 8 3 1 l 5 6 2 3 2 2.2 1 5 9 3 3 3 2 1 4.8 3 7 2 2 1 l 2.6 ft. Sta. 60 D Sta. 55 D=2.3 ft. Sta. 50 D=2.4 ft. 2.4 ft. Sta. 45 D Sta. 40 D=2.4 ft. Sta. 35 D=2.5 ft. Sta. 30 D=2.5 ft. February 14, 1967, Section 220, Right bank station 4, Left bank station 68 Sta. 25 D=2.5 ft. 2.5 ft. Sta. D: Sta. 15 D=2.5 ft. Sta. 10 D=2.4 ft. 0 8 5 3 0 4 332 272 777 751 333 2.8 3 8 O 4 6 5 1 3 3 3 383 3 1 0 4 1.5 4.4 3 383 9 0 9 O 7.8 543 383 73/4 7.8 0 5 4 4 1.8 3 7.8 0 270 5 4 4 3 8 3 4.8 5 9.7 9 4.4.3 383 769 0 5 7 5 4 3 3 8 3 O 0 8 0.6 8 4 4.3 1.8 3 325 2 7 5 3 2 l 3 8 3 Sta. 55 D 3.4 ft. Sta. 50 D=3.0 ft. Sta. 45 D=2.7 ft. Sta. 40 2.6 ft. D Sta. 35 D=2.6 ft. 2.5 ft. D February 14, 1967, Section 225, Right bank station 2, Left bank station 66 2.5 ft. D 2.4 ft. Sta. 20 D Sta. 15 D 2.3 ft. Ste. 10 D=2.3 ft. 1 7 0 9 4 0 6 4 2322 9383 l l 7.0 5 4.8 8 1.2 1 4.8 3 903 205 4.4 3 1.8 3 907 7 4 7 4.4.3 3 8 3 4.1.7 7.8 0 544 3 8 3 530 4102 5 5.4 383 297 5 0 2 5 5 4 383 8 4.1 3 9 l S.A.4 1.8 3 l 7.7 626 “43 1.8 3 309 4.1 6 332 3 8 3 Sta. 60 D=2.5 ft. Sta. 55 D=2.6 ft. Sta. 50 D=2.l ft. 2.2 ft. Sta. 45 D Sta. 40 2.3 ft. D Sta. 35 D=2.4 ft. Sta. 30 D 2.4 ft. February 14, 1967, Section 230, Right bank station 3, Left bank station 70 Sta. 25 D 2.5 ft. Sta. 20 D=2.6 ft. Sta. 15 D=2.6 ft. 10 2.7 ft. Sta. D= 2 4 l 9 l 9 7 l 3 2 2 2 9 3 8 3 l 1 6 6 8 3 6 8 6 2 3 3 3 3 7.1 6 l 1.1 3/491 6 5 2 7 4.4 4.3 9 3 3 3 l l l 9 O 8 3 9 6 8 5 4 4 3 8 2 7 2 9 6 1 5 4 1 8 1 5 5 4 4 9 3 8 3 6 7 8 9 5 2 7 0 5 5 4 4 8 2 7 2 1 l 7 4 0 5 6 3 9 1 5 5 4 4 0.3 8 3 l 1 6 2 3 7 5 2 8 0 5 5 4 4 9 3 8 3 1.1 8 0 0 2 8 6 2 6 4 4 4 3 9 3 3 3 l 1 2 7 3 l 6 5 2 7 3 3 3 2 9 3 8 3 l l J31 60 3.4 ft. Sta. D: 2.8 ft. Sta. 55 D Sta. 50 2.5 ft. 2.5 ft. D Sta. 45 D 2.4 ft. Sta. 40 D 35 D=2.4 ft. Sta. Sta. 30 D=2.3 ft. Sta. 25 2.3 ft. D 20 February 14, 1967, Section 235, Right bank station 1, Left bank station 69 2.3 ft. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS Sta. D 15 D=2.2 ft. TABLE 2,—Measured velocity at indicated heights above riverbed—Continued Sta. Sta. 10 D=2.2 ft. Sta. 5 D=2.0 ft. 02471 67530 22222 48272 211 81145 26413 23332 48272 211 94.04 0083 4433 9383 11 4873 7527 4443 9383 11 9157 2060 5544 9383 11 1594 5170 5544 9383 11 3545 4179 5 5 A.l 9383 11 8586 3170 5544 9383 11 2733 2969 5443 9383 11 7949 6425 4443 9383 11 0075 0072 4 A.3 3 9 3 8 3 1 l 4 6 7 7 7 1 222 0.3 8 3 1 1 Sta. 60 D=2.9 ft. Sta. 55 2.6 ft. D 2.6 ft. Sta. 50 D 2.2 ft. Sta. 45 D 2.2 ft. Sta. 40 D Sta. 35 D=2.2 ft. 30 D=2.3 ft. Sta. February 14, 1969, Section 240, Right bank station 2, Left bank station 68 25 D=2.3 ft. Sta. Sta. 20 D=2.3 ft. Sta. 15 2.4 ft. D 10 D=2.6 ft. Sta. 1284 7973 2222 59383 211 82244 01974 33221 37161 211 89109 68633 33332 37161 211 1196 8626 4443 9383 11 1784 1818 5443 8272 11 1928 5291 5544 9383 11 1344 6392 5544 9383 11 0420 6392 5544 9383 11 7018 4281 5544 9383 11 4730 2960 5444 9383 0826 4182 4433 9383 Sta. 65 D=3.2 ft. Sta. 60 D=3.0 ft. Sta. 55 D=2.1 ft. Sta. 50 D=2.3 ft. 2.4 ft. Sta. 45 D Sta. 40 D 2.5 ft. Sta. 35 D=2.4 ft. Sta. D=2.4 ft. February 14, 1969, Section 250, Right bank station 4, Left bank station 71 25 D=2.4 ft. Sta. Sta. 20 D=2.4 ft. Sta. 15 D=2.4 ft. 10 7 ft. / Sta. D=2. 25384 78626 22221 59383 211 85851 45402 33332 48272 211 0567 7963 3333 9383 11 8344 7638 4443 9383 11 5938 2969 5443 9383 11 12000 5282 5544 9383 11 5624 6392 5544 9383 11 2714 7413 5554 9383 11 5314 6413 5554 9383 11 0846 4070 5544. 9383 11 5088 8738 4443 9383 L 1 28246 58637 33332 59383 L L 1 Sta. 65 D=2.5 ft. V Sta. 60 D=2.6 ft. 55 2.4 ft. Sta. D 2.7 ft. Sta. 50 D Sta. 45 D=2.5 ft. Sta. 40 2.5 ft. D Sta. 35 D=2.5 ft. Sta. 30 D 2.4 ft. 25 2.4 ft. February 14, 1967, Section 260, Right bank station 4, Left bank station 71 Sta. D 2.4 ft. Sta. D= 15 2.3 ft. Sta. D Sta. 10 D=2.7 ft. 0255 6640 2222 9383 11 104 653 333 8272 11 7680 5209 3332 9383 11 0773 4294 4433 9383 11 5746 2958 5443 8272 11 1212 52000 5544 9383 11 0989 6280 5544 9383 11 7048 6491 5544 8272 11 9414 [4280 5544 9383 11 6980 9638 4443 9383 11 2176 5394 4433 9383 11 8956 2961 «L222 9383 11 3.1 ft. V Sta. 55 D Sta. 50 D=2.2 ft. Sta. 45 2.4 ft. D 40 D=2.4 ft. Sta. 2.5 ft. Sta. 35 D Sta. 30 D 2.5 ft. February 14, 1967, Section 270, Right bank station 2, Left bank station 65 25 D=2.6 ft. Sta. Sta. 20 D=2.6 ft. Sta. 15 D 2.5 ft. 2.3 ft. Sta. 10 D 37038 53164 33321 48272 211 2483 5295 4433 8272 11 2995 9627 4443 9383 11 5369 4170 5544 9383 1557 6280 5 5.4 4 9383 0862 7392 5544 9383 0329 7390 5544 9383 4257 5280 5544 9383 11 5635 2181 5544 93003 11 4761 2204 4443 9383 11 2.9 ft. V Sta. 60 D Sta. 55 D=2.7 ft. 2.5 ft. Sta. 50 D Sta. 45 D=2.5 ft. D=2.5 ft. Sta. Sta. 35 D=2.4 ft. Sta. 30 D=2.4 ft. Sta. 25 =2.4 ft. February 14, 1967, Section 280, Right bank station 3, Left bank station 70 D 2.5 ft. Sta. D= Sta. 15 D=2.5 ft. Sta. 10 D=2.5 ft. 5 .6 ft. Sta. D=2 2887 9974 2222 9383 11 3464 5364 3333 9383 11 2654 4320 4444 9383 11 5082 1950 5444 8272 11 5483 4281 55lm4 9383 11 7825 6392 5544 8272 .11 [4036 7403 5554 8272 11 1389 6380 5544 8272 11 <37 0 7 2 9 6 9 5 L A.3 9383 11 0340 6638 4443 9383 11 4120 4638 3332 9383 11 3981 2941 2111 8272 11 3.1 ft. Sta. 55 D 2.7 ft. Sta. 50 D Sta. 45 D=2.4 ft. 2.3 ft. Sta. 40 D Sta. 35 D=2.4 ft. Sta. 30 D=2.5 ft. Sta. 25 D=2.6 ft. February 15, 1967, Section 220, Right bank station 0, Left bank station 64 20 2.6 ft. Sta. D= 2.5 it. D 2.5 ft. D 2.6 ft. D 50898 09530 32222 59383 211 87259 03551 33333 59383 211 3244 1084 4433 9383 11 8048 8639 4443 9383 11 8989 5284 5544 9383 11 2657 7382 5544 9383 11 6132 7504 R.5 5 4 6.3 8 3 1 1 6172 7.<,0 4 ESSA. 9383 1 1 0.7 4.7 2072 5 5 A.4 9383 1.1 6766 5206 4443 9383 11 8002 4383 3322 9383 11 60 3.3 ft. V Sta. D Sta. 55 3.5 ft. D Sta. 50 D=2.9 ft. Sta. 45 2.5 ft. D 2.7 ft. Sta. 40 D 2.6 ft. Sta. 35 D Sta. 30 2.5 ft. D 2.5 ft. Sta. 25 D February 15, 1967, Section 225, Right bank station 2, Left bank station 66 20 2.4 ft. Sta. D= Sta. 15 D=2.4 ft. Sta. 10 D=2.4 ft. 5 2.2 ft. Sta. D: 66837 44220 22222 59383 211 01644 40755 33222 48272 211 60276 08531 43333 59383 211 0160 6307 4443 9383 11 S 8 9 1 18/49 5443 9383 11 7175 4169 5543 9383 11 1582 5170 5544 9383 11 7253 4281 5544 9383 11 9102 9860 4444 9383 11 4502 7426 4443 9383 11 9547 5538 3332 9383 11 0176 3432 1111 9383 11 Sta. 65 D=4.3 ft. y V 60 V D=3.5 ft. Sta. Y Sta. 55 D=2.8 ft. y V Sta. 50 -2.2 ft. v y D Sta. 45 D=2.2 ft. y V Sta. 40 D=2.3 ft. y V 35 2.3 ft. V Sta. D Y 2.5 ft. V Sta. 30 y D V February 15, 1967, Section 230, Right bank station 4, Left bank station 70 25 Sta. D=2.5 ft. y 20 V R10 GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965—69 2.6 ft. Sta. Y TABLE 2.—Measm‘ed velocity at indicated heights above riverbed—Continued D Sta. 15 D=2.6 ft. y V Sta. 10 D 2.7 t:. V Y J32 2 9 4 8 6 76521 2 2 2 2 l 5 9 3 8 3 2 1 l 7.1 2 2 5 3 l 7 3 3 3 2 5 9 3 8 3 2 1 1 0 8 7 9,6 3 4 3 1 7 3 3 3 3 2 5 9 3 8 3 2 1 1 3600 1.0 8 3 4.4 3 3 9 3 8 3 3 2 4 3 6 5 2 7 4 4.4 3 9 3 8 3 11 5 7 6 7 0 8 5 9 5 4.4 3 9 3 8 3 3850 4.1 8 2 5 5 m L 00272 9 4 9 2 4 6 5 2 9 2 6 5 5 4 4 5 9 3 8 3 2 1 1 .20814 6 4 1 8 2 6 5 5 4 4 5 9 3 8 3 2 1 1 6 5 8 9 1 7.1 8 4 9 6 5 4 4 3 5 9 3 8 3 7.1 1 6 8 7 1 7 9 7 6 3 7 4.4 4 4 3 5 9 3 8 3 2 1 1 1.1.4 2 5 0 4.4 1 6 3 3 3 3 2 5 9 3 8 3 2 l 1 Sta. 65 D 3.4 ft. Sta. 2.6 ft. D 60 3.7 ft. 2.8 ft. Sta. D= Sta. 55 D: 50 3.1 ft. 2.4 ft. Sta. 55 D= Sta. D= 50 Sta. =2.6 ft. Sta. 45 D=2.4 ft. D 2.6 ft. Sta. 45 Sta. 40 D=2.3 ft. D D=2.5 ft. 2.3 ft. Sta. 40 Sta. 35 D 35 2.5 ft. 2.3 ft. Sta. D= Sta. 30 D: 25 2.3 ft. Sta. 30 D=2.4 ft. Sta. D: 25 20 2.4 ft. 2.4 ft. February 15, 1967, Section 240, Right bank station 2, Left bank station 68 February 15, 1967, Section 235, Right bank station 1, Left bank station 69 Sta. Sta. D: D 2.3 ft. 2.4 ft. D: Sta. 15 D: 2.3 ft. 2.7 ft. D= Sta. 10 D= 5 ft. Sta. 10 =2.3 ft. Sta. 3.0 D D 8551.. 9 8 6 4 7.2 2 2 9 3 8 3 1 1 4694 3 2 1 9 3332 3 2 7 2 1 1 8028 9 8 5 0 3 3 3 3 9 3 8 3 1.1 6 8 6 2 5 3 O 6 4 4.4.3 9 3 8 3 1.1 5 3 3 2 2060 5 5 4.4 9 3 8 3 1 1 O l 0 2 4.170 5 5 4 4 9 3 8 3 1 l 8 7 2 1 5 0 9 3 5 5 L L 9 3 8 3 1 1 7 8 5.3 4 1 8 1 5 5 4.4 9 3 8 3 11 9300 2 0 7 2 5 5 4.4 9 3 8 3 1 1 5 4 5 8 00748 4.4.4.3 9 3 8 3 l l 4.0 2 8 2 8 5 0 4 3 3 l 9383 ll 6 6 0 2 n.1 9 3 1.1 L L 0494 Sta. 65 D=2.6 ft. V 2.3 ft. Sta. 60 D Sta. 55 D=2.1 ft. Sta. 50 2.1 ft. D Sta. 45 D=2.2 ft. Sta. 40 2.2 ft. D Sta. 35 D=2.2 ft. Sta. 3O D=2.3 ft. February 15, 1967, Section 245, Right bank station 4, Left bank station 78 25 2.3 ft. Sta. D Sta. 20 D-2.4 ft. 2.5 ft. Sta. 15 D 10 D=3.1 ft. Sta. 0 6 6 4 3 2 7 5 3 3 2 2 9 3 8 3 11 3 5 4 4 7 5 3 9 3 3 3 2 9 3 8 3 ll 3 8 6 3 3 3 l 7 4.4 4.3 9 3 8 3 1 1 8 8 2 5 7 7 5 9 4.4.4 3 9 3 8 3 l l 8 9 7 6 1960 5 4.4 4 9 3 8 3 1 1 3 7 3 6 306° 5 5 4.4 9 3 8 3 1 l 3 5 4 6 3 1 7 0 5 5 4 4 9 3 8 3 1 1 2 7 0 8 2 0 7 9 5 5 4 L 9 3 8 3 l 1 2 6 3 3 2 9 6 1 5 4 4.4 8 2 7 2 1.2 6 3 6 4.1 7 4 4 4.3 9 3 8 3 11 5 3 5 9 9 7 5 1 3 3 3 3 9383 7 9 2 1 9 3 l 7 8 0 3 3 2 1 1 5 9 3 8 3 2 1 1 Sta. 60 D=3.1 ft. V Sta. 55 D=2.6 ft. Sta. 50 D=2.6 ft. Sta. 45 D=2.5 ft. Sta. 40 D=2.4 ft. Sta. 35 2.4 ft. D 30 D=2.4 ft. Sta. Sta. 25 2.4 ft. D February 15, 1967, Section 250, Right bank station 0, Left bank station 67 Sta. 20 D 2.3 ft. 2.3 ft. Sta. 15 D 10 D-2.4 ft. Sta. Sta. 5 D=2.8 ft. 72 .76 72 .32 2 2 2 2 2 4 8 2 7 2 8801 8 8 7.4 3 3 3 3 9 3 8 3 1 1 4.8 6 6 8 8 6 2 3 3 3 3 9 3 8 3 1.1 9714 4 2 9 4 4 4 3 3 9 3 8 3 1 l 6 3 4.6 1.0 7 0 5 5 4 4 9 3 8 3 1.1 3 2 8 4 47.002 5 5 4.4 9 3 3 3 1.1 2 1 6 2 8 1 i m L 9 3 8 3 1.1 0816 4 l 8 1 5 5 4 4 9 3 8 3 1 l 8632 1960 5 4 4.4 9 3 8 3 3858 0 7 4 8 5 4 4 3 9 3 8 3 1 1 4 3 8 7 3 1 8 3 4 4 3 3 9 3 8 3 9 1 6 3 3 5.4.1 8 4 3 3 1.7.2 48272 2 1 1 .07 Sta. 65 D=2.6 ft. 2.0 ft. Sta. 60 D 55 D=2.5 ft. Sta. 2.4 ft. Sta. 50 D 2.4 ft. Sta. 45 D Sta. 40 D 2.4 ft. Sta. 35 D=2.4 ft. Sta. 30 2.4 ft. February 15, 1967, Section 260, Right bank station 4, Left bank station 71 D 2.4 ft. Sta. 25 D Sta. 20 D=2.4 ft. Sta. 15 D=2.4 ft. Sta. 10 D=2.8 ft. 0212 9 7 5 9 2 2 2 1 9 3 8 3 7 8 3 3 0 8 3 3 2 9 3 8 3 6 2 0 7 1.0 8 3 4 4 3 3 9 3 8 3 1 1 8 0.4.4 7 4 2 8 44.43 9 3 8 3 1 l 7 7 4 0 4.0 7 2 5 5 4 4 9 3 8 3 l l 8 5 4 3 5 1 7 1 5544 9 1.8 3 1 1 9 9 2 0 6 2 9 2 5 5 4 4 9 3 8 3 11 9680 6 3 8 2 5 5.4.4 9 3 8 3 l 1 8 5 1 7 5 1 3 2 5 5 4 4 9 3 8 3 1 1 2 7 2 1 9 6 4 9 4.4.4 3 9 3 8 3 1 1 4 9 4.4 3 O 8 4 4 4 3 3 9 3 8 3 1 1 3 4 4 4 2 9 5 1 3 2 2 2 8 2 7 2 11 60 D=2.7 ft. Sta. 3.9 ft. Sta. 55 D Sta. 50 =3.0 ft. D Sta. 45 D=2.5 ft. Sta. 40 2.5 ft. D Sta. 35 D=2.5 ft. 2.6 ft. Sta. D: D=2.6 ft. February 15, 1967, Section 270, Right bank station 3, Left bank station 66 Sta. 25 Sta. 20 D=2.6 ft. 2.5 ft. Sta. 15 D Sta. 10 D=2.5 ft. 5 2.5 ft. Sta. D= 9 6 0 K 3 9 7 1 2 1 l 1 9 3 8 3 1 1 0 5 9 8 9 6 3 7 2 2 2 1 9 3 8 3 0 4.3 2 7 3 4 6 3 3 2 1 9 3 8 3 1 l 8 6 l 4 7538 4.4.4.3 9 3 8 3 7 2 5 8 4 7.8 3 5 5 4.4 9 1.8 3 1 1 1 1.6 2 6 3 9 4 5 5 4 4 9383 11 2 3 7.4 7 4 0 3 5 5 5 4 9 3 8 3 11 4.7.8 4 5 2 8 3 5 <.4.4 9 3 8 3 1 1 2 9 3 9 2 9 6 0 5 4 4 4 9 3 8 3 l 1 7218 6 5 3 8 4 4 4 3 9 3 8 3 1 1 050° 6 4.2 7 4 4.4 3 9 3 8 3 11 5 5 6 5 8 8.6 5 L 1 1 1 9 3 8 3 1.1 Sta. 60 2.8 ft. D Sta. 55 D=2.5 ft. 50 D=2.6 ft. Sta. Sta. 45 2.4 ft. D Sta. 40 D=2.4 ft. Sta. 35 D=2.4 ft. Sta. 30 D 2.4 ft. February 15, 1967, Section 280, Right bank station 3, Left bank station 70 2.4 ft. Sta. D: Sta. 20 D=2.4 ft. 2.5 ft. Sta. 15 D Sta. 10 D=3.0 ft. 7 6 4 2 5 3 1 9 6 3 3 3 2 2 2 5 9 3 8 3 2 1 l 1 3 4 9 9 7 4 1 3333 9 1.8 3 1 1 0644 7 5 2 3 mmm& 9383 1 1 5 6 3 3 7.0.6 1 5444 8 2 7 2 1 1 1 3 1 4 6 1.8 3 5 5 4 4 9 3 8 3 1 1 8 5 2 0 5 2 9 2 5 5 4.4 9 3 8 3 11 l 3 8 1 6 3 8 3 5544 9 3 8 3 1 1 1 9 5 7 6 2 8 Z 5 5 4 4 9 3 8 3 2 8 0.2 2840 544.4 0.1.8 3 8 9 3 4 3073 4 4.3 3 9 3 8 3 1 1 6 4 6 2 5 6 4 2 1 3 3 1.3 3 2 5 9 3 8 3 2 1 1 J33 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS TABLE 2.—Measured velocity at indicated heights above riverbed—Continued February 1, 1968, Section 99, Right bank station 0, Left bank station 62 Sta. 55 50 Sta. Sta. 45 4O D=3.0 ft. Sta. 20 Sta. 25 Sta. 30 Sta. 35 2.9 ft. D 2.9 ft. D 2.9 ft. D 3.0 ft. Sta. D Sta. 15 6 Sta. 10 3.3 ft. Sta. D 3.5 ft. D= 3.3 ft. D= 3.1 ft. D= 2.9 ft. D= 3.0 ft. D= February 1, 1968, Section 100, Right bank station 0, Left bank station 57 Sta. 50 D 4.3 ft. 45 3.7 ft. Sta. D Sta. 40 35 3.1 ft. Sta. D 30 Sta. Sta. 25 Sta. 15 Sta. 20 D 2.5 ft. D 2.6 ft. 10 Sta. 3.4 ft. D= 2.9 ft. D= 2.7 ft. D= D32.7 ft. V 3 6 5 4 5 8 7 4 2 9 [44/4/43 5 7 2 8 4 2 l l 5 Z 8 3 2 1.0 5 4 9 5.4 3 3 2 3 5 0 6 2 2 l 1 February 1, 1968, Section 101, Right bank station 1, Left bank station 67 Sta. 25 Sta. 30 Sta. 35 Sta. 4O Sta. 45 Sta. 50 Sta. 55 Sta. 60 Ste. 20 Sta. 15 3.8 ft. D: 3.5 ft. D= 3.4 ft. D= 3.3 ft. D= 3.1 ft. D= 2.8 ft. D: D=2.6 ft. 2.4 ft. D: D=2.4 ft. 2.3 ft. D= 1‘1 2 0 9 2 6.6 5 1 3 3 3 3 3 5 7 2 3 4 2 1 l 7 0 3 2 0 8 7 4 2 0 4.4.4 6.4 5 7.2 8 4 2 l 1 11950 5 l 6 4 2 5 5 4 4.4 5 7 2 8 4 2 l l 9 8 7 9 0 2 8 4 2 0 5 4 4 4.4 5 7 2 8 4 2 l l l 8 5 4.8 0 5 0 7 3 6 5 5 4.4 5 7 2 8 4 2 l 1 February 1, 1968, Section 159, Right bank station 1, Left bank station 88 65 1.8 ft. Sta. D Sta. 60 55 1.9 ft. Sta. D Sta. 45 Sta. 50 Sta. 40 35 D=2.3 ft. Sta. 30 D=2.5 ft. Sta. Sta. 25 D 2.6 ft. Ste. 20 Sta. 15 D 2.6 ft. 10 3.1 ft. Sta. D 1.9 ft. D= 2.1 ft. D= D=2.2 ft. D=2.3 ft. D=2.6 ft. V 6 7 l 0 l O 9 7 4.4 3 3 7 2 8 4 l l 6 9 9 6 5 4.2 0 A.A.4 4 728/4 11 1.1.2 6 1853 5 L 4.4 7 2 8 4 1 9 6 6 5 0 7 3 5 5 4.4 7 2 8 4 1.1 3 3 l 3 6 1 8 4 5 S.4 4 7 2 8 4 1 1 9752 6 0 8 4 5 5 4 4 7 2 8 4 1.1 Sta. D=1.6 ft. 70 1.7 ft. 5 6 8 3 2 0 3 3 3 2 8 4 7 6 3 7 6 4 3 3 3 2 8 4 February 1, 1968, Section 160, Right bank station 0, Left bank station 85 Sta. 70 Sta. 65 60 D-1.9 ft. 50 Sta. 55 Sta. D=1.9 ft. Sta. 25 Sta. 30 Sta. 35 Sta. 40 Sta. 45 Sta. Sta. 19 14 2.7 ft. Sta. D D=1.9 ft. 1.9 ft. D: D=1.9 ft. 2.0 ft. V D=2.1 ft. D 2.2 ft. D= D=2.3 ft. 2.4 ft. D: 2.6 ft. D: 835/4 6 5 3 1 3 3 3 3 728/4 11 3 5 l 4 3 l 9 6 A.A.3 3 7 2 8 A 1 l 8 5 5 7 §.4 2 9 A.A.4 3 May 21, 1968, Section 225, Right bank station 2, Left bank station 63 55 D=4.6 ft. Sta. 50 Sta. Sta. 45 4O D=3.7 ft. Sta. 35 D=3.8 ft. Sta. 30 Sta. Sta. 25 20 D=4.8 ft. Sta. 15 Sta. Sta. 10 5 D=4.7 ft. Sta. 4.9 ft. D: D=4.2 ft. 4.0 ft. D= 4.2 ft. D= D=6.0 ft. D=6.2 ft. V V l 1 2 4.2 6 6 5 4 3 3 3 3 3 3 5 5 6 0 5 3 2 1 l 9 0 5 l 0 3 8 7 7 3 3 3 3 3 2 2 2 3 7 2 3 2 1 May 21, 1968, Section 227, Right bank station 3, Left bank station 70 Sta. 65 D-3.3 ft. Sta. 60 D=4.2 ft. Sta. 55 D=4.5 ft. Sta. 50 D=5.3 ft. Sta. 45 D=5.3 ft. Sta. 40 D=6.6 ft. 35 D-6.0 ft. Sta. Sta, 30 D-5.3 ft. Sta. 25 D=4.6 ft. 20 D=4.5 ft. Sta. Sta. 15 D=4.8 ft. Sta. 10 D=4.0 ft. V Y V Sta. 55 D-4.7 ft. V 4.8 ft. Sta. 50 D Sta. 45 D=4.7 ft. Sta. 40 D 5.3 ft. 35 D=4.9 ft. Sta. 30 D-4.4 ft. Sta. 25 D=4.2 ft. May 21, 1968, Section 229, Right bank station 0, Left bank station 64 Sta. Sta. 20 D-4.3 ft. 15 D-5.5 ft. RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965—69 TABLE 2.——Measured velocity at indicated heights above riverbed—Continued Sta. 10 D=5.5 ft. Sta. Sta. 5 D=5.5 ft. J34 6 9 9 5 7 9 9 8 4.0 2 2 2 2 2 9 2 4.4 7 3 3 2 l 7 9 l 3 4 1 l 0 5 3 3 3 3 2 2 9 2 4.4 7 3 3 2 1 4 4 8 3 4 [43053 3 3 3 2 2 8 1 3 3 8 3 3 2 l 6 2 5 7 0 5 7 8 8 6 2 2 2 2 2 03558 4321 3 4 8 9 2 6 5 5 4 3 2 2 2 2 2 9 2 4.4.7 3 3 2 l 5 6 7 l 5 8 9 0 8 6 2 2 3 2 2 7 0 2 2 5 3 3 2 l l 0 0 0 0 2 3 3 1 9 3 3 3 3 2 9 2 4.4 7 3 3 2 l 6 l 7 9 4 1 2 1 9 9 3 3 3 2 2 0 3 5 5 8 4 3 2 1 1 l 6 0 3 4.4.4 5 4 3 3 3 3 3 9 2 4 4 7 3 3 2 1 03359 5 4 2 8 8 3 3 3 2 2 03558 4 3 2 1 3 3 8 5 9 0 4.2 8 8 3 3 3 2 2 0 3 5 5 8 4.3 2 l 60 D-5.1 ft. v Sta. Sta. 55 D-5.0 ft. Sta. 50 D-4.3 ft. 4.0 ft. Ste. 45 D 3.7 ft. Sta. 40 D Sta. 35 5.0 ft. D 30 D=3.9 ft. May 21, 1968, Section 231, Right bank station 4, Left bank station 70 Ste. D=4.0 ft. 5.0 ft. Sta. n= Sta. 15 D-5.9 ft. Sta. 10 D=4.7 ft. 6 9 0 7 2 6 5 3 0 6 3 3 3 3 2 8 0 9 3 6 3 3 l l 6 9 0 5 5 l 9 9 8 6 3 2 2 2 2 0 2 l 5 8 4 3 2 l 6 3 8 8 l 2 2 0 9.4 3 3 3 2 2 5 9 8 2 5 3 2 l 1 3 4.5 9 1 6 9 0 9 8 2 2 3 2 2 8 2 l 5 8 3 3 2 1 9 8 3 2 7 6 9 0 9 6 2 2 3 2 2 5 9 8 2 5 3 2 l l 3 2 2 0 9 4.3 l 9 1 3 3 3 2 l 5 9 8 2 5 3 2 l l 7 9 2 9 8 1 5 6 5 4 3 3 3 3 3 8 2 1 5 8 3 3 2 l 7 1.9 0.4 3 6 5 3 1 3 3.3 3 3 8 l 3 3 6 3 3 2 l 2 2 3 0 6 1 l 0 9 1 3 3 3 2 2 9 2 4 4.7 3 3 2 l 5 8 4 5 7 0 9 9 6 3 3 Z 2 2 2 03558 4.3 2 l 0 5 7 4.6 90071 2 3 3 2 Z 0 3 5 5 8 4 3 2 1 65 D=4.2 ft. V Sta. Sta. 60 D-4.3 ft. Sta. 55 D=6.0 ft. Sta. 50 D=4.4 ft. Sta. 45 D=4.1 ft. 40 D-4.3 ft. Sta. Sta. 35 D=3.8 ft. 30 D=3.5 ft. Sta. 3.6 ft. Sta. 25 D May 21, 1968, Section 233, Right bank station 1, Left bank station 72 20 D=3.9 ft. Sta. 15 D=4.7 ft. Sta. 10 D-5.0 ft. Sta. Sta. 5 D-4.6 ft. 2 3 8 1 5 00885 9 9 9 0 8 22232 4.6 8 1.5 3211 05117 9 8 7 5 0 22222 3 5 7 0.4 3 2 1 1 1 4.8 3 4 0 7 9 5.3 3 2 1 1 l 4 6 8 1 5 3211 8 5 0 0 9 2 2 1 9 6 33322 4 6 8 1 5 3 2 1 1 6 8 S 2 0 7 9 8 7 6 2 2 2 2 Z 3 5 7.0.4 3 2 1 1 37934 0 8 8 0 9 32232 2 4 6 9 3 7 9 2 l l l 0 l 3 3 3 3 2 l 5 8 2 l 3 0 7 5 4.2 1.6 3 3 3 3 2 0 2 l 5 8 4 3 2 1 87791 6 5 3 8 0 3 3 3 2 2 3 0 9 3 6 3 3 1 1 7 4.3 7 2 8 l 2 l 9 2 3 3 3 2 9 l 0 4.7 3 3 2 1 Sta. 50 D=6.3 ft. 45 D-5.4 ft. Sta. 4.7 ft. Sta. 40 D Sta. 35 D=4.5 ft. Sta. 30 D=5.3 ft. Sta. 25 6.0 ft. D May 29, 1968, Section 225, Right bank station 4, Left bank station 63 6.4 ft. Sta. 20 D Sta. 15 D=5.6 ft. Sta. 10 D 6.0 ft. YY Sta. 5 D-5.7 ft. 8 9 l 7 0 9 7 3 3 2 2 2 3 0 0 3 7 4 3 2 1 8 7 0 7 7 8 9 8 2 2 2 2 3 0 0 3 7 4.3 2 l 0 4 1 0 3 3 4 3 3 3 3 3 0 0 0 3 7 4.3 2 1 l 5 0 6 6 5 5 2 3 3 3 3 0 0 0 3 7 4 3 2 l 0 4.3 6 0 6 0 7 4 1.3 2 1 8 8 1 5 4 2 1 1 3 9 3 1 1 5 8 5 4 3 2 2 30037 4 3 2 l 5 7 5 4 9 5 0 8 5 9 3 3 2 2 1 1 8 8 l 5 4 2 1 1 6 2 3 0 7 8 6.4 l 8 3 3 3 3 2 2 9 9 2 6 4.2 1 l 8 2 5 6 l 6 3 2 2 2 3 3 2 1 1 30.0.37 4 3 2 1 5 6 l 1 4 6 4.7 8 6 2 3 2 1 1 2 9 9 2 6 4.2 1 l 8.0 ft. V Sta. 55 Y D Sta. 50 D=6.3 ft. Sta. 45 5.0 ft. D Sta. 40 D=4.9 ft. 35 D=6.2 ft. Sta. Sta. 30 D 5.1 ft. May 29, 1968, Section 227,I Right bank station 1, Left bank station 70 25 D-4.0 ft. Sta. Sta. 20 D=5.0 ft. Sta. 15 D=5.0 ft. Sta. 10 D 4.9 ft. 0 2 7.9 7 1 3 2 3 3 3 3 8 5 8 l 5 3 2 l 1 5051 7 5 8 4 3 3 2 l 7.4 7 0 4 3 2 1 l 2 0 l 9 0 7 6 3 4 3 3 3 9 6 9 2 6 3 2 1 l 2 9 0 7 0 8 8 5 4.3 3 3 0 7 0 3 7 4.2 2 l 8 6 6 1 4.2 l 5 3 3 3 2 0 7 0 3 7 4.2 2 l 7 8 4 l 7 6 6 4 3 3 3 3 9 6 9 2 7 3 2 l l 6 4 2 9 0 0 0 8 4.4 4 3 5 7 0 3 7 3 2 2 1 9 0 0 3 7 3 3 2 1 0 5 4 6 3 5 5 4 7 5 3 3 3 2 1 9 0 0 3 7 3 3 2 1 5 1 8 1 7 3 4 2 8 l 3 3 3 2 2 3 0 0 3 7 4 3 2 1 4.7 ft. Sta. 55 D 4.7 ft. Sta. 50 D Sta. 45 5.5 ft. D Sta. 40 D—4.9 ft. Sta. 35 D=4.6 ft. Sta. 30 4.0 ft. D May 29, 1968, Section 229, Right bank station 1, Left bank station 65 Sta. 25 D 3.4 ft. 4.1 ft. Sta. 20 D Sta. 15 D=4.4 ft. Sta. 10 D=5.1 ft. 1 8 2 3 2 4 6 5 2.3 3 3 7 5./ 8 3 2 1 2 4.3 7 8 6 4 1 3 3 3 3 7.5 7 8 1.2 1 116 0 8 7 6 7.4 3 3 3 3 7 5 7 8 3 2 1 4.0 9 2 8 8 7 6 1.3 3 l 7.5 7 8 132 l 3.5 9 2 9 9 8 8 3 3 3 3 6.4 6 7 1.2 l 6.1 0 5 :46 7 7 3.3 3 3 2 8 0 2 3 2 2 l 2 6 9 2 5 6 7 8 3 3 3 3 2 8 0 2 3 2 2 1 6 2 2 9 5 5.5 4 4.4.4 4 9 7.9 l 3 2 l 1 4 5 6 7 3 9 3 2 4.1.4 4 0802 4 2 2 2 5.0 012 4.1414 0 8 0 4.2 2 60 5.3 ft. V Sta. D y Sta. 55 D=4.5 ft. Sta. 50 D=S.0 ft. Sta. 4S D=4.9 ft. Sta. 40 D=4.5 ft. Sta. 35 D=4.l ft. 30 D=4.3 ft. Sta. May 29, 1968, Section 231, Right bank station 1, Left bank station 71 25 Sta. D-4.3 ft. Sta. 20 D=5.3 ft. 5.1 ft. Sta. 15 D 1.2 3.93 Sta. 10 D=5.0 ft. 6 l 0 1 4.6 5 4 3 3 3 2 0 4.0 8 4 3 2 3 0 l 2 l 0 9 6 4 4.3 3 8 2 8 6 3 3 l 9396 0 9 7 4 4.3 3 3 8 2 8 6 3 3 1 4.8 5.4 0 6 3 l 4.3 3 3 0 4.0 8 4.3 2 5 2 2 7 5 3 9 6 3 3 2 2 5 2 8 6 3 3 1 6006 8 5 l 5 3 3 3 2 7 4 0 8 3 3 2 5 4 5.4 5 3 0 9 3 3 3 2 0 4 0 8 4 3 2 8 4.1 8 4.3 0 7 3 3 1 L 0 4 0 8 4.3 2 5 3 6 7 7 7.6 3 3331 0 4 0 8 4 3 2 5 3 6 3 7 7 6 2 3 3 3 3 0 4.0 8 4.3 2 7 l 7 5 3 6 5 2 3 3 3 3 0 4.0 8 4.3 2 Sta. 60 —5.0 ft. V Y D Sta. 55 D=4.5 ft. Sta. 50 D=4.5 ft. Sta. 45 4.1 ft. D Sta. 40 4.2 ft. D Sta. 35 D=4.8 ft. Sta. 30 D=5.0 ft. May 29, 1968, Section 233, Right bank station 0, Left bank station 75 25 0-5.3 ft. Sta. 20 D=5.0 ft. Sta. Sta. 15 D=4.9 ft. Sta. 10 D 4.4 ft. 3 5 0 7 5 3 8 l 3 3 2 2 7408 3 3 2 6 6.4 4 8817 3 3 3 2 7 4.0 8 3 3 2 6 4.9 6 2 1.8 9 3 3 2 l 4.1./ 5 3 3 l 0 3 1 7 9 8 8 6 2 2 2 2 6 3 9 7 3 3 l 1 l 9 8 4 4 3 9 3 3 3 2 6 3 9 7 3 3 1 l 6 2 8 6 2 9 5 3 3 2 2 8 2 8 6 3 3 l 5 0 3 3 9 7 5 2 3 3.3 3 0 4.0 8 4 3 2 117.7 0 l 0 0 7 4.4 4 3 0/408 4 3 2 5 l 7 2 7 6 3 l 3 3 3 3 8 2 8 8 3 3 l 8 6 7 6 4 2 8 5 3 3 2 2 9 3 9 7 3 3 l 6 6 7 7 2 2 0 3 3 3.x L 0 4.0 8 4.3 2 J35 65 6.6 ft. V Sta. D Sta. 60 5.1 ft. D Sta. 55 6.2 ft. D 7.2 ft. Sta. 50 D Sta. 45 D86.2 ft. 40 0-5.9 ft. Sta. 35 D-5.8 ft. Sta. June 11, 1969, Section 245, Right bank station 7, Left bank station 86 3O D-4.9 ft. Sta. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 25 D=4.8 ft. Sta. TABLE 2,—Measu7‘ed velocity at indicated heights above m'verbed—Continued 4.8 ft. Sta. 20 D 15 Sta. D=4.8 fc. O t V 6 9 9 8 4 6 6 9 4.4 3 f . . . M N 5 fl 7 2 2 2 2 2 t 9 9 6 1.6 . . . . _ 1 5 f V . 1.3 3 2 . . 6 7.2 2 2 l u .0 v: .0 n2 n2 a; :4 . am 32235 SD 4321 méy £2235 ¢ 77715 t O 9 7 2 6 5 f V . 5 l 4 2 6 1 4 3 3 3 2 L N m “NW N 7 5.15. .. osv . . 3 3 3 3 a 6 0 2 2 3 5 6 3 3 3 2 t % Y . . 4 3 J 2 3 J t = Y . 4.3 2 1 S D 4 3 2 1 . 5 4 1 3.4 t “2741 OfV I. 6 2 4 4 3 3.3 O 6 2 6 4791 - O 9632 .u c 3271 0 7 o 1 . _ 9 a 5 O 2 2 3 5 4. 5 f V . . _ 7 6 8 1 2222 7 t-y :4: 7 5 3321 S D 4.3 2 1 9 n n n n n n .. o o o o 2 1 1 2 4 m m u % v. 0 J J J 5 i i i i L L L 1 t . 6 7 7 0 7 t S D 4.3 2 1 fl fl M H a t 1.0 5 3 3 a t t t t t <.f V . t s s s s S 58 44333 S . k .K . k .K 1 7 k . . k . 0 5 6 2 4 w M 6 m m d Y 0 2 2 3 5 m 0 h V 8 9 1 l _ m m m u m m . . _ . . . . . . . 3 3 3 2 b S D 4.3 2 1 b 5 1.3 3 l b b M b b t t .J . t t . t C 21124 f f 67 02235 N d fl N d a . . e . 8 0 l 5 8 e t . Y . s L L a L L 4 3 2 1 L 0 H V 3.4 3 l 9 L S D 4.3 2 l 1. n . m , y o y a y 5 4 4 4.4 3 s 2 9 1 M 0 0 m. 0 0 . . r n n a n n 5 9 5 0 2 n a 4 0 2 2 3 5 n . 9 1 1.6 6 9 7 6 9 7 o t - Y ..... o t 4.6 5 3.4 m .m m C m m . . .1 S D 4 3 2 1 i 5 f V ..... t t 1. t t 3 3 2 1.1 t a 4 4.4 4 4 3 n a a a a a m t .J % fi 6 l 1. 3 fl 8 K M 2 1.1.2 4 s . 6 6 0 1.8 s a 5 0 2 2 3 5 L 7 0.4.% 0 M ..... k 5 H V 0.0 8 6 2 k R M Y L l L L . r k 5 f V . k k k 4 3 2 l . . 6 5 5 n 4 4.4.3 3 3 n n, m 5 8 5 6 m n m m M .A M n b m L 0 0 0 2 5 b e b b 7 9 2 4 l t m # V. 0 2 2 3 5 t 1.1.4.9 2 d t t = v. L L L L . t n t t ..... . S 0 7 1 1 6 h S D 4.3 2 1 h t 1.5 4.0 2 n .W D .W d .R fl ..... 8 8 0 f V . . n i i n 1 i 4 3 3 2 1 .1 i 4. 4 4.4.4 4 a R R n R R R . 1.3 7 5 0 R .6 w L M N w b N . 8 7 6 8 6 a L w w H M 2 1 1 2 4 m. 0 R V 7 4.0 8 8 an m A Y O J J 3 5 3 3 f V . . 2 <.fi V 0 5 J 8 0 w n. 0 f V . . . . O 4 3 2 1 5 4. 3 3 3 2 2 <. S D 4.3 2 l a H 5 7 7 7.6 6 5 % 5 6 6 6 5 4 4. a M 7 7. 4 4 4.3 W 2 2 2 m M a L 0 0 0 2 5 M . . c M & L O 0 m . . 7.5 m m % Y 0 J J 3 5 m Y H t = Y . .L . . H m 6 Y 0 3 fl 2 5 m a. t = Y . . . . H l 3 9 4 8 i S D 4.3 2 1 i . 8 3 3 9 0 W S D 4.3 1 S D 4 3 2 1 W 1. S D 3 2 1 9 7 5 3 9 a u 5 h V 3 4.3 0 8 n n n v n n . ..... u o o n o o 3 3 3 3 2 e e 3 4.4.4 4 3 c .1 . 4 9 4 9 4 i . i . 6 1 4 1. .1 S . 6 3 3 6 0 S .J t t 5 5 l 5 5 t t M N W N H w t t 1.5 9 0 t t 1 1 9 6 5 , 8.4 0 2 2 3 5 e C 0 f V ..... c 0 f V . . c 0 f V . . . . c 3 2 2 3 5 , 5 f V . d e 5 7 7.7.6 5 e 5 7 7 6 6 5 e e 6 7 6 5 5 e . . 9 3 4 4 3 3 3 9 t a Y . . . n S 7. S 4 d S 6 S 4 3 2 l 6 1 % S D 4 3 2 1 l . . . . n .. 9 . . r ) a 4 0 0 0 2 S . y a 4 0 0 2 5 , 1 a 4 0 2 2 3 5 l G 5 t = Y ..... 5 m 6 Y fl 3 0 J J m E. t = Y . . . . 5 t - Y ..... 6 S D 4.3 2 1 6 S D 4 3 2 1 G 6 S D 3 2 1 6 : S D 4.3 2 1 y 9 9 9 9 7 l 6 1 6 1 l . 3 4 S 8 4 o 1 1 o l 1 5 6 4 2 9 1 1. 0 H V 4 5 4 1.0 M i 3 ..... . . u . 6 , . y . 3 , . 1.6 9 33332 m :. umwww m 37 4243 1 c 33““ 1 .. nmnmm R 2 t .7023 zoav 0155 2 5 f V ..... 2 5 f V . 7. 0 f V . . . . 2 . . . u 0 f ..... u . . 9 5 5 4 3 2 1.1.2 4 J 3 3 V 4.4 4 3 3 J. m fl v. 0 2 2 3 5 r 4 7 7 7 7 6 5 r 4.2 7 7 7.6 5 r 5 9 7 7.6 5 t 7 ..... . . e . . e . . e . . e . . 4.3 2 1 . . S D 4.3 2 l b a 4. 0 0 0 2 5 b b a 4 0 0 2 5 b a 2 5 5 9 3 m d v. D J J 3 J m R = v. L l L L . m w 6 v. fl 0 J J J m t = Y .L L . m & m v. I L . . S D 4 3 2 l c D c S D 4.3 2 1 m S D 3 c e e e e 4.7.2 6 2 . 1.2 3 6 3 D D D D 8 9 8 6 5 t 6 7 6 5 3 . 2.3 fi.1 8 . . R.7.3 1. . 6 9 l 5 . . . 2 9 O 0 9 5 f V ..... t 6 9 2 7 7 t M W % w m t 7 0 5 5 t 1 5 0 8 3 3 3 3 3 t 6 7 8 7 5 2 4.4.4 4 4 5 f V ..... 5 f V . . . 0 f V . . . . 0 f V . . . . 5 f V ..... 6 3 7 7 7 6 5 3 7 8 7 6 5 4 7 7 6 5 7 7.6 6 4 2 1.3 1.3 3 . . 7 9 9 9 3 2 2.4.5 3 u.fl Y O 2 2 3 5 . . . . . . 3 . . . . . 4 0 O 2 5 2 5 a 2 5 5 9 4 3 2 1 m d v. 0 2 2 3 5 S D 4.3 2 l m = v. 0 . . H d V. J J J J J m % V. fl 0 . . t W v. L L . . . . . S D 4.3 2 1 S D 4.3 2 1 S D 4.3 2 1 S D 3 2 1 S 3 5 5 O 7 . O 0 3 3 . 2 6 1.8 6 . 4.5 8 8 8 . . 3 3 . 4 2 0 6 9 2 l 0 7 5 H V 7 8 7 O L W n M M N O R V 4.5 J J 3 t V 1.2 6 0 1 t M w W N M t 1 w 2 M 0 h V 3 6 1 7 . . . . . 5 f . . . f . . . O f V . . . . . . . . 3 3 3 0 f V . 2 4.4 4.4 4 D V 5 7 6 6 4 4 4.4 7 8 3 3 3 2 3 3 3 3 3 3 3 2 7 7.7 6 6 5 z 7 7 7 7 6 5 3 0 7 6 6 S 4 1 0 0 1 3 L i 2 1 l 2 . . 3.4 9 l 1 2 4 a L 0 0 O 2 5 . . .i 0 0 2 5 m L 5 5 9 3 k L L 1 R M v. L L L L m fl v. A J J J 5 R m v. 3 3 L L t = Y .1 L L . m A v. 0 A J J J m a Y . . . . k k v. L L . . S D 4.3 2 1 S D 4 S D 4.3 2 1 S D 3 2 l . (.6 8 6 1 . . 2.6 5 . 1.7 8 2 1 2 2 3 4. . 4.4.6 8 . 6 7 5 7 . 2 7 3 7 5 t 8 0 5 1.6 t M M m n M t W 7 4 O t R.0.5 4 0 8 8 7.6 t 6 8 8 6 t 4.5 7 7 t 2 2 1 O 9 5 f V ..... 5 f V ..... O f V . . . . O f V . . . . . . O f V . . . . 5 f V . . _ 5 f V . l 5 6 5 5 4 1 5 5 5 5 4 2 4.3 3 3 3 6 5 5 4 33333 7 3333 18 3333 11 44443 7 5 3 5 8 . . . . . . . . . . . . . 4 O 2 5 2 5 a 3 5 5 9 3 3 2 2 3 5 a 5 v. 2 1 1 2 m fl v. 9 1 1 2 4 m 6 v. D J J J J m = v. 3 A . . . m A v. 0 3 m 2 5 m a v. D D . . t = v. L L . . 4.1 L 1 & W L l 2 L S D 3 3 2 1 S D 4.3 2 l S D 4.3 2 1 S D 4 1.2 1 S D 1.2 1 S D J36 RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965—69 TABLE 3. —Summary of size analyses and related data for point-integrated sediment samples Concentration in mg/l, Water Water Total Height 9:): Percent finer than indicated size, f 51175 (:11 s J-nm, Date Station Discharge Tempera— Depth above y in mm Finer 0.062 0.125 0.250 0.500 Coarser (ft) 0 ture of Flow Bed Sample than to to to to than (ft3 per T D y 0.062 0.125 0.250 0.500 1.00 0.062 0.125 0.250 0.500 1.00 0.062 second) (0c) (ft) (ft) Rio Grande conveyance channel near Bernardo, N. Mex. Sampling section 255, Right bank station 4, Left bank station 71 1965 Nov. 29 20 1,250 6 4.2 3.7 0,14 66 93 100 -— -- 2,690 1,780 726 188 0 0 910 4.2 1.5 1.80 41 75 99 100 -- 4,530 1,860 1,540 1,090 45 0 2,670 4.2 1.0 3.20 44 75 99 100 -- 4,490 1,980 1,390 1,080 45 0 2,510 4.2 .5 7.40 38 68 97 100 -- 5,120 1,950 1,540 1,480 154 0 3,170 4.2 .3 13.0 17 34 89 100 -— 12,100 2,060 2,060 6,660 1,330 0 10,000 30 1,250 6 4.2 3.7 .14 67 92 100 -— —— 2,680 1,800 670 214 0 0 880 4.2 1.5 1.80 50 81 100 —— -— 3,710 1,860 1,150 705 0 0 1,850 4.2 1.0 3.20 -- —— —— —— -— —— -- —— —- — -— 4.2 .5 7.40 27 50 94 100 —— 7,340 1,980 1,690 3,230 440 0 5,360 4.2 .3 13.0 22 40 86 100 —- 9,000 1,980 1,620 4,140 1,260 0 7,020 40 1,250 6 4.2 2.7 .56 55 88 100 -- -— 3,400 1,870 1,120 408 0 0 1,530 4.2 1.5 1.80 45 78 100 —— —— 4,400 1,980 1,450 968 0 0 2,420 4.2 1.0 3.20 34 66 99 100 -- 5,860 1,990 1,880 1,930 59 0 3,870 4.2 .5 7.40 28 54 96 100 -— 7,440 2,080 1,930 3,120 298 0 5,360 4.2 .3 13.0 15 33 90 100 —- 15,200 2,280 2,740 8,660 1,520 0 12,900 50 1,250 6 3.8 2.7 .41 55 85 100 -— —- 3,380 1,860 1,010 507 0 0 1,520 3.8 1.5 1.53 53 82 100 —- —- 3,500 1,860 1,020 630 0 0 1,640 3.8 1.0 2.80 49 79 100 -— -— 3,770 1,850 1,130 792 0 0 1,920 3.8 5 6(60 38 65 96 100 —— 5,190 1,970 1,400 1,610 208 0 3,220 3.8 3 11.7 15 26 71 99 100 13,300 2,000 1,460 5,990 3,720 133 11,300 Sampling section 252, Right bank station 4, Left bank station 69 Nov. 30 20 1,250 4 4.0 3.0 .33 54 84 100 ._ —— 2,980 1,610 894 477 0 0 1,370 4.0 1 5 1.67 46 77 99 100 -— 3,500 1,610 1,090 770 35 0 1,890 4.0 1.0 3.00 38 68 98 100 —- 4,390 1,670 1,320 1,320 88 0 2,720 4.0 .5 7.00 36 63 96 100 —— 4,560 1,640 1,230 1,500 182 0 2,920 4.0 .3 12.3 13 26 77 100 -- 14,100 1,830 1,830 7,190 3,240 0 12,300 30 1,250 4 4.0 3.0 .33 57 87 100 ~— —— 2,760 1,570 828 359 0 0 1,190 4.0 1.5 1.67 43 76 100 -- -- 3,900 1,680 1,290 936 20 0 2,220 4.0 1.0 3.00 37 67 98 100 —- 4,500 1,670 1,340 1,400 90 0 2,830 4.0 .5 7.00 23 45 90 100 -— 7,280 1,670 1,600 3,280 728 0 5,610 4.0 .3 12.3 18 42 93 100 —- 9,390 1,690 2,250 4,790 657 0 7,700 Sampling section 245, Right bank station 3, Left bank station 78 1966 May 4 15 1,280 17 4.2 3.7 .14 55 85 99 100 -— 1,650 908 495 231 16 0 742 4.2 2.5 .68 46 76 97 100 -- 2,080 957 624 437 62 0 1,120 4.2 1.2 2.50 38 69 95 100 —- 2,490 946 772 647 125 0 1,540 4.2 .8 4.25 41 69 94 100 —- 2,300 943 644 575 138 0 1,360 4.2 .5 7.40 36 66 95 100 —- 2,620 943 786 760 131 0 1,680 4.2 .3 13.0 35 64 94 100 -— 2,740 960 795 822 164 0 1,780 25 1,280 17 4.3 3.8 .13 52 80 99 100 -— 1,790 931 501 340 18 0 859 4.3 2.5 .72 42 70 96 100 —- 2,200 924 616 572 38 0 1,280 4.3 1.2 2.58 36 63 89 100 -— 2,610 940 705 679 287 0 1,670 4.3 .8 4.38 33 58 88 100 —- 2,870 947 718 861 344 0 1,920 4.3 .5 7.60 33 58 85 100 —- 2,830 934 708 764 424 0 1,900 4.3 .3 13.3 35 61 89 100 —— 2,640 924 686 739 290 0 1,720 35 1,280 17 5.1 4.6 .11 54 83 99 100 —- 1,690 913 490 270 17 0 777 5.1 2.5 1.04 41 68 93 100 —— 2,310 947 624 578 162 0 1,360 5.1 1.2 3.25 39 66 93 100 —— 2,380 928 643 643 167 0 1,450 5.1 .8 5.38 36 64 94 100 —— 2,710 976 759 813 163 0 1,730 5.1 .5 9.20 26 50 88 100 —— 3,990 1,040 958 1,520 479 0 2,950 5.1 .3 16.0 23 47 85 100 -— 4,320 994 1,040 1,640 648 0 3,330 45 1,280 17 5.8 5.3 .09 49 77 96 100 —- 1,870 916 524 355 75 0 954 5.8 2.5 1.32 35 58 82 100 —— 2,650 928 610 636 477 0 1,720 5.8 1.2 3.83 32 55 83 100 -- 2,810 899 646 787 478 0 1,910 5.8 .8 6.25 31 51 79 100 —— 2,980 924 596 834 626 0 2,060 55 1,280 17 4.5 4.0 .12 54 79 96 100 -— 1,700 918 425 289 68 0 782 4.5 2.5 .80 40 64 86 100 —- 2,360 944 566 519 330 0 1,420 4.5 1.2 2.75 35 57 82 100 -— 2,660 931 585 665 479 0 1,730 4.5 .8 4.62 36 61 85 100 —— 2,530 911 633 607 380 0 1,620 4.5 5 8.00 32 54 79 100 v- 2,920 934 642 730 613 0 1,990 4.5 3 14.0 32 54 81 100 «— 2,960 947 651 799 562 0 2,010 65 1,280 17 5.3 4.8 .10 68 91 100 —- —- 1,270 864 292 114 0 O 406 5.3 2.5 1.12 44 69 88 100 —- 2,120 933 530 403 254 0 1,190 5.3 1.2 3.42 34 55 80 100 —- 2,650 901 557 663 530 0 1,750 5.3 .8 5.62 26 42 69 100 —— 3,530 918 565 953 1,090 0 2,610 5.3 .5 9.60 28 46 74 100 —— 3,320 930 598 930 863 0 2,390 5.3 3 16.7 29 45 70 99 100 3,100 899 496 775 899 31 2,200 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS TABLE 3.——Summary of size analyses and related data for point-integrated sediment samples— Continued J37 Concentration, in mg/l, Water Water Total Height 9-! Percent finer than indicated size, . of Size class, ‘ Wm ' - Date Station Discharge» Tempera— Depth above y in mm Finer 0.062 0.125115.250 0.500 Coarse: (ft) Q ture of Flow Bed Sample than to to to to , tnan (ft3 per T D y 0.062 0.125 0.250 0.500 1.00 0.062 0.125 0.250‘ 0.500 1.00 0.062 second) (°C) (ft) (it) Rio GranJe conveyance channel near Bernardo, N. MEX.--Continued Sampling section 255, Right bank station 3, Left bank station 72 May 4 20 1,280 20 3.8 3.3 .15 70 93 100 —— —— 1,220 854 281 85 0 0 366 3.8 2.5 .52 54 84 100 —— —- 1,700 918 510 272 0 0 782 3.8 1.2 2.17 38 72 100 —- -— 2,620 996 891 734 0 0 1,620 3.8 .8 3.75 31 63 100 -— -— 3,290 1,020 1,050 1,220 O 0 2,270 3.8 .5 6.60 26 56 96 100 —— 3,900 1,010 1,170 1,560 156 0 2,890 3.8 .3 11.7 12 29 90 100 -- 9,520 1,140 1,620 5,810 952 0 8,380 30 1,280 20 3.7 3.2 .16 72 94 100 —— -— 1,170 842 257 70 0 0 328 3.7 2.5 .48 57 88 100 —— —- 1,610 918 499 193 0 0 692 3.7 1.2 2.08 41 75 100 —— —- 2,000 820 680 500 0 0 1,180 3.7 .8 3.62 32 63 100 —- —- 3,110 995 964 1,150 0 0 2,120 3.7 .5 6.40 26 57 98 100 —— 3,780 983 1,170 1,550 76 0 2,800 3.7 .3 11.3 14 34 91 100 —- 7,970 1,120 1,590 4,540 717 0 6,850 40 1,280 20 3.8 3.3 .15 77 96 100 —— -- 1,110 855 211 44 0 0 255 3.8 2.5 .52 58 89 100 —— —— 1,580 916 490 174 0 0 664 3.8 1.2 2.17 38 71 100 —- -- 2,530 961 835 734 0 0 1,570 3.8 .8 3.75 30 60 98 100 —- 3,360 1,010 1,010 1,280 67 0 2,350 3.8 .5 6.60 22 49 96 100 —— 4,530 997 1,220 2,130 181 0 3,530 3.8 .3 11.7 11 29 88 100 -— 9,800 1,080 1,760 5,780 1,180 0 8,720 50 1,280 20 3.8 3.3 .15 64 89 100 -— —- 1,330 851 333 146 0 0 479 3.8 2.5 .52 53 85 100 —- -— 1,690 896 541 254 0 0 794 3.8 1.2 2.17 39 71 99 100 —— 2,440 952 781 683 24 0 1,490 3.8 .8 3.75 37 67 98 100 —- 2,590 958 777 803 52 0 1,630 3.8 .5 6.60 31 59 97 100 -- 3,080 955 862 1,170 92 0 2,130 3.8 .3 11.7 19 42 91 100 —— 4,880 927 1,120 2,390 439 0 3,950 60 1,280 20 4.0 3.5 .14 64 89 100 -— —— 1,370 877 343 151 0 0 490 4.0 2.5 .60 56 83 99 100 -— 1,570 879 424 251 16 0 691 4.0 1.2 2.33 48 72 94 100 —— 1,940 931 466 427 116 0 1,010 4.0 .8 4.00 42 67 92 100 —— 2,130 895 533 533 170 0 1,230 4.0 .5 7.00 37 64 88 100 —— 2,450 907 662 588 294 0 1,540 4.0 .3 12.3 15 27 64 100 -— 5,910 886 709 2,190 2,130 0 5,020 Rio Grande conveyance channel near San Marcial, N.Mex. Sampling section 2249 + 93, Right bank station 0, Left bank station 70 1965 Dec. 21 25 1,860 3 4.7 4.0 .18 59 88 100 —- -- 2,350 1,390 681 282 -— —- 960 4.7 3.0 .57 46 79 100 -- -— 3,120 1,440 1,030 655 —- -— 1,680 4.7 2.0 1.35 41 73 100 —— —— 3,530 1,450 1,130 953 -- —— 2,080 4.7 1.2 2.92 27 55 98 100 —- 5,530 1,490 1,550 2,380 111 —— 4,040 4.7 0.5 8.40 22 47 97 100 —- 7,340 1,610 1,840 3,670 220 -- 5,730 35 1,860 3 4.7 4.0 .18 59 85 100 -— —— 2,290 1,350 595 344 —— —— 940 4.7 3.0 .57 47 77 100 —— -- 3,010 1,410 903 692 -- —— 1,600 4.7 2.0 1.35 36 69 100 —— -- 3,980 1,430 1,310 1,240 -- —- 2,550 4.7 1.2 2.92 26 53 98 100 -— 5,890 1,530 1,590 2,650 118 —— 4,360 4.7 0.5 8.40 16 36 93 100 -— 9,950 1,590 1,990 5,670 696 -- 8,360 50 1,860 3 4.7 4.0 .18 65 92 100 —- —— 2,140 1,390 577 171 —— -- 750 4.7 3.0 .57 50 83 100 * —— —— 2,940 1,470 970 500 —— -- 1,470 4.7 2.0 1.35 38 73 100 —- -- 3,840 1,460 1,340 1,040 -- —— 2,380 4.7 1.2 2.92 27 60 100 —- —— 5,740 1,550 1,890 2,290 -- -— 4,190 4.7 0.5 8.40 19 44 96 100 -- 8,360 1,590 2,090 4,350 335 -- 6,770 Sampling section 2243 + 62, Right bank station 0, Left bank station 67 Dec. 21 25 1,860 3 4.7 4.0 .18 59 88 100 —- —— 2,650 1,560 769 318 —- -- 1,090 4.7 3.0 .57 46 79 100 -— -— 3,550 1,630 1,170 745 -- -— 1,920 4.7 2.0 1.35 37 68 100 —— -- 4,450 1,650 1,380 1,420 —- -— 2,800 4.7 1.2 2.92 28 56 98 100 -— 5,990 1,680 1,680 2,520 120 —— 4,310 4.7 0.5 8.40 21 46 95 100 -- 8,370 1,760 2,090 4,100 418 —— 6,610 35 1,860 3 4.9 4.0 .23 53 86 100 —— -- 3,060 1,620 1,010 428 -- -- 1,440 4.9 3.0 .63 44 78 100 -— -— 3,850 1,690 1,310 847 —- -- 2,160 4.9 2.0 1.45 37 72 100 -- —— 4,770 1,760 1,670 1,340 —- -- 3,010 4.9 1.2 3.08 29 62 100 -- —- 6,200 1,800 2,040 2,360 —— -- 4,400 4.9 0.5 8.80 21 52 99 100 —- 8,620 1,810 2,670 4,050 86 —— 6,810 50 1.860 3 5.4 4.0 .35 54 84 100 —— -— 2,830 1,530 850 453 —- -- 1,300 5.4 3.0 .80 42 73 100 -— -— 3,780 1,590 1,170 1,020 -- —- 2,190 5.4 2.0 1.70 34 66 99 100 —— 4,760 1,620 1,520 1,570 48 -- 3,140 5.4 1.2 3.50 27 58 98 100 -— 6,380 1,720 1,980 2,550 128 -- 4,660 5.4 0.5 9.80 23 49 93 100 —— 7,660 1,760 1,990 3,370 536 -- 5,900 Rio Grande conveyance channel near Nogal Canyon, N. Mex. 1965 Sampling section 1318 + 00, Right bank station 0, Left bank station 80 Dec. 22 20 1,750 3 4.3 4.0 .075 46 79 99 100 -— 3,490 1,600 1,150 698 35 -— 1,890 4.3 3.0 .43 42 75 97 100 -— 3,720 1,560 1,230 818 112 —— 2,160 4.3 2.0 1.15 39 71 97 100 —— 4,130 1,610 1,320 1,070 124 —— 2,520 4.3 1.2 2.58 37 69 96 100 —- 4,470 1,650 1,430 1,210 179 —- 2,820 4.3 0.5 7.60 32 59 91 100 —— 4,990 1,600 1,350 1,600 442 —— 3,390 J38 RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965—69 TABLE 3.——Summary of size analyses and related data for point-integrated sediment samples— Continued Concentration in mg/l, Water Water . Total Height 9‘2 Percent finer than indicated size, of size clq‘s in nm Date Station Discharge Tempera— Depth above y inmm Finer 0.052 0.125 0.250 0,500 Coarser (ft) Q3 ture of Flow Bed Sample than to to to to than (ft per T D y 0.062 0.125 0.250 0.500 1.00 0.062 0.125 0.250 0.500 1.00 0.062 second) (°C) (ft) (ft) Rio Grande conveyance channel near Nogal Canyon, N. Mex.-—Continued Sampling section 1318 + 00, Right bank station 0, Left bank station 80--Continued 40 1,750 3 4.7 4.0 .18 53 87 100 —— —— 2,820 1,490 960 367 -— —— 1,330 4.7 3.0 .57 40 73 100 -— -— 3,960 1,580 1,310 1,070 —— —— 2,380 4.7 2.0 1.35 35 69 100 —— —— 3,960 1,390 1,350 1,230 —— —— 2,570 4.7 1.2 2.92 26 60 99 100 -— 6,270 1,630 2,130 2,450 63 —- 4,640 4.7 0.5 8.40 20 51 98 100 —— 8,710 1,740 2,700 4,100 174 -- 6,970 60 1.750 3 4.6 4.0 .15 73 95 100 —- -— 1,930 1,410 425 96 —- —- 520 4.6 3.0 .53 54 85 100 —— —— 2,850 1,540 884 427 -— —— 1,310 4.6 2.0 1.30 40 75 100 —— —— 4,020 1,610 1,410 1.000 -— —— 2,410 4.6 1.2 2.83 32 65 100 —- -- 5,020 1,610 1,660 1,760 -— -— 3,410 4.6 0.5 8.20 26 53 99 100 —— 6,200 1,610 1,680 2,850 62 —— 4,590 TABLE 4.—Summary of size analyses and related data for depth-integrated sediment samples San— Water Water Concentration, in mg/L Date Time gllhg Discharge Tempera- Percent f ner than indicated size in mm of Size class, in rm Median Grada- ec g ture Finer 0.062 0.125 0.250 0.500 Coarser Diameter tion tiOn (ft per OT 0.002 0.004 0.016 0.062 0.125 0.250 0.500 1.00 Sample than to to to to than dsg a second) ( C) 0.062 0.125 0.250 0.500 1.00 0.062 (mm) 1965 Rio Grande conveyance channel near Bernardo, N. Mex. Feb. 3 0945 Weir 560 6 16 19 28 32 40 88 100 -— 2,230 710 178 1,070 268 0 1,520 0.18 1.41 1320 do 550 9 21 26 34 40 52 85 99 100 1,790 720 215 591 251 18 1,020 .19 1.58 1505 do 540 11 15 17 25 29 38 80 100 —- 2,520 730 227 1,060 504 0 1,790 .19 1.52 1700 do 550 10 18 21 30 35 45 86 99 100 2,160 760 216 886 281 22 1,400 ..18 1.47 Feb. 3 1205 236 550 8 19 24 34 40 50 86 100 -— 1,880 750 188 677 263 0 1,130 .19 1.51 1430 236 540 10 29 36 51 62 76 99 100 -— 1,190 738 167 274 12 0 452 .14 1.42 1630 236 550 10 27 30 49 60 75 98 100 —— 1,320 792 198 304 26 0 528 .14 1.46 Feb. 3 1030 255 560 7 27 33 47 56 70 99 100 -- 1,340 750 188 389 13 0 590 .14 1.35 1400 255 540 9 27 33 50 60 76 100 —- -— 1,260 756 202 302 0 0 504 .13 1.36 1600 255 550 10 28 35 53 61 77 100 —— —— 1,240 756 198 285 0 0 484 .14 1.38 Feb. 4 0830 Weir 575 6 15 17 27 31 40 85 100 -- 2,490 770 224 1,120 373 0 1,720 .18 1.45 1000 do 575 7 13 15 24 28 40 91 100 —- 2,690 750 323 1,370 242 0 1,940 .17 1.38 1220 do 575 8 17 20 30 34 45 89 99 100 2,280 780 251 1,000 228 23 1,500 .18 1.43 1415 do 575 9 14 18 26 30 40 90 100 —— 2,600 780 260 1,300 260 0 1,820 .17 1.39 Feb. 4 0900 255 575 5 24 31 43 51 67 99 100 -- 1,520 775 243 486 15 0 745 .14 1.36 1100 255 575 7 28 35 50 59 64 100 -- —— 1,320 779 198 343 0 0 541 .14 1.36 1340 255 575 9 29 36 51 60 75 100 -— -— 1,360 816 204 340 0 O 544 .14 1.36 May 12 0750 Weir 980 14 —— -— —— 72 87 98 100 -— 3,530 2,540 529 388 71 0 990 0.11 1.60 0900 do 930 14 —— —- —— 73 88 97 100 -— 3,300 2,410 495 297 99 0 890 .11 1.65 1000 do 910 15 20 23 38 70 86 97 100 —- 3,420 2,390 547 376 103 0 1,030 .12 1.71 1100 do 910 15 -— —— —- 71 86 97 100 —— 3,380 2,400 507 372 101 0 980 .12 1.67 1200 do 910 16 —— -- —- 74 88 97 100 —- 3,270 2,420 458 294 98 0 850 .11 1.63 1335 Weir 910 17 -- -— —— 75 89 98 100 —- 3,110 2,330 435 280 62 0 780 .11 1.65 1430 do 920 17 -- —— —- 74 89 98 100 —— 3,220 2,380 483 290 64 0 840 .11 1.61 1530 do 1,110 17 -- -- -- 71 88 98 100 —— 3,680 2,610 626 368 74 0 1,070 ..11 1.62 1630 do 1,090 17 —— -- —— 74 89 98 100 —- 3,360 2,490 504 302 67 0 870 .10 1.63 1730 do 1,010 17 -— -— —- 72 86 96 100 -— 3,210 2,310 449 321 128 0 900 .12 1.72 May 12 0920 240 930 14 22 26 41 74 90 99 100 -- 3,120 2,340 468 281 31 0 780 .11 1.60 1030 240 910 14 —— -— -- 77 91 99 100 —— 3,130 2,410 438 250 31 0 720 .11 1.61 1230 240 910 16 -— -— —— 76 91 100 —- -— 3,150 2,390 472 284 0 0 760 .10 1.58 1420 240 910 17 -- —— —— 78 92 99 100 -- 2,990 2,330 419 209 30 0 660 ..10 1.64 1615 240 1,100 17 —— —- -- 75 89 98 100 -- 3,650 2,740 511 328 73 0 910 .11 1.67 1730 240 1,010 17 —— -- -- 76 91 99 100 -- 3,300 2,510 495 264 33 0 790 .10 1.58 1.58 1 0800 W i 900 15 -- -— —- 72 89 98 100 -- 3 000 2,160 510 270 60 0 840 .10 May 3 0900 :or 890 15 —- -- —- 70 87 97 100 —— 3:020 2,110 513 302 91 0 910 .11 1.63 1060 do 890 16 -- -- —- 70 87 97 100 —- 3,060 2,140 520 306 92 0 920 .11 1.60 1110 do 890 16 19 21 34 69 86 98 100 -- 3,120 2,150 530 374 62 0 970 .11 1.59 1.62 W 890 16 —— —- —— 72 88 98 100 —- 3,090 2,220 494 309 62 0 870 .11 132? Sir 900 16 -— —— -- 69 86 97 100 -— 3,100 2,140 527 341 93 0 960 .12 1.65 1440 do 910 16 -— —- —- 71 86 97 100 -- 3,020 2,140 453 332 91 0 880 .12 1.63 .57 Ma 13 0840 240 900 15 20 23 36 75 91 99 100 -- 2,940 2,200 470 235 29 0 740 .10 1 Y 1120 240 890 16 -— -— -- 73 89 99 100 --— 3,020 2,200 483 302 30 0 820 .11 1.60 1300 240 900 16 —— —— —— 61 76 88 99 100 3,550 2,170 532 426 390 36 1,380 .16 2.08 SEDIMENT TRANSPORTIN ALLUVDUJCHANNELS J39 TABLE 4.—Summary of size analyses and related data for depth-integrated sediment samples—Continued Sam— Water Water Concentration, in mg/L Date Time pling Discharge Tempera- Per en: 5 net than indicated size in mm of Size cla s, in mm Median Grada— Sec- Q ture Finer 0.062 0.125 0.250 0.500 Coarser Diameter tion tion (ft3 per T 0.002 0.004 0.016 0.062 0.125 0.250 0.500 1.00 Sample than to to to to than dso 0 second) (°C) 0.062 0.125 0.250 0.500 1.00 0.062 (mm) Rio Grande conveyance channel near Bernardo, N. Mex.--Continued June 2 0850 Weir 1,190 17 —- —— -- 52 75 94 99 100 2,810 1,460 646 534 140 28 1,350 .13 1.67 1045 do 1,190 17 -— -- -— 53 76 94 99 100 2,810 1,490 646 506 140 28 1,320 .13 1 62 1145 do 1,190 18 —- —— —- 51 73 93 99 100 2,870 1,460 631 574 172 29 1,410 .13 1.68 1350 do 1,180 19 —- -- -- 47 67 92 99 100 3,030 1,420 606 758 212 30 1,610 .15 1.64 1500 do 1,180 19 17 19 32 56 80 96 100 —’ 2,430 1,360 583 389 97 00 1,070 .12 1 59 1600 do 1,160 19 -— -- —— 46 67 91 99 100 3,010 1,380 632 722 241 30 1,630 .15 1.67 June 2 1025 250 1,190 17 -— —- —- 56 79 96 100 —- 2,890 1,620 665 491 116 0 1,270 .12 1.57 1130 250 1,190 18 22 24 39 69 89 98 100 -- 2,040 1,410 408 184 41 0 630 .10 1.57 1545 250 1,180 19 18 21 33 59 83 98 100 -— 2,380 1,400 571 357 48 0 980 .11 1.53 June 3 0850 Weir 1,280 16 -- —— -- 59 79 95 100 -- 3,090 1,820 618 494 155 0 1,270 .12 1.63 1100 do 1,300 17 14 18 27 62 81 96 100 -— 3,330 2,060 633 500 133 0 1,270 .12 1.59 1205 do 1,300 17 -- —- -- 52 68 90 99 100 4,080 2,120 653 898 367 41 1,960 .17 1.75 1330 do 1,280 17 —- —— -— 62 80 94 100 -- 3,290 2,040 592 461 197 0 1,250 .12 1.70 June 3 —— 322 1,290 17 -— —— —— 66 87 99 100 -— 2,900 1,910 609 348 29 00 990 .11 1.46 Nov. 29 1000 Weir 1,250 3 —— —— __ _- __ __ -_ __ 3,430 1,590 __ __ __ — 1,840 -_ -- 1030 do 1,250 3 —~ -— —— —— -— —— —— -- 3,510 1,550 —- -— -- — 1,960 -- —- 1100 do 1,250 4 8 11 17 41 68 93 100 -— 4,220 1,730 1,140 1,060 290 0 2,490 .13 1.61 1200 do 1.250 4 —— -- —— —— -— —- -— -— 4,750 1,990 -- -— -- - 2,760 —- -— 1230 do 1.250 4 -- -— —— —— —— —— —— -— 4,710 1,950 -— —- -- — 2,760 —_ -— 1300 Weir 1,250 5 -- —— —— -— —— —— —— —- 4,210 1,910 -- -- —— — 2,290 —— —— 1330 do 1.250 6 -- *— —- —- —— —- —- —- 4,690 1,870 —— -- —— - 2,820 __ -— 1400 do 1,250 6 1 4 15 37 63 92 100 —— 4,730 1,750 1,230 1,370 380 0 2,980 .14 1.61 1430 do 1.250 6 -— -- -— -- -— ~— —— -— 4,790 1,800 -— —— —— — 2,990 __ -_ 1500 do 1,250 6 —— -— —— -— —— —— —- —- 5,390 1,810 —— -- -— — 3,580 __ -— 1530 Weir 1,250 6 —- —— —— —— —— —— —— -- 4,590 1,770 -- -— —— - 2,820 —— —— 1600 do 1.250 6 -- -- —— —- —— -- —- —- 4,820 1,770 ‘— —- -— — 3,050 —_ -— Nov. 29 1030 245 1,250 3 —- —— —— —— —- —- —— —— 3,520 1,780 —— _, _- -1 1,740 __ __ 1120 245 1,250 4 9 11 18 43 72 97 100 —- 4,060 1,750 1,180 1,010 122 0 2,310 .12 1.50 1205 245 1.250 4 -- —- —— -— -— —- —— -— 5,070 2,110 -- —- -— -- 2,960 —— —— 1310 245 1,250 5 -- —— —— -— —— —— —— —— 3,950 1,940 -- -- —— —— 2,010 -- -— 1425 245 1,250 6 11 13 25 49 77 98 100 __ 3,550 1,740 994 746 71 0 1,810 .12 1.52 1450 245 1,250 6 -- —— —- —- -— -— —— __ 3,520 1,830 -— —- —— -— 1,690 —— —— 1550 245 1.250 7 -— —- —— —- —— —— —— —- 3,900 1,890 -- —- —— —— 2,010 __ __ Nov. 30 0800 Weir 1,250 3 —— —— —- —— —— —- —— —— 4,550 1,550 —_ -_ -_ __ 3,000 __ __ 0900 do 1,250 3 -- -- —- -— -— —— —— -— 4,120 1,450 -- ~- -- —— 2,670 —— -— 1000 do 1,250 3 7 9 15 33 53 87 100 —- 4,560 1,460 958 1,550 593 0 3,100 .16 1.63 1100 do 1.250 3 -- -- -- —— -— -— —- -- 4,100 1,540 -- -— -— -— 2,560 —— -— 1200 Weir 1.250 4 -- -— —- -— —— —- —- —- 4,380 1,570 -- -- —— —— 2,810 —— -— 1230 do 1.250 4 -- -— -- —— —- -— -— —— 4,480 1,580 —- —- —— —— 2,900 —— -— 1300 do 1,250 4 7 8 15 34 57 86 100 -— 4,590 1,560 1,060 1,330 640 0 3,030 .15 1.72 Nov. 30 0835 245 1,250 2 -— —- -— -- -- —- —— —— 3,520 1,580 __ _— _- -_ 1.940 __ __ 0935 245 1,250 3 -— -— —- —- —- -— -— -- 3,260 1,540 -— —— —— —— 1,720 —— —— 1030 245 1,250 3 11 13 22 48 74 99 100 —- 3,070 1,470 798 768 31 0 1,600 .13 1.42 1130 245 1,250 3 —- —— —— -- —- —— —- —— 3,320 1,550 —- —— —— —- 1,770 —— —— 1225 245 1,250 4 -— —— —— -- —- -— —— —— 3,590 1,580 —- -— —- —- 2,010 —— -- 1330 245 1,250 4 10 12 20 46 76 99 100 -- 3,380 1,550 1,010 777 34 0 1,830 .12 1.48 1420 245 1.250 5 -— -— —— —— -— -— -— —— 3,390 1,550 -— -— -- -— 1,840 —— —— 1966 May 4 0800 Weir 1,280 16 —— —— —— 26 50 90 97 100 3,320 860 797 1,330 332 0 2,460 0.16 1.58 0830 do 1,280 16 —— —— —— 29 53 89 99 100 3,080 890 739 1,110 308 31 2,190 .15 1.63 0900 do 1,280 16 —— —- —- 32 60 92 100 —- 2,780 890 778 890 222 0 1,890 .14 1.55 0930 do 1,280 16 -- —— —— 33 60 91 100 —— 2,710 890 732 840 244 0 1,820 .14 1.63 1000 do 1,280 16 6 8 12 26 47 86 100 —- 3,490 910 733 1,360 489 0 2,580 .17 1.62 1030 Weir 1,280 17 -— —- —— 24 46 85 100 —— 3,780 910 832 1,470 567 0 2,870 .14 1.63 1100 do 1,280 17 —— —- -— 27 51 90 100 —— 3,440 930 826 1,340 344 0 2,510 .16 1.59 1130 do 1,280 18 —— —— —— 26 48 86 ‘ 99 —- 3,350 870 737 1,270 436 34 2,480 .16 1.64 1200 do 1,280 18 -— —— —— 28 50 83 99 100 3,320 930 730 1,100 531 33 2,390 .17 1.70 1230 do 1,280 18 -— -— —— 28 50 87 100 -- 3,390 950 746 1,250 407 34 2,440 .16 1.64 1300 Weir 1,280 19 -- -— —— 28 51 90 100 -— 3,340 940 768 1,300 334 0 2,400 .16 1.58 1330 do 1,280 19 -- —- -- 27 47 85 100 -- 3,360 900 672 1,280 504 0 2,460 .17 1.65 1400 do 1,280 20 7 8 13 29 52 92 100 -- 3,280 950 754 1,310 262 0 2,330 .15 1.54 1430 do 1,280 20 —— —— —— 34 56 88 100 —— 2,770 940 609 886 332 0 1,830 .16 1.67 1500 do 1,280 21 -— -- -- 29 49 88 100 -- 2,870 830 574 1,120 344 0 2,040 .17 1.57 1530 do 1,280 21 -— —— —— 29 49 83 99 100 3,060 890 612 1,040 490 31 2,170 .17 1.70 May 4 0920 240 1,280 16 -— —— -- 52 81 98 100 —- 1,720 894 499 293 34 o 826 0.11 1.47 1020 240 1,280 17 12 15 23 50 79 96 100 -— 1,750 875 508 297 70 0 875 .12 1.51 1115 240 1,280 17 —— —— —— 52 79 95 100 -— 1,730 900 467 277 86 0 830 .12 1.58 1450 240 1,280 20 —— —- -— 53 78 95 100 -— 1,760 933 440 299 88 0 827 .12 1.55 J40 RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965—69 TABLE 4.—Summary of size analyses and related data for depth-integrated sediment samples— Continued Sam- Water Water Concentration, in mg/l Date Time pling Discharge Tempera- Percent finer than indicated size in mm of Size class, in mm Median Grada- SEC‘ cure Finer 0.062 0.125 0.250 0.500 Coarser Diameter tion tion (ft3 per T 0.002 0.004 0.016 0.062 0.125 0.250 0.500 1.00 Sample than to to to to than d50 a second) (°C) 0.062 0.125 0.250 0.500 1.00 0.062 (mm) Rio Grande conveyance channel near Bernardo, N. Mex.--Continued May 4 1005 260 1,280 16 ‘— —- —— 45 77 99 100 —— 2,070 930 662 455 21 0 1,140 .11 1.33 1050 260 1,280 17 11 14 20 44 74 98 100 —- 2,100 920 630 504 42 0 1,180 .12 1.47 1140 260 1,280 18 —- -- —— 44 70 96 100 -— 2,010 880 523 523 80 0 1,130 .13 1.55 1215 260 1,280 18 -- -- —- 48 75 97 100 -- 1,910 917 516 420 57 0 993 .12 1.48 1325 260 1,280 19 -- —~ —— 48 75 97 100 —— 1,860 893 502 409 56 0 967 .12 1.53 1410 260 1,280 20 —— -- —— 58 86 100 -- —- 1,520 882 426 213 0 0 638 .10 1.41 Nov. 23 13:3 :23 1,270 8 e— -— e— 53 77 99 100 —— 3,900 2,070 936 858 39 0 1,830 .12 1.45 1340 255 1.533 8 -- -- —- 55 77 99 100 —— 4,320 2,380 950 950 43 0 1,940 .13 1.47 , 8 -- -— —- 58 79 99 100 -— 4,560 2,640 958 912 46 0 1,920 .13 1.48 1967 1425 260 1.570 8 —- -— —- 62 a1 99 100 —- 4,800 2,980 912 864 48 0 1,820 .12 1.48 Feb. 2 1120 240 650 6 -— -- -- 40 70 99 100 -- 1 930 770 57 1200 245 650 7 -- —- —- 41 71 98 100 -- 2:000 920 600 :23 40 g 1’133 :12 1'53 1315 250 650 7 -- —- -— 45 73 88 100 -- 1,830 850 526 489 19 0 1,030 12 1.37 1330 255 650 7 -- -- -— 43 72 100 —— -- 1,950 940 566 546 o 00 1,110 '12 1.39 1420 260 650 8 -- —- —— 47 75 100 —— —— 1,880 884 526 470 O 0 ,996 :12 1:38 Feb. 14 1115 260 630 6 —— —— —— —— —— —— —— —— 1,550 750 —— —— __ __ 810 __ -_ 1050 280 630 6 —— —- —— —— —— ——- —- —- 1,730 780 —— —_ —— _— 950 -_ _- Feb. 15 1540 220 630 9 —— —— —— —- —— ——— -_ __ 1,540 730 __ __ __ _- 760 -_ __ 1320 240 630 8 -— —— —— —— -- —— -— -— 1 530 760 , —- —~ -- —- 770 —— -- 1150 260 630 6 —- —— —— -— —— -—— —— —— 1,700 310 _— —— _- __ 890 -_ __ 1968 1045 280 630 6 —— -- —- —— —— —— —- —— 2,070 990 —- -- -— -- 1,080 —_ —— Feb. 1 1030 99 750 5 —— —— —— 52 71 99 100 —— 2,300 1,200 437 644 23 0 1,100 0.13 1.44 1125 100 750 6 —- -— -— 54 74 100 -- -— 2,430 1 310 486 632 0 0 1,120 .13 1.45 1210 101 750 6 -- -- -— 55 73 99 100 —- 2,140 1:180 385 556 21 0 960 .14 1.44 1425 159 750 7 —- -- -— 58 78 100 —— -- 2,140 1,240 428 471 0 0 900 .13 1.42 1530 160 750 8 —— -— —— 55 73 99 —— -— 2,230 1,230 401 580 22 0 1,000 .14 1.45 May 21 1025 Weir 860 18 20 23 33 74 88 97 100 -- 2,840 2,100 398 256 85 -- 740 .12 1.69 1230 do 860 20 -- -- —— 74 87 98 100 —- 2,770 2,050 360 305 55 -- 720 .12 1.69 1240 do 860 20 —— —- —— 76 90 99 100 —— 2,580 1,960 361 232 26 —— 620 .11 1.65 1530 do 860 20 -- ~— —- 77 89 98 100 —- 2,640 2,030 317 238 53 -— 610 .12 1.69 1610 do 860 20 —- —- -- 76 88 97 100 —— 2,830 2,150 340 255 85 —— 680 .12 1.77 May 21 1130 225 860 -- -— —~ -— 74 88 99 100 —- 2,770 2,050 388 305 28 -— 720 .12 1.61 1255 227 860 20 —— —— —— 77 90 99 100 —- 2,610 2,010 339 235 26 —— 600 .11 1.60 1335 229 860 20 —- —- -- 62 73 88 99 100 3,180 1,970 350 477 350 32 l 210 .17 1.94 1410 231 860 20 —— —— —- 66 77 88 100 -- 2,970 1,960 327 327 356 —— 1:010 .16 2.11 1500 233 860 21 —- —- —— 79 92 100 -- -— 2.530 2.000 329 202 -- —~ 530 .10 1.56 May 29 1125 225 1,010 —- —- --— -— 74 90 99 100 —- 3,050 2,260 488 275 31 -- 790 .10 1.61 1300 227 1,010 21 -- —- -— 70 89 99 100 —- 3,220 2,250 612 322 32 -- 970 .10 1.61 1400 229 1,010 21 —— —- -— 74 92 99 100 -- 3,020 2,230 544 211 30 -— 790 .09 1.59 1969 1440 231 1,010 22 -- —— -— 73 90 98 100 -- 3,050 2.230 519 244 61 -- 820 .10 1.61 June 11 1010 Weir 1,560 18 -- -— -— 75 90 98 100 -— 5,530 4,150 830 442 111 —— 1,380 .11 1.46 1300 do 1,390 19 -— —— —— 80 92 98 100 —- 7,210 5,770 865 432 144 —- 1,440 .10 1.52 1145 245 1,410 18 —— —— ~- 81 94 99 100 -- 5,910 4,790 768 295 59 —- 1,120 .10 1.46 1400 250 1,370 19 -— —— —- 77 88 94 100 —- 7,700 5 930 847 462 462 -— 1 770 13 2 00 1430 255 1,330 19 -- --- -- 83 94 99 100 —- 7,690 6:380 842 385 77 —— 1:310 .11 1.50 Rio Grande conveyance channel near San Marcial, N. Mex. 1965 Dec. 21 1035 2249+93 1,800 3 8 10 16 33 64 98 100 -- 4,530 1,490 1,410 1,540 90 0 3,040 0.13 1.42 1200 2243+62 1,800 3 7 9 14 34 65 97 100 -— 4,870 1,650 1,510 1,560 150 0 3,220 .13 1.47 Rio Grande conveyance channel near Nogal Canyon, N. Mex. Dec. 22 0323 1:32:33 i,;§g 3 8 9 16 35 67 97 100 —- 4,360 1,530 1,390 1,310 130 0 2,830 .13 1.50 , 3 8 9 16 37 71 99 100 -- 4,130 1,530 1,400 1,160 40 0 2,600 .12 1.43 TABLE 5.—-—Summary of size analyses of bed material Bed Material Water Water Sampling Discharge Tempera— Percent finer than indicated size, in mm Nedian Grada- Bed Section Q cure D1ameter tion Form (1:3 per T 0.062 0.125 0.250 0.500 1.00 2.00 dso 0 second) (00) (mm) Rio Grande conveyance channel near Bernardo, N. Mex. February 4, 1965 233 575 7 o 3 60 96 100 -— 0.24 1.38 Dune. 255 575 9 0 4 76 99 100 —— .19 1.28 Flat. SEDIMENT TRANSPORT 1N ALLUVIAL CHANNELS TABLE 5.—Summary of size analyses of bed material— Continued Bed Material Water Water Samp1ing Discharge Tempera- Percent finer than indicated size, in mm Median Grada- Bed Sect1on Q ture Diameter tion Form (ft3 per T 0.062 0.125 0.250 0.500 1.00 2,00 dso a second) (°C) (mm) Rio Grande conveyance cfiannel near Bernardo, N. Mex.--Continued May 12, 1965 240 910 15 0 4 61 95 100 —— .23 1.38 Dune. 243 910 15 0 3 57 95 100 —— .22 1.37 Do. 244 910 15 0 6 75 97 100 -- .20 1.35 Do. 245 910 15 0 5 50 91 100 —— .25 1.52 Do. 246 910 15 0 5 67 96 100 —— .22 1.38 Do. 247 910 15 O 4 58 92 99 100 .24 1.47 Do. 248 910 15 0 8 69 97 100 -- .22 1.40 Do. 249 910 15 0 4 43 87 98 100 .27 1.62 Do. 250 910 15 0 3 42 82 99 100 .28 1.75 Do. 251 910 15 0 4 58 96 100 —- .23 1.36 Do. 252 910 15 0 7 56 94 100 -- .24 1.48 Do. 253 910 15 0 5 79 99 100 -— .20 1.29 Do. 254 910 16 0 5 58 96 100 —— .23 1.43 Do. 255 910 16 O 5 68 98 100 -- .22 1.32 Do. 260 910 16 O 3 48 93 100 ~— .25 1.41 Do. May 13, 1965 240 890 15 0 5 68 97 100 -- .22 1.34 Do. 250 890 15 0 10 71 98 100 —— .21 1.42 Do. 260 890 15 0 9 61 97 100 -- .23 1.42 Do. June 2, 1965 250 1,190 17 0 4 75 98 100 _— 0.20 1.30 Transition 250 1,180 17 0 7 58 99 100 -- .24 1.42 Do. June 3, 1965 322 1,290 17 O 11 85 99 100 -— .18 1.34 Flat. November 29, 1965 295 1.250 4 0 12 82 99 100 —- .18 1.40 Do. November 30, 1965 245 1,250 3 0 12 84 99 100 -- .18 1.42 Do. May 4, 1966 246 1,280 17 0 1 26 79 99 100 .33 1.52 Transition 248 1,280 17 1 5 43 89 100 -- .27 1.54 Do. 250 1,280 18 l 8 66 98 100 —- .21 1.46 Do. 252 1,280 18 1 7 70 91 99 100 .20 1.55 Do. 254 1,280 19 1 9 69 93 100 —- .21 1.48 Do. November 23, 1966 __ —— 1 30 Flat 240 1,270 8 0 6 85 100 .18 . 245 1,330 8 0 4 65 96 100 —— .22 1.36 Do. 250 1,480 8 0 5 71 95 100 —- .21 1.35 Do. 255 1,500 8 0 5 69 99 100 —- .21 1.36 Do. 260 1,570 8 0 5 77 100 —- -— .20 1.30 Do. February 2, 1967 ‘ 84 99 100 -- 0.19 1.30 Flat [40 650 6 0 6 77 99 100 -— .19 1.36 Do. 245 650 7 0 7 6 82 100 —- -- .19 1.29 Do. 250 650 7 0 255 650 7 0 7 79 100 -— -— .19 1.34 Do. 260 650 8 0 12 92 100 —— -— .17 1.32 Do. February 14, 1967 8 79 99 100 -— .19 1.38 Do. 233 233 6 g 11 86 100 —— —- .18 1.35 Do. 240 630 6 0 15 89 100 —- -- .17 1.36 Do. 91 100 -— -- .17 1.34 Do. 250 630 6 O 16 260 630 6 0 11 81 100 -- —- .18 1.38 Do. 89 100 —- —- .18 1.29 Do. 270 630 6 0 8 18 1 26 Do 280 630 6 0 7 90 100 —— —— . . . February 15, 1967 4 64 99 100 -— .22 1.35 Do. 238 633 8 g 4 70 9B 100 -— .20 1.37 Do. 260 630 6 0 8 85 100 -— —— .19 1.31 Do. 280 630 6 0 7 80 100 -— -— .19 1.33 Do. February 1, 1968 99 750 5 0 3 63 99 100 -— .23 1.32 Flat. 60 100 _- —— .18 1.37 Do. 100 750 6 0 5 101 750 6 0 13 82 99 100 -— .18 1.40 Do. 159 750 7 O 5 73 100 -- -— .20 1.76 Do. 160 750 8 0 5 79 100 -— —— .20 1.32 Do. J41 J42 RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965—69 TABLE 5.—Snmmary of size analyses of bed material— Continued Bed Material Water Sampling Discharge Tempere- Percent finer than indicated size, in mm Median Grada- Bed Section Q ture Diameter tion Form (ft3 per r 0.062 0.125 0.250 0.500 1.00 2.00 €150 a second) (°C) (mm) Rio Grande conveyance channel near fiernardo, N. Mex.——Continued May 21, 1968 225 860 —— 0 3 47 87 98 100 .26 1.55 Dune 227 860 20 0 6 61 96 100 . -- .22 1.50 Do. 229 860 20 0 3 44 94 100 —— .26 1.45 Do. 231 860 20 0 2 27 85 99 100 .32 1.51 Do. 233 860 21 O 2 38 93 100 —— .28 1.51 Do. May 29, 1968 225 1,010 —— 0 4 58 94 100 -— .23 1.46 Do. 227 1,010 21 0 5 60 96 100 —- .23 1.44 Do. 229 1,010 21 0 3 44 88 99 100 .26 1.57 Do. 231 1,010 22 0 5 47 89 100 —— .26 1.57 Do. 233 1,010 22 0 4 56 92 99 100 .24 1.52 Do. June 11, 1969 245 1,480 18 0 5 45 87 99 100 .27 1.52 Do. 250 1,390 19 0 3 32 83 99 100 .30 1.58 P0 255 1,370 19 0 3 45 95 100 —— .26 1.36 Do. Rio Grande conveyance channel near San Marcial, N. Mex. December 21, 1965 2,249+93 1,860 3 0 21 90 100 —— —- 0.16 1.44 Standing Wave. 2,243+62 1,860 3 0 14 80 100 —— —- .18 1.43 Do. Rio Grande conveyance channel near Nogal Canyon, N. Mex. December 22, 1965 1,318+00 1,750 3 0 14 79 100 —— —— .18 1.45 Standing Wave. 1,300+00 1,750 3 0 19 91 100 -- —— .17 1.38 Do. TABLE 6.—C7'oss-sectional data for channel near Bernardo ;/ Bed Material Water Water Water Mean S;:§:;::: Sampling Discharge Surface Tempera- Width Area Velocity Mean Concen— Median Grada— Bed Section Q Elevation ture B A V Depth t . Diameter tion Form 3 2 ration (ft per Hm '1' (ft) (ft ) (fr. per D c bu a second) (ft) (°C) second) (ft) (mg/l) (mm) January 9, 1965 0 580 38.0 -— 160 252 2.30 1.57 -— —- -— Dune-Ripple. 40 580 35.0 —— 85 208 2.79 2.44 —— —— -- Dune. 80 580 32.0 -— 108 220 2.64 2.05 -- -— -- Do. 120 580 29.5 -- 95 200 2.90 2.10 —— -- -— Do. 160 580 26.9 —— 79 146 3.97 1.84 —- -- —— Flat. 193 580 25.0 11 73 140 4.14 1.91 1,600 —- —- Do. 194 Weir Structure 200 580 24.3 —— 63 138 4.20 2.20 -- —— -— Do. 240 580 22.5 —- 68 206 2.82 3.00 -— -— —— Dune. 280 580 20.3 —— 64 154 3.76 2.41 -- —- -— Dune—Ripple. 320 580 18.6 —— 82 163 3.56 1.98 —- -— —— Dune—Flat. 340 580 17.8 —- 110 209 2.77 1.89 -- —- -- Dune. January 15, 1965 0 630 37.2 —— 156 167 3.77 1.07 —- —- —- Dune-Flat. 40 630 34.5 —— 85 168 3.75 1.98 —- -' -- DO- 80 630 31.8 —— 107 155 4.06 1.45 —- —- —- Flat. 120 620 29.4 -- 93 190 3.26 2.04 —- —— -— Dune—Flat. 160 620 27.3 —— 81 233 2.66 2.88 —— —— -- Dune. 193 620 25.2 8 75 189 3.28 2.52 2,300 -— -- Flat. 194 Weir Structure 200 620 24.0 —— 63 167 3.71 2.65 -- -- -- Do. 240. 620 22.0 -— 68 162 3.83 2.38 -— -- " D9. 280 610 20.0 —— 64 174 3.50 2.72 -- -— “ DO. 320 610 18.4 -- 82 179 3.40 2.13 —- —- -- D0- 340 610 17.5 —— 107 186 3.28 1.74 -- -- “ D0- SEDIMENT TRANSPORT 1N ALLUVIAL CHANNELS J43 TABLE 6.——-Crosssecflonal data for channel near Bernard0~—-Confinued Ll Bed Material Suspended Mean diment Water Water Water , 59 d- G 1— Bed _ V 1 t Mean _ Me 1an rata Sampling Discgarge Eiurfiien Te:§::a Wigth Azea e :61 Y Depth Eggiign Diameter tion Form Section eva o 2 0 ft ) (ft per D C 50 (2:3 per Hm r (5:) ( second) (ft) (°C) se°°“d) (ft) (mg/l) (mm) February 18-19. 1965 O 545 37 2 6 103 186 2.93 1.81 —— 0.20 1.22 Dune-Flat. 545 36.0 6 102 238 2.29 2.33 —— .26 1.55 Dune. 20 545 34.7 6 85 178 3.06 2.10 —— .25 1.28 Do. 60 545 33-1 6 137 166 3.28 1.21 -- .24 1.38 Flat. 83 545 31:9 6 108 157 3.47 1.45 -- .18 1.31 Do. 135 4.03 2.44 —- .22 1.35 DO- 133 22? 33:2 2 35’. 2.2 2.2. 2.... -- .2. 13g 3;... 1 3.89 2.22 —— .20 1- at~ 123 222 232i 2 $3 12? 3... 1.89 -- .19 “g 3.. 193 545 25.0 7 75 164 3.32 2.19 1.300 .19 1.3 o. 194 Weir Structure 8 7 63 158 3.38 2.51 __ .17 1'27 Dune—Flat. 200 535 $3.9 7 60 151 3.54 2.52 -- .18 1.29 Flat- 220 535 21.9 7 68 136 3.94 1.98 -- .18 1.26 Do. 240 535 20.8 7 64 143 3.74 2.22 -- .17 1.29 Do. 283 535 19:9 7 64 160 3.34 2.52 —- .17 1.26 Do. 35 19 1 7 72 167 3.20 2.32 —— .18 1.29 Dune-Flat. 323 535 18.1 8 82 161 3.32 1.96 —— .18 1.28 Do. 3 ' a 08 162 3.30 1.50 —- .19 1.25 Do. 3‘0 535 17'2 March 4—5, 1965 0 590 37.4 3 113 253 2.33 2.24 —— —- -— Ripples. 20 590 36.3 3 103 281 2.10 2.73 -- —- —- Dune—Ripple. 40 590 34.8 3 86 258 2.29 3.00 -- -- -- Dune. 60 590 33.2 4 138 246 2.40 1.79 —- -— -- Dune—Ripple. 80 590 31.9 4 108 204 2.89 1.88 -— -- —- Do. 100 590 30.5 4 55 155 3.80 2.82 —- —— :: Fist. 120 590 29.4 4 94 164 3.60 1.75 —— -— _ Do- 140 590 28.4 5 63 154 3.83 2.44 —- —- - D - 27 4 6 82 240 2.46 2.92 -- -— —— une. 160 590 . __ Flat 193 590 25.1 6 75 167 3.54 2.22 2.300 -- . 194 Weir Structure . 2.48 -- —- —— Do. 200 590 :3-3 2 21 123 3.33 2.71 —- -— —— Do. 220 590 22.0 4 68 172 3.43 2.54 —- —— -- D0. 263 533 21.0 4 63 168 3.51 2.67 -— -— -- go. ‘ -_ —— —- o. 280 590 20.1 5 63 177 3.33 2.81 Do . 2.35 —- -- -- ~ 1:: 2 2: :2: 2 :3 2 l. -- -- -- 320 590 - ‘ ' __ _- Do. . 1.77 -- 340 590 17.2 7 107 Mar63018—19,31935 0 475 37.5 9 151 248 1.91 1.64 -- 0.20 1.46 DUne. 20 480 36.1 9 103 210 2.28 2.04 —- .24 1.46 Do. 40 480 34.7 9 85 223 2.15 2.62 -- .32 1.64 Do. 60 485 33.1 9 138 226 2.14 1.64 —- .22 1.31 Do. 80 485 31.8 9 108 230 2.11 2.13 -- .17 1.50 Do. 100 490 30.8 10 56 198 2.47 3.53 —- .24 1.33 Do. 120 490 29.6 10 94 213 2.30 2.25 —— .25 1.36 Do. 140 495 28.5 11 63 198 2.50 3.14 -— .26 1.38 Do. 160 495 27.3 11 82 203 2.44 2.48 -- .22 1.40 Do. 193 500 24.9 11 75 180 2.78 2.40 1,200 .22 1.31 Do. 194 — Weir Structure 200 350 23.9 7 65 162 2.16 2.49 -- .22 1.33 Do. 220 350 22.8 7 60 149 2.35 2.48 -— .22 1.31 Do. 240 350 21.6 7 67 108 3.24 1.61 —- .16 1.24 Flat. 260 350 20.7 7 65 139 2.52 2.13 -- .19 1.30 Dune. 280 350 19.9 8 64 164 2.14 2.56 -- .23 1.32 Do. 300 350 19.0 8 71 160 2.19 2.25 -- .24 1.34 Do. 320 350 18.1 9 82 163 2.15 1.99 -~ .19 1.37 Dune—Ripple. 340 350 17.0 10 107 172 2.04 1.61 —- .21 1.31 Dune—Ripple. April 1, 1965 0 180 36.9 12 157 112 1 61 0 71 -— —— 23 128 35.2 12 100 114 1.58 1.14 -— -- -: D626. 1 33.7 12 31 108 1.67 1 33 —— _- _ ' 60 180 32.3 13 134 123 1.46 .92 -- -— -: :1nE-glat. 80 180 30.8 13 103 122 1.48. 1.18 -- —- -— aDo “me. 100 180 29.3 13 50 102 1 77 2 02 -— - i 120 180 28.5 13 90 106 1.70 1:18 —- —- :: Féat. 140 180 27.3 13 58 106 1.70 1.83 -— —- —— Duze 160 180 26.2 14 75 104 1.73 1.39 —— -- -— F1 t. 193 180 24.3 14 73 116 1.55 1.59 790 -— —— n: I 194 — Weir Structure ' 200 180 23.2 14 61 98 1.84 1.60 —- -— -— Dune 220 180 22.1 15 58 96 1.88 1.65 —- -- -- D0. 240 180 21.2 16 66 105 1.71 1.59 -- -— —— Do. :28 138 20.3 16 63 96 1.88 1.52 —— —- —— Do. 19. 17 62 107 1.68 1.72 -- —- —— — 300 180 18.5 18 70 117 1.54 1.67 —- -1 —- Fliiagune 320 180 17.6 18 80 114 1.58 1.42 —- —- —— Do. 340 180 16.7 18 105 114 1.58 1 08 -- __ " Do. J44 RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965—69 TABLE 6.—Cross-sectional data for channel near Bernardo—Continued d1/ Bed Material Mean 5223:3125..— Water Water Water Sampling Discharge Surface Tempera- Width Area Velocity Mean Concen— D$Ed12n Gzigi— 3:2“ Section Q Elevation ture B A V Depth tration gme er 0 (ft3 per Hm '1' (ft) (ftz) (ft per D (50) second) (ft) (°C) second) (ft) (mg/l) m April 15vl6, 1965 0 1,000 33.4 12 162 462 2.16 2.85 -— 0.23 1.54 Flat-Dune. 20 1,000 37.3 12 106 428 2.34 4.05 -— .24 1.39 Dune. 40 1,000 36.0 12 89 385 2.60 4.33 —— .23 1.35 Do. 60 1,000 34.3 13 139 424 2.36 3.04 -- .23 1.34 Do. 80 990 33.0 13 111 311 3.18 2.80 —— .18 1.26 Flat-Dune. 100 985 31.8 13 60 233 4.23 3.89 -— .19 1.27 Flat. 120 985 31.0 13 99 358 2.75 3.62 —— .27 1.42 Dune. 140 980 29.7 14 66 286 3.43 4.34 —- .23 1.30 Flat—Dune. 160 960 28.1 14 83 269 3.57 3.24 -— .20 1.27 Dune. 193 960 25.6 14 77 203 4.74 2.64 2,000 .18 1.26 Flat. 194 — Weir Structure 200 710 24.5 12 65 153 4.64 2.36 1,400 .19 1.35 Do. 220 715 23.3 12 61 157 4.55 2.58 —- .18 1.31 Do. 240 715 22.2 12 68 181 3.95 2.64 —— .18 1.35 Do. 260 715 21.3 13 65 182 3.93 2.80 -- .19 1.34 Do. 280 715 20.3 13 64 188 3.80 2.94 -— .18 1.30 Do. 300 715 19.3 13 72 202 3.54 2.81 -— .22 1.35 Flat—Dune. 320 715 18.3 14 83 190 3.76 2.29 —- .17 1.29 Flat. 340 715 17.3 14 110 209 3.42 1.90 -- .18 1.29 Do. April 29-30, 1965 0 900 37.6 14 160 305 2.95 1.91 —— —— ~- Dune. 20 900 36.6 14 105 243 3.70 2.31 —- —— —- Do. 40 900 35.5 14 87 357 2.52 4.10 —— —— —— Do. 60 900 34.1 14 139 336 2.68 2.42 -~ -— —- Do. 80 900 32.6 15 109 277 3.25. 2.54 —— —— —— Do. 100 900 31.5 15 59 310 2.90 5.25 —— —- -- Do. 120 900 30.7 16 98 316 2.84 3.23 —- -~ —- Do. 140 900 29.1 16 64 191 4.71 2.99 —— —— —— Flat. 160 900 28.1 16 84 309 2.91 3.68 —- —— —— Dune. 193 900 25.8 16 77 255 3.53 3.31 3,900 —- —— Do. 194 — Weir Structure. 200 740 25.0 14 66 239 3.10 3.62 3,200 —- —— Do. 220 740 23.9 14 64 275 2.69 4.30 —— —— -— Do. 240 740 22.7 14 68 280 2.64 4.12 -— —— —— Do. 260 740 21.4 14 63 184 4.02 2.92 -— —— —- Flat. 280 740 20.5 14 64 212 3.49 3.31 —— -- -- Do. 300 740 19.5 14 72 196 3.78 2.72 —- -- —— no. 320 740 18.7 14 83 212 3.49 2.55 -- -- -- DO- 340 740 17.7 14 109 217 3.41 1.99 -- -- —- DO- May 17«18, 1965 0 835 37.9 —- 160 365 2.28 2.28 —— 0.18 1.40 Dune. 20 835 36.7 —— 111 293 2.85 2.64 —— .23 1.48 Dune—Flat. 40 835 35.5 -— 88 316 2.64 3.59 —— .27 1.48 Dune. 60 835 34.1 —— 140 346 2.41 2.47 -- .24 1.53 Flat-Dune. 80 835 32.9 21 110 265 3.15 2.41 —— .26 1.77 Dune. 100 835 31.7 —- 60 304 2.74 5.07 -- .23 1.36 Do. 120 835 30.8 -— 100 320 2.61 3.20 3,500 .25 1.42 Do. 140 795 29.4 —— 66 296 2.68 4.48 3,600 24 1.56 Do. 160 795 28.3 —— 84 325 2.44 3.87 -— .24 1.39 Do. 193 795 26.0 —— 79 292 2.72 3.70 -— .29 1.70 Dune-Flat. 194 - Weir Structure 200 795 25.6 —- 68 308 2.58 4.53 —- .23 1.46 Dune. 220 795 24.6 —- 66 279 2.85 4.23 —— .23 1.37 Flat. 240 795 23.5 -— 72 275 2.89 3.82 -— .22 1.34 Flat—Dune. 260 795 22.5 22 65 275 2.89 4.24 -- .28 1.66 Dune. 280 795 21.4 —— 67 289 2.75 4.32 —— .25 1.39 Dune—Flat. 300 795 20.3 -— 74 304 2.61 4.11 —— .38 1.52 Dune. 320 795 19.1 —- 84 391 2.03 4.65 —— .24 1.42 Do. 340 795 17.9 —- 111 290 2.74 2.61 -- .20 1.40 Do. May 27—28, 1965 0 1,170 37.6 18 162 399 2.94 2.46 4,500 0.23 1.36 Dune. 20 1,170 37.0 18 106 354 3.31 3.34 2,620 25 1.38 Do. 40 1,170 35.6 19 89 299 3.92 3.36 2,640 .24 1.39 Transition. 60 1,170 34.3 19 140 374 3.13 2.67 3,430 .21 1.37 Dune. 80 1,170 33.3 19 112 368 3.18 3.28 2,530 .14 1.35 Do. 100 1,170 32.2 19 62 406 2.88 6.55 2,410 .29 1.62 Do. 120 1,170 31.1 21 99 351 3.34 3.55 3,150 .26 1.44 Do. 140 1,170 30.0 21 68 327 3.58 4.81 2,470 .24 1.50 Dune-Flat. 160 1,170 28.7 21 85 377 3.10 4.43 2,650 .23 1.42 Flat—Dune. 193 1,170 26.5 21 81 355 3.30 4.38 3,810 .25 1.38 Dune—Flat. 194 - Weir Structure 200 1,090 25.9 18 70 295 3.70 4.22 3,150 .23 1.64 Transition. 220 1,090 24.8 18 67 343 3.18 5.12 2,910 .19 1.69 Dune. 240 1,090 23.6 18 71 276 3.95 3.89 3,110 .23 1.30 Transition. 260 1,090 22.4 18 64 301 3.62 4.71 3,260 .20 1.45 Dune. 280 1,090 21.2 18 66 313 3.48 4.74 3,230 .24 1.49 Do. 300 1,090 20.0 18 73 273 3.99 3.74 3,330 .18 1.39 Transition 320 1,090 18.6 18 82 245 4.45 2.99 3,080 .18 1.29 Flat. 340 1,090 17.6 18 110 281 3.88 2.56 2,890 .19 1.31 Do. TABLE 6.—Cross-sectional data. for channel near Bernardo— Continued SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS J45 1/ Bed Material Water Water Water Mean S;:§:;::: Sampling Discharge Surface Tempera- Width Area Velocity Mean Concen- Median Grada— Bed Section 0 Elevation ture B A V Depth tration Diameter tion Form (fc3 per Hm I (ft) (£122) (ft per D C dsu a second) (ft) (°C) second) (ft) (mg/1) (mm) June 10-11, 1965 0 720 38.0 17 159 313 2.30 1.97 -- -- -- Dune. 20 720 36.7 17 105 306 2.35 2.91 -- —— -- Do. 40 720 35.4 17 89 288 2 50 3.24 —— -- -— Do. 60 720 33.9 17 138 303 2.38 2.20 -- -- —— Do 80 720 32.6 17 110 268 2.68 2.44 ~— -- —— Dune-Flat. 100 720 31.1 17 57 183 3.93 3.21 —- -— —- Flat. 120 720 30.4 17 98 264 2.72 2.70 -- -- -— Dune-Flat. 140 720 29.1 17 64 231 3 12 3.61 —- —— -- Dune. 160 720 27.9 17 83 274 2 62 3.30 -- —— —- Do. 193 720 25.7 18 77 273 2 64 3.55 2,200 -— -— Do. 194 - Weir Structure 200 685 25.0 16 66 248 2.76 3.76 2,500 0.24 1.37 Flat-Dune. 220 685 24.0 16 64 303 2.26 4.74 —— .24 1.37 Dune. 240 685 22.7 17 69 254 2.70 3.69 —— .24 1.40 Dune—Flat. 260 685 21.4 17 64 179 3.82 2.80 -- .18 1.28 Flat. 280 685 20.4 17 65 265 2.58 4.08 -- .26 1.38 Dune. 300 685 19.4 18 72 258 2.66 3.59 -— .23 1.33 Do. 320 685 18.0 18 81 277 2.47 3.43 -- .26 1.40 Do. 340 685 17.1 19 108 313 2.18 2.90 -— .24 1.41 Do. June 24—25, 1965 0 1,140 38.7 —- 163 419 2.72 2.57 -- 0.24 1.36 Dune. 20 1,160 37.3 —— 106 411 2.82 3.88 -- .24 1.45 Do. 40 1,160 35.9 -- 89 346 3.35 3.89 —- .23 1.43 Do. 60 1,170 34.5 —— 140 393 2.98 2.81 -- .20 1.36 Do. 80 1,180 33.3 -- 112 385 3.06 3.44 —— .20 1.40 Do. 100 1,320 32.2 —- 62 346 3.82 5.58 —- .21 1.45 Do. 120 1,330 31.3 20 100 407 3.27 4.07 -— .24 1.36 Dune—Flat. 140 1,330 29.9 —- 69 287 4.63 4.16 -- .18 1.30 Flat. 160 1,310 28.8 -- 85 333 3.93 3.92 -- .24 1.44 Dune. 193 1,240 26.6 —— 81 361 3.43 4.45 2,800 .30 1.77 Flat. 194 - Weir Structure 200 1,000 25.8 —- 68 325 3 08 4.78 2,800 .25 1.43 Dune. 220 1,000 24.7 —— 67 272 3.68 4.06 -— .22 1.39 Flat-Dune. 240 1,000 23.5 —- 70 307 3.26 4.39 —- .24 1.48 Dune. 260 1,000 22.4 21 66 320 3.12 4.85 -- .26 1.50 Do. 280 1,000 21.2 —- 66 304 3.29 4.61 -- .23 1.54 Flat—Dune. 300 1,000 20.0 —- 72 317 3.15 4.40 -— .26 1.46 Dune-Flat. 320 1,000 18.8 -— 83 318 3.14 3.83 —— .22 1.35 Flat. 340 1,000 17.5 -- 110 336 2.98 3.06 —- .24 1.48 Dune. July 22, 1965 0 1,060 38.0 26 164 380 2.79 2.32 —— 0.21 1.34 Dune. 20 1,060 37.6 26 106 354 2.99 3.34 -- .21 1.34 Do. 40 1,060 35.9 26 89 234 4.53 2.63 -— .18 1.28 Flat. 60 1,060 34.4 26 140 252 4.21 1.80 —— .17 1.36 Do. 80 1,060 33.3 27 112 406 2.61 3.63 —— .18 1.45 Dune. 100 1,060 32.0 27 60 290 3.66 4.83 -- .22 1.47 Flat—Dune. 120 1,060 31.0 27 99 316 3.35 3.19 -— .23 1.42 Do. 140 1,060 29.9 27 68 294 3.61 4.32 —— .25 1.49 Dune. 160 1,060 28.6 27 85 322 3.29 3.79 —- .28 1.48 Do. 193 1,060 26.3 27 81 347 3.05 4.28 960 .26 1.52 Do. 194 — Weir Structure 200 1,060 25.9 27 68 306 3.46 4.50 -— .24 1.36 Do 220 1,060 24.7 27 68 315 3.37 4.63 —- .24 1.32 Do 240 1,060 23.5 27 70 228 4.65 3.26 -- .22 1.29 Flat. 260 1,060 22,3 27 65 322 3.29 4.95 __ .20 1.39 Dune 280 1,060 20.9 27 67 286 3.71 4.27 -- .26 1.34 Do 300 1,060 19.7 27 73 314 3.38 4.30 —— .28 1.57 Do 320 1,060 18.2 27 82 334 3.17 4.07 -— .26 1.50 Do 340 1,060 16.5 27 108 288 3.68 2.67 —— .22 1.34 Transition. August 25, 1965 O 127 38.1 26 124 82.9 1.53 0.67 -- 0.20 1.39 Flat. 20 127 35.8 26 103 84.3 1.51 .82 -— .20 1.39 Do. 40 127 34.2 26 84 84.1 1.51 1.00 -- .18 1.60 Do. 60 127 32.9 26 137 88.5 1.44 .64 -- .21 1.35 Do. 80 127 31.2 28 107 78.9 1.61 .74 —— .20 1.27 Do. 100 127 29.6 28 53 77.5 1.64 1.46 —— .20 1.34 Do. 120 127 28.5 28 91 48.7 2.61 .54 -- .18 1.32 Do. 140 127 26.7 29 59 88.7 1.43 1.50 —- .24 1.64 Do. 160 127 25.8 29 76 81.8 1.55 1.08 —— .18 1.30 Do. 193 127 24.1 29 74 133.0 0.95 1.80 2,400 -- —- Do. 194 - Weir Structure 200 127 22.0 29 58 78.9 1.61 1.37 —- .27 1'37 Do. 220 127 20.9 29 56 75.8 1.68 1.34 -- .25 1.42 Do. 240 127 19.6 29 55 76.0 1.67 1.38 —- .24 1.60 Do. 260 127 18.6 29 62 71.7 1.77 1.15 -- .25 1.36 Do. 280 127 17.6 29 60 82.8 1.53 1.39 —- .20 1.58 Do. 300 127 16.8 29 68 84.5 1.50 1.23 -— .22 1.42 Do. 320 127 15.8 29 78 80.2 1.58 1.03 -— .23 1.42 Do. 340 127 14.5 29 103 79.8 1.59 .77 -- .24 1.42 Do. J46 RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965—69 TABLE 6,—Cross-sectional data for channel near Bernardo—Continued Suspendedlir Bed Material Water Water Water Mean Sediment 1 B d Sampling Discharge Surface Tempera- Width Area Velocity Mean Concen- gadian Gr6ca- Fe Section Elevation ture B A V Depth tration Dlgmeter tlon orm (ft3 per Hm T (f:) (fez) (ft per D C Su 0 second) (ft) (00) ‘ second) (ft) (mg/1) (nun) September 23, 1965 0 160 38.2 18 86 108.5 1.47 1.27 —— 0.18 1.41 DUne. 20 160 36.5 18 105 95.2 1.68 .91 —- .18 1.34 Dune—Ripple. 40 160 34.8 18 88 96.4 1.66 1.10 -— .19 1.32 Ripple. 60 160 33.1 18 138 108.5 1.47 .79 -- .20 1.35 Do. 80 160 31.5 18 107 99.1 1.61. .93 —- .22 1.34 Ripple-Dune. 100 160 30.0 19 54 90.8 1.76 1.67 -- .19 1.31 Do. 120 160 28.8 19 92 98.0 1.63 1.07 -- .18 1.32 Ripple 140 160 27.3 19 61 95.4 1.68 1.56 v- .20 1.41 Dune 160 160 26.1 19 78 101.5 1.58 1.30 —- .16 1.44 Do. 193 160 24.2 20 75 116.8 1.37 1.56 1,200 .13 1.59 -- 194 — Weir Structure 200 160 22.2 20 59 87.5 1.83 1.48 -— .25 1.32 Dune 220 160 21.0 20 57 88.9 1.80 1.56 -— .24 1.43 Do. 240 160 19.8 20 66 87.2 1.83 1.32 -- .25 1.48 Do. 260 160 18.8 21 64 89.8 1.78 1.40 -w .27 1.43 Do. 280 160 17.8 20 60 96.2 1.66 1.59 -— .21 1.55 Ripple. 300 160 17.0 20 69 100.6 1.59 1.46 —- .22 1.43 Do. 320 160 16.1 20 79 102.2 1.56 1.29 -- .22 1.38 Do. 340 160 14.9 20 106 127.2 1.26 1.20 —- .26 1.62 Ripple—Flat. October 28—29, 1965 20 520 36.9 14 105 144 3.62 1.37 —— 0.17 1.33 Flat 40 520 35.4 15 89 151 3.45 1.69 -- .16 1.35 D0. 60 520 33.7 16 140 154 3.38 1.10 —- .16 1.38 D0- 80 520 32.3 16 109 150 3.47 1.38 -- .16 1.30 D0. 100 520 30.7 16 55 128 4.07 2.32 —- .18 1.33 Do. 120 520 29.6 16 94 155 3.36 1.65 -- .18 1.40 Do. 140 520 28.3 16 63 135 3.85 2.15 -- .15 1.35 Do. 160 520 27.1 16 81 150 3.46 1.85 -- .16 1.30 00. 193 520 24.9 16 77 150 3.48 1.94 -- .16 1.42 Do. 1,200 194 — Weir Structure 1,100 200 520 23.9 16 62 134 3.89 2.15 —- .17 1.41 Do. 220 520 22.8 16 62 134 3.88 2.16 -- .17 1.30 Do. 240 500 21.4 11 67 169 2.96 2.52 —- .19 1.40 Dune. 260 500 20.5 11 66 199 2.51 3.02 -- .24 1.44 Do. 280 500 19.4 11 64 188 2.66 2.94 -- .22 1.45 Do. 300 500 18.3 11 70 193 2.59 2.76 —- .24 1.44 Do. 320 500 17.1 11 81 201 2.49 2.48 —- .22 1.38 Do. 340 520 16.1 16 107 234 2.22 2.19 —— .23 1.48 00. November 9e10, 1965 20 1,490 37.9 12 107 388 3.84 3.63 —— 0.28 1.49 Dune-Flat. 40 1,490 36.3 12 90 292 5.10 3.24 —- .21 1.42 Flat. 60 1,490 35.1 12 140 309 4.82 2.21 -- .18 1.33 Do. 80 1,490 33.8 12 114 305 4.89 2.68 —- .19 1.37 Do. 100 1,490 32.2 13 61 264 5.64 4.33 ~— .23 1.44 00. 120 1,490 31.1 13 100 292 5.10 2.92 -— .18 1.46 Do. 140 1,490 29.8 13 68 266 5.60 3.91 -- .20 1.47 Do. 160 1,490 28.6 13 85 291 5.12 3.42 -— .20 1.40 Do. 193 1,490 26.1 13 80 280 5.32 3.50 -- .19 1.34 Do. 3,300 194 — Weir Structure 3,200 200 1,490 25.3 13 68 260 5.73 3.82 -- .20 1.53 Do. 220 1,490 24.2 13 65 260 5.73 4.00 -- .19 1.32 00. 240 1,490 23.0 13 69 269 5.54 3.90 -- .23 1.36 Do 260 1,490 21.8 10 67 280 5.32 4.18 -- .20 1.29 Do. 280 1,490 20.5 10 66 277 5.38 4.20 -— .22 1.45 Do. 300 1,490 19.3 10 72 270 5.52 3.75 -- .19 1.35 Do. 320 1,490 18.1 10 83 270 5.52 3.25 —— .19 1.37 Do. 340 1,490 17.0 10 109 298 5.00 2.73 —- .18 1.37 Do. November 30, 1965 194 - Weir Structure 4,500 200 1,250 24.6 w- 67 244 5.12 3.64 -- —- -- Flat. 220 1,250 23.5 e- 64 253 4.94 3.95 -- -- -- Do. 240 1,250 22.5 v- 68 251 4.98« 3.69 —- —— -— Do. 260 1,250 21.4 «v 65 251 4.97 3.87 —— -- -- Do. 280 1,250 20.3 -- 66 251 4.97 3.81 —— —— -— Do. 300 1,250 19.2 -- 72 245 5.10 3.40 -— -- —- Do. 320 1,250 18.1 -v 82 243 5.14 2.97 -- -- —— Do. 340 1,250 17.0 -- 109 270 4.62 2.48 -— —— -— Do. TABLE 6.—Cross-sectional data for channel near Bernardo—Continued SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS J47 1/ Bed Material Water Water Water Mean S::§::::: Sampling Discharge Surface Tempera- Width Area Velocity Mean Concen- Median Grada- Bed Section Elevation ture B A V Depth tration Diameter tion Fonn .(ft3 per Hm I (ft) (ftz) (ft per D C 50 a second) (ft) (°C) ' second) (ft) (mg/l) (mm) January 4-5, 1966 0 1,130 38.2 2 160 256 4.42 1.60 -- 0.18 1.36 Flat. 20 1,130 36.7 2 105 247 4.58 2.35 —— .18 1.46 Do. 40 1,130 35.2 2 88 233 4.85 2.65 —- .19 1.47 Do. 60 1,130 33.9 2 140 257 4.40 1.84 —- .19 1.40 Do. 80 1,130 32.8 3 110 250 4.52, 2.27 —- .19 1.40 Standing Waves. 100 1,130 31.3 3 58 221 5.11 3.81 —— .21 1.51 Do. 120 1,130 30.2 3 98 249 4.55 2.54 -— .17 1.44 Flat. 140 1,130 29.1 3 66 229 4.94 3.47 -- .20 1.50 Do. 160 1,130 28.0 3 84 249 4.55 2.96 -— .19 1.44 Do. 193 1,130 25.8 3 80 243 4.65 3.04 -- .18 1.38 Do. 4,200 194 - Weir Structure 3,800 200 1,000 23.9 1 68 221 4.52 3.25 -- .24 1.60 Do. 220 1,000 22.9 1 62 225 4.44 3.63 -- .22 1.51 Do. 240 1,000 21.8 1 67 221 4.52 3.30 -- .20 1.53 Do. 260 1,000 20.7 1 64 220 4.55 3.44 —— .20 1.48 Do. 280 1,000 19.6 1 63 230 4.35 3.65 -— .19 1.42 Do. 300 1,000 18.6 1 71 222 4.50 3.13 -— .17 1.42 Do. 320 1,000 17.6 1 81 228 4.39 2.81 —— .18 1.41 Do. 340 1,000 16.5 1 107 256 3.91 2.39 —— .18 1.52 Do. February 16, 1966 20 820 36.4 2 105 206 3.98 1.96 —- 0.17 1.36 Flat. 40 820 35.1 2 88 199 4.12 2.26 -- .18 1.40 Do. 60 820 33.7 2 140 209 3.92 1.49 -- .16 1.32 Do 80 820 32.5 2 111 208 3.94 1.87 —— .17 1.33 Do. 100 820 31.1 2 58 182 4.50 3.16 —- .19 1.35 Do. 120 820 30.1 2 97 198 4.14 2.04 —— .16 1.36 Do. 140 820 28.8 3 66 183 4.48 2.77 —- .17 1.33 Do. 160 820 27.6 4 83 195 4.20 2.35 —- .18 1.36 Do. 193 820 25.4 4 78 195 4.20 2.50 -— .19 1.47 Do. 2,100 194 — Weir Structure 200 820 23.9 4 63 182 4.50 2.89, —- .17 1.38 Do. 220 820 22.7 4 62 178 4.60 2.87 —— .20 1.41 Do. 240 820 21.7 4 67 193 4.25 2.88 -— .20 1.52 Do. 260 820 20.6 4 66 190 4.31 2.88 —- .17 1.38 Do. 280 820 19.6 4 64 198 4.14 3.09 —- .18 1.44 Do. 300 820 18.6 4 72 191 4.30 2.65 —— .18 1.40 Do. 320 820 17.6 5 82 197 4.16 2.40 -— .16 1.33 Do. 340 820 16.7 5 109 220 3.72 2.02 —— .16 1.39 Do. March 8, 1966 20 600 35.4 8 107 175 3.42 1.64 —- 0.18 1.40 Flat. 40 600 35.0 8 89 173 3.47 1.94 —— .18 1.38 Do. 60 600 33.4 8 140 196 3.07 1.40 —— .18 1.35 Do. 80 600 32.2 9 109 165 3.64 1.51 —- .17 1.36 Do. 100 600 30.7 9 56 147 4.09 2.62 -— .22 1.53 Do. 120 600 29.6 9 94 173 3.46 1.84 —- .17 1.34 Do. 140 600 28.4 9 64 149 4.03 2.33 —- .19 1.40 Do. 160 600 27.3 9 82 168 3.56 2.05 —- .18 1.44 Do. 193 600 25.1 10 78 174 3.45 2.23 -- .18 1.45 Do. 1,800 194 - Weir Structure 200 600 23.5 11 63 148 4.07 2.34 —- .18 1.40 Do. 220 600 22.5 11 61 159 3.77 2.61 -— .21 1.47 Do. 240 600 21.5 11 66 164 3.66 2.48 -- .22 1.52 Do. 260 600 20.4 11 65 157 3.81 2.42 —— .18 1.44 Do. 280 600 19.5 12 64 175 3.43 2.73 -— .19 1.51 Do. 300 600 18.5 12 72 170 3.54 2.36 —— .19 1.42 Do. 320 600 17.6 12 82 176 3.40 2.15 -— .16 1.28 Do. 340 600 16.5 12 109 193 3.12 1.77 —— .16 1.34 Do. March 31, 1966 0 1,180 38.4 14 163 373 3.16 2.29 -— 0.19 1.39 Dune-Flat. 60 1,210 35.2 14 140 349 3.47 2.49 —— .26 1.44 Dune. 80 1,260 33.6 16 114 346 3.64 3.04 -— .21 1.31 Dune—Flat. 120 1,280 31.0 16 103 299 4.28 2.90 -- .18 1.52 Flat-Dune. 160 1,310 28.5 16 86 294 4.45 3.42 -- .23 1.57 Flat. 193 1,330 26.1 16 81 290 4.58 3.58 -- .23 1.48 Do. 3,700 194 — Weir Structure 200 1,350 25.1 17 68 268 5.04 3.94 -— .21 1.44 Do. 220 1,350 24.0 17 65 251 5.38 3.86 -- .20 1.41 Do. 240 1,350 22.8 17 68 273 4.95 4.01 -— .18 1.41 Do. 260 1,350 21.7 17 67 279 4.84 4.16 —— .21 1.51 Do. 280 1.350 20.4 17 66 267 5.05 4.04 —— .19 1.57 Do. 300 1,350 19.2 17 73 262 5.15 3.59 -— .19 1.47 Do. 320 1,350 17.9 17 83 262 5.15 3.16 —- .18 1.34 Do. 340 1,350 16.7 18 109 280 4.82 2.57 —- .17 1.38 Do. J48 RIO GRANDE CONVEYANCE CHANNEL, NEW MEXICO, 1965—69 TABLE 6,—Cross—sectional data, for channel near Bernardo—— Continued Suspendedl/ Bed Material Water Water Water Mean Sediment Sampling Discharge Surface Tempera- Width Area Velocity Mean Concen- Median Grada- Bed Section Elevation ture B A V Depth tration Diameter tion Form (ft3 per HA» '1‘ (n) (i=2) (ft per 1: C 50 a second) (ft) (°C) ' second) (ft) (mg/1) (mm) May 12, 1966 0 1,050 38.2 16 161 392 2.68 2.43 -- 0.19 1.32 Dune. 20 1,050 36.8 17 107 244 4.30 2.28 —- .18 1.28 Flat. 40 1,050 35.7 17 89 371 2.83 4.17 —— .25 1.47 Dune. 60 1,050 34.1 17 140 259 4.05 1.85 —— .16 1.33 Flat. 80 1,050 33.0 18 113 269 3.90 2.38 -- .18 1.37 Do. 100 1,050 31.6 18 59 211 4.98 3.58 -— .19 1.40 Do. 120 1,050 30.8 18 104 356 2.95 3.42 -— .22 1.43 Dune. 140 1,050 29.6 18 69 308 3.41 4.46 —- .24 1.47 Do. 160 1,050 28.4 18 85 347 3.03 4.08 —— .26 1.44 Do. 193 1,050 25.8 18 80 230 4.57 2.88 -- .22 1.31 Flat-Dune. 1,500 194 - Weir Structure. 200 1,050 25.0 18 67 232 4.53 3.46 -- .19 1.38 Flat. 240 1,050 22.5 18 69 224 4.69 3.25 -- .17 1.36 Do 260 1,050 21.8 18 66 325 3.23 4.92 -— .32 1.92 Dune. 280 1,050 20.6 18 69 330 3.18 4.78 -- .27 1.62 Do. 300 1,050 19.3 18 73 338 3.11 4.63 -- .25 1.49 Do. 320 1,050 18.1 18 83 335 3.13 4.04 -- .28 1.79 Do. 340 1,050 16.8 19 110 377 2.79 3.43 —- .24 1.87 Do. June 14, 1966 20 250 35.4 24 102 134 1.87 1.31 -— 0.21 1.50 Dune. 40 250 34.0 24 85 144 1.74 1.69 -- .20 1.52 Do. 60 250 33.1 24’ 138 141 1.77 1.02 -— .24 1.34 Do. 80 250 31.6 24 108 144 1.74 1.33 —— .24 1.38 Do. 100 250 29.9 24 53 139 1.80 2.62 -— .16 1.32 Flat. 120 250 28.7 25 95 132 1.89 1.39 -— .18 1.57 Dune. 140 250 27.2 27 62 130 1.92 2.10 —— .24 1.54 Do. 160 250 26.0 27 78 129 1.94 1.65 —- .26 1.54 Do. 193 250 24.5 27 77 157 1.59 2.04 -- .23 1.34 Do. 1,100 194 — Weir Structure 200 250 23.1 27 64 129 1.94 2.02 —- .24 1.45 Do. 220 250 21.6 27 62 82 3.05 1.32 —— .17 1.28 Flat. 240 250 20.1 27 66 85 2.94 1.29 -- .17 1.27 Do. 260 250 19.0 26 65 127 1.97 1.95 —- .23 1.50 Dune. 280 250 17.8 26 63 134 1.87 2.13 —— .22 1.60 Do. 300 250 16.9 26 70 147 1.70 2.10 -— .23 1.54 Ripple. 320 250 16.4 26 79 170 1.47 2.15 -- .28 1.63 Do. 340 250 15.4 26 107 142 1.76 1.33 -- .21 1.27 Do. May 23, 1968 0 815 38.1 17 156 358 2.28 2.29 —~ 0.23 1.90 Dune 20 815 36.9 17 106 326 2.50 3.08 —— .27 1.38 Do. 40 815 35.8 18 89 336 2.42 3.78 -— .25 1.37 Do. 80 815 33.0 18 111 312 2.61 2.81 -- .24 1.33 Do. 100 815 31.7 18 59 180 4.53 3.05 -- .18 1.23 Flat. 120 815 30.6 18 93 330 2.46 3.55 -- .26 1.63 Dune. 140 815 29.6 18 67 279 2.92 4.17 —- .25 1.46 Do. 160 815 28.4 18 86 298 2.73 3.47 -- .23 1.36 Do. 193 815 26.0 18 80 281 2.90 3.51 -- .25 1.47 Do. 3,800 194 — Weir Structure 200 885 —— 19 70 314 2.82 4.48 -— .24 1.36 Do. 220 885 24.6 19 69 301 2.94 4.36 -- .24 1.40 Do. 240 885 23.1 20 68 301 2.94 4.43 —- .25 1.53 Do. 260 885 21.9 20 69 250 3.54 3.63 —— .22 1.36 Do. 280 885 20.8 20 69 302 2.93 4.37 —- .27 1.65 Do. 300 885 19.6 20 72 321 2.76 4.46 —- .24 1.41 Do. 340 885 17.1 20 109 326 2.71 2.99 —- .25 1.45 Do. y 1965, the concentration listed is the total concentration measured at the weir, section 194. Prior to October 1, 1965, the concentration listed is the measured suspended concentration at the section. Following October 1, SEDIMENT TRANSPORT 1N ALLUVIAL CHANNELS J49 TABLE 7,—Summary of average values for streamflow and sediment data for channel near Bernardo Water Water Mean Water Water Bed Materi_1 Suspendedl/ 7 Discharge Reach SUrface Depth Mean Surface Tempere— Median Fall'» Grada37 Dominant Sediment ‘Manning C//E— Date Q Length Width of flow Velocity Slope ture Diameter Velocity tion Bed Concentrationi n . (ft3 per (ft) B V S _ T 850 m a Form c second) (it) (fps) (x10 “) (°C) (mm) (fps) 1 (mg/1) j Aug. 25, 1965 127 19,700 91 0.93 1.50 7.4 27 0.20 0.089 1.40 Flat. 2,500 0.026 10.1 Aug. 25 127 14,000 68 1.16 1.61 5.4 29 .24 .115 1.45 Do. 2,500 .024 11.3 Sept. 23 160 14,000 70 1.39 1.64 5.2 20 .24 .103 1.46 Dune. 1,180 .026 10.8 April 1 180 19,700 92 1.21 1.62 6.6 13 -- -- -- Transition 790 .027 10.1 April 1 180 14,000 71 1.49 1.70 4.7 17 —— -— -— Dune. 790 .025 11.3 June 14, 1966 250 17,300 89 1.56 1.80 6.4 26 .22 .098 1.45 Do. 1,100 .028 10.0 Mar. 19, 1965 350 14,000 73 2.08 2.30 4.9 8 .21 .069 1.32 Do. 1,200 .023 12.7 Mar. 18 485 19,700 96 2.22 2.28 6.6 10 .23 .082 1.42 Do. 1,200 .028 10.5 Oct. 29 500 8,000 70 2.71 2.63 5.4 10 .22 .077 1.42 Do. 1,100 .026 12.1 Oct. 28 520 16,000 92 1.62 3.56 7.0 15 .16 .053 1.35 Flat. 1,200 .015 18.6 Feb. 18 540 19,700 90 1.96 3.08 6.3 6 .22 .072 1.33 Transition 1,300 .019 15.4 Feb. 19 540 14,000 73 2.12 3.48 4.8 7 .18 .053 1.27 Flat. 1,300 .015 19.2 Jan. 9 580 12,000 112 1.96 2.64 6.9 —- -- -- —— Dune. 1,600 .023 12.6 Mar. 4 590 19,700 92 2.30 2.78 6.3 4 -— -— —- Transition. 2,300 .023 12.9 Mar. 5 590 14,000 72 2.38 3.45 4.8 5 -- —— —‘ Flat. 2,300 .017 18.0 Mar. 8, 1966 600 13,300 89 1.89 3.57 6.5 9 .18 .056 1.41 Do. 1,800 .016 18.0 Mar. 8 600 14,000 73 2.30 3.57 5.0 11 .19 .064 1.42 DO. 1,800 .016 18.6 Jan. 15, 1965 615 14,000 77 2.26 3.53 4.6 8 —— -— -- Do. 2,300 .016 19.2 Jan. 15 625 19,700 99 1.86 3.40 6.4 8 —- -- -- Do. 2,300 .017 17.4 June 11 685 14,000 74 3.54 2.61 5.6 17 .24 .098 1.37 Dune. 2,500 .031 10.3 April 16 715 14,000 74 2.47 3.91 5.1 13 19 066 1.32 Flat. 1,400 .016 19.4 June 10 720 19,700 98 2.76 2.67 6.4 17 -- -- —- Dune. 2,200 .028 11.2 April 30 740 8,000 78 2.62 3.63 4.6 14 —— —— —— Flat. 3,200 .017 18.4 May 17 795 14,000 76 3.96 2.64 5.5 19 .25 .107 1.44 Dune. 3,600 .033 10.0 May 23, 1968 815 19,700 94 3.19 2.72 6.1 18 .24 .100 1.46 Do. 3,800 .029 10.9 Feb. 16, 1966 820 17,300 92 2.14 4.16 6.4 2 .17 .044 1.37 Flat. 2,100 .015 19.8 Feb. 16 820 14,000 73 2.66 4.23 5.1 4 .18 .051 1.41 DO. 2,100 .015 20.2 May 17, 1965 835 12,400 110 2.87 2.64 6.1 17 .24 .098 1.49 Dune. 3,600 .028 11.1 May 23, 1968 885 10,000 69 4.32 2.97 6.2 19 .24 .100 1.45 Do. 3,800 .033 10.0 April 29 900 19,700 98 2.96 3.10 6.0 15 -- -- —— Do. 3.900 -024 13-0 Apr. 15, 1965 980 19,700 99 3.39 2.92 6.6 13 0.22 0.082 1.34 Dune. 2,000 0.029 10 9 June 25 1,000 14,000 75 4.16 3.21 5.9 22 .24 .108 1.45 Do. 2,800 .029 11.4 Jan. 5 1,000 14,000 73 3.14 4.37 5.2 3 .20 .058 1.49. Flat. 3,800 .017 19.2 May 12 1,050 19,700 101 2.96 3.51 6.3 18 .21 .082 1.38 Transition. 1,500 .022 14.3 May 12 1,050 14,000 75 4.12 3.40 6.2 18 .24 .098 1.63 Dune. 1,500 .028 11.9 July 22. 1,060 15,300 100 3.20 3.31 6.4 27 .22 .100 1.42 Transition. 1,900 .025 12.9 July 22 1,060 14,000 75 3.99 3.54 6.7 27 .24 .115 1.40 Dune. 1,900 .027 12.1 May 27 1,090 14,000 75 3.88 3.74 5.9 18 .21 .082 1.44 Do. 3,100 .024 13.8 Jan. 4, 1966 1,130 19,700 99 2.45 4.65 6.4 4 .19 .055 1.44 Flat. 4,200 .015 20.7 May 28, 1965 1,170 15,300 94 3.80 3.28 6.1 19 .23 .095 1.43 Dune. 2,900 .027 12.0 17,300 Nov. 30 1,250 14,000 74 3.39 4.98 5.5 3 —— —— -- Flat. 4,500 .016 20.3 Mar. 31, 1966 1,350 14,000 75 3.57 5.04 6.0 17 .19 .071 1.44 Do. 3,700 .017 19.2 Nov. 9. 1965 1,490 15,300 94 3.18 4.98 6.8 13 .21 .077 1.41 Do. 3,300 .017 18.9 Nov. 10, 1965 1,490 14,000 75 3.64 5.46 6.0 10 .20 .067 1.38 Do. 3,200 .016 20.6 llPrior to October 1, 1965, the concentration listed is the measured suspended concentration at the section. Following October 1, 1965, the concentration listed is the total concentration measured at the weir, section 194. TABLE 8.—Summary of measured suspended-sediment analyses, May 27—28, for channel near Bernardo Sam— Water Water Concentration, in mg/l, pling Discharge Mean Tempera- Percent finer than indicated size f Size 1353 11 mm Median Grade- Sec— Q Velocity ture in mm 5 1 Finer 0.062 0.125 0.250 0.500 Coarser Diameter tion tion (5:3 per v T 0.062 0.125 0.250 0.500 V1.00 a“? 8 than to to to to than .150 0 second) (fps) (°C) 0.062 0.125 0.250 0.500 1.00 0.062 (mm) 0 1,170 2,94 18 37 47 77 96 100 4,500 1,670 450 1,350 855 180 2,830 0.22 1.65 20 1,170 3.31 18 63 79 92 99 100 2,620 1,650 419 341 183 26 970 .14 1.95 40 1,170 3.92 19 65 84 98 100 -- 2,640 1.720 502 370 53 0 920 .12 1.55 60 1,170 3.13 19 48 64 91 100 -- 3,430 1,650 549 926 309 0 1,780 .16 1.65 80 1,170 3.18 19 67 91 100 —— -- 2,530 1,700 607 228 O 0 830 .10 1.36 100 1,170 2.88 19 69 91 99 100 -- 2,410 1,660 530 193 24 0 750 .10 1.42 120 1,170 3.34 21 53 70 86 99 100 3,150 1,670 536 504 410 32 1,480 .18 1.94 140 1,170 3.58 21 68 89 99 100 -- 2,470 1,680 519 247 25 0 790 .11 1.52 160 1,170 3.10 21 63 85 97 100 —- 2,650 1,670 583 318 80 0 980 .11 1.58 193 1,170 3.30 21 49 68 90 99 100 3,810 1,870 724 838 343 38 1,940 .15 1.72 200 1,090 3.70 18 65 88 98 100 -- 3,150 2,050 725 315 63 0 1,100 .10 1.53 220 1,090 3.18 18 ‘72 93 100 —— —- 2,910 2,100 611 204 0 0 810 .10 1.44 240 1,090 3.95 18 67 87 98 100 —- 3,110 2,080 622 342 62 0 1,030 .11 1.56 260 1,090 3.62 18 65 86 98 100 -- 3,260 2,120 685 391 65 0 1,140 .11 1.59 280 1,090 3.48 18 66 85 97 100 -— 3,230 2,130 614 388 97 0 1,100 .11 1.61 300 1,090 3.99 18 65 88 99 100 -— 3,330 2,160 766 366 33 0 1,170 .10 1.45 320 1,090 4.45 18 69 90 100 —- —- 3,080 2,130 647 308 0 0 950 .10 1.46 340 1,090 3.88 18 72 93 100 -— —— 2,890 2,080 607 202 0 0 810 .09 1.42 U. S. GOVERNMENT PRINTING OFFICE : 1972 O - 472—032 ' EARTH Max:553 Mme? 75’ An Experimental Study of 797’“ Heavy-Mineral Segregation Under Alluvial-Flow Conditions GEOLOGICAL SURVEY PROFESSIONAL PAPER 562—K DOCUMENTS DEPARTMENT AU G 13 19.73 .0 s (2! IF '\_/r thl-jilgr'x‘i‘rlél ' An Experimental Study of Heavy-Mineral Segregation Under Alluvial-Flow Conditions By LAWRENCE L. BRADY and HARVEY E. JOBSON SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS GEOLOGICAL SURVEY PROFESSIONAL PAPER 562—K UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1973 i UNITED STATES DEPARTMENT OF THE INTERIOR ROGERS C. B. MORTON, Secretary GEOLOGICAL SURVEY V. E. McKelvey, Director Library of Congress catalog-card No. 73-600017 For sale by the Superintendent of Documents, US. Government Printing Office Washington, DC. 20402 — Price 85c domestic postpaid or 600 GPO Bookstore Stock Number 2401-00294 CONTENTS Page ________________________________________ K1 Experimental results—Continued Introduction _____________________________________ 1 Summary of ' bed form and opaque-heavy- Theoretical considerations ________________________ 2 mmeral segregating.characteristlcs—Con. . . . Bed forms of movmg flat-bed Relative velocities of water-transported d' . ' 1 with differin densities ____________ 2 .°°“ “1°“ (“1.94) --------------------- p artlc es . g . Relation of fall velocities of dark opaque Shear stress as a dens1ty-segregat10n 6 and light- density grains ____________________ parameter "'"""""T """"""""""""" Relation of grain entrainment to critical Bed forms produced by flow In an shear stress and grain size __________________ alluv1a1 channel """"""""""""""" 8 Heavy-mineral transport and deposition Relation of grain entrainment to turbulence --__ 9 in a flat-bed flow __________________________ Summary ——————————————————————————————————— 10 Discussion of data _______________________________ Experimental runs and results 0f sediment analysis-- 10 Relations among sediment samples ____________ Hydraulic measurements _____________________ 10 Bed forms and hydraulic variables ____________ Sediment analysis ___________________________ 12 Conclusions _____________________________________ Sediment characteristics __________________ 12 References -------------------------------------- Size analyses—total bed material __________ 12 Appendix: Size analyses—suspended sediment ________ 13 A' Symbols and nomenclature """ . """"" Size analyses—core samples ______________ 13 B. Gram-mount preparatlon and relation- _ shlp of direct grain measurements Experimental results """"""""""""""" 14 to sieve-size equivalents _________________ Summary of bed form and opaque-heavy- C. Analyses of opaque-heavy-mineral mineral segregating characteristics _________ 14 grains and light-mineral grains Dune bed forms (run 1) ————————————————— 14 from core samples (runs 2—4) ____________ Dune bed forms (run 2) ————————————————— 15 D. Sediment concentration and size Transition bed forms (run 3) _____________ 17 analyses of suspended-sediment samples __ ILLUSTRATIONS Graph showing resistance of a particle to motion as a function of the ratio of its size to the size of the bed material ________________________________________________________________________ Schematic diagram of forces acting on a discrete moving particle in a fluid _____________________ Graph showing— 3. Velocity ratios for spheres of equal size but of different densities _______________________ 4. Velocity ratios of spheres that have equal submerged weight but different densities ______ Shields diagram showing sediment entrainment as a function of the particle Reynolds number ____ I‘de’alized diagram of bed forms in an alluvial channel __________________________________________ Dune profile showing dune terminology _______________________________________________________ Schematic diagram of the fiume used in the four experimental runs ____________________________ Size distribution curves for sand used in the flame ___________________________________________ Photographs: 10. Dune bed configuration and opaque-heavy-mineral accumulations at the bed surface follow- ing run 1 _______________________________________________________________________ 11. Dune bed configuration of run 2 _______________________________________________________ 12. Accumulations of dark opaque heavy minerals on the upstream sides of dunes (run 2) __ III Page K17 19 22 25 25 25 27 29 29 32 33 34 38 Page K3 4 15 16 16 IV FIGURE TABLE 13. 14—19. 20—23. 24. .4955"?pr CONTENTS Sketch of a dune showing structures and locations of different types of opaque-heavy—mineral ac- cumulations ____________________________________________________________________________ Photographs : 14. Opaque-heavy-mineral accumulations in foreset and topset beds of dunes formed in run 2-- 15. Bed configuration and opaque-heavy—mineral accumulation at the bed surface formed during run 3 ___________________________________________________________________________ 16. Accumulations of opaque heavy minerals formed along the crestal region of a dune (run 3)- 17. Opaque-heavy-mineral accumulations formed in topset and foresetbeds during run 3 _______ 18. Flat-bed surface formed by run 4 _____________________________________________________ 19. Profile of flat-bed flow deposits showing opaque-heavy—mineral layers within the flat-lying beds ____________________________________________________________________________ Graph showing— 20. Fall-velocity relationship of light-mineral grains to opaque-heavy-mineral grains obtained from the bed-material sample and core samples of runs 2, 3, and 4 _________________ 21. Plot of median fall velocities of opaque-heavy—mineral grains and light-mineral grains ___ 22. Critical shear relationship of light minerals to opaque heavy minerals for the bed material and core samples ________________________________________________________________ 23. Relation of magnetite in transport to time in 20-cm flume and under flat-bed conditions ____ Photograph of sections of core samples showing opaque-heavy-mineral beds ____________________ TABLES Classification of flow regimes _________..-_-_____________________-__-__-__---_---___-__-______, Hydraulic variables and parameters of runs ____________________________________________________ Mean dune size (with standard deviations) measured by sonic sounder ___________________________ Results of a resistance-to—motion experiment using a poorly sorted quartz bed material ___________ Size analyses of opaque heavy minerals from core samples ____________________________________ Size analyses of light minerals associated with opaque heavy minerals in the core samples ________ Size analyses and concentration of suspended-sediment samples ________________________________ Page K17 18 19 20 21 22 23 25 25 26 27 34 Page K9 11 15 24 35 36 38 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS AN EXPERIMENTAL STUDY OF HEAVY-MINERAL SEGREGATION UNDER ALLUVIAL-FLOW CONDITIONS By LAWRENCE L. BRADY and HARVEY E. JOBSON ABSTRACT Segregation of opaque minerals (mainly ilmenite and mag- netite) from the light minerals in a natural sand was ob- served in a large (61 x2.44x1.22 meters) recirculating water- sediment flume. Bed material (median size 0.286 millimeter) used in the study was taken from the Rio Grande near Bernardo, N. Mex. Opaque heaVy minerals (median size 0.144 millimeter) amounted to 0.38 percent of the bed-material volume. Significant hydraulic variables and the sorting and bedding patterns of the bed material were observed for four different bed configurations: a flat bed (upper flow regime), a transition bed, and two difl’erent dune beds (lower flow regime). Accumulations of opaque heavy minerals were formed as three basic types: 1. Thin accumulations of small extent that were associated with the upstream or stoss slopes of dunes; 2. Accumulations associated with the topset deposits of large dunes and with dunes formed in the transition flow; 3. Accumulations associated with the flat—bed condition. The most important factors influencing the type and amount of accumulation of opaque heavy minerals are bed configuration and grain density. The most widespread de- posits were the segregations of heavy minerals associated with the base of the flat beds. The thickest deposits of opaque-heavy-mineral grains were associated with topset deposits of dune beds, but local conditions must be optimum for thick accumulations to occur. The importance of a min- eral’s density to segregation is shown by considering theoreti- cally the forces necessary to move grains of two different densities and by analyzing the size distribution of light and heavy minerals in the bed-material and core samples of the laboratory experiments using a Shields’ type criteria for initiation of motion. Sediment size, sorting, and shape were determined for each mineral group from core samples taken from the bed. The sorting of the opaque heavy minerals for the flat—bed run was significantly different from the sorting of these minerals for the other runs. Median sizes of the light minerals which were obtained from laminae adjacent to or within the heavy-mineral laminae also showed a significant variation among runs. Fall velocities of the grains of the two different mineral groups were found to have little importance as local segre- gating mechanisms. INTRODUCTION In an alluvial channel, bedding patterns produced in sediment are responses to the hydraulic variables of flow. Variations in sorting as well as the segre- gation of materials according to shape and density are important elements in the production of bed- ding structures and in recognition of the structures in sediments and sedimentary rocks. Relatively little is understood about the local hydraulic conditions or the sediment responses to these conditions that are responsible for sorting of sediments. The relative densities of particles and the streamflow characteristics have long been as- sumed to be important factors in sorting, but their relative contributions to the sorting process have not been well understood. The relationship of heavy minerals to the more common low-density minerals was first described in relation to given hydraulic conditions by Rubey (1933). Fall velocity was considered by Rubey to be the most important segregating mechanism accounting for the close association of small high- density grains with low-density but larger mineral grains in a sediment. Other factors considered im- portant by Rubey (1933, p. 3) were density and hardness of the minerals, differences in original sizes of the grains in the source rock, amount of abrasion during transport, and degree of sorting at the site of deposition. Rittenhouse (1943) used the concept of hydraulic equivalence to explain mineral relations in sands of the Rio Grande in New Mexico. He described hydraulic equivalence (p. 1749) as “whatever the hydraulic conditions may be that permit the depo- sition of a grain of particular physical properties, these conditions will also permit deposition of other grains of equivalent value.” The distribution of heavy minerals in the streambed was considered by K1 K2 Rittenhouse (1943, p. 1742—1743) to be caused by varying hydraulic conditions at the time and place of deposition, equivalent hydraulic size of each of the heavy minerals, availability of the minerals, and unknown factors. Studies on sorting of minerals with different densities were conducted simultaneously with studies of turbulence, bed resistance, and sediment trans- port at the Engineering Research Center at Colo- rado State University. Experiments were conducted in a large recirculating sediment flume using natural sand from the Rio Grande south of Albuquerque, N. Mex. This research was undertaken in an effort to find what sediment properties and hydraulic vari- ables are responsible for the rapid segregatiOn of certain heavy minerals during movement and deposi— tion of a sediment load. Four flow conditions were studied at near equi- librium conditions. Observations were made of the significant hydraulic variables, sediment transport rate, sediment segregation, and the physical char- acteristics of the sediments entrained by each flow to obtain information necessary to explain the sort- ing process. This study contributes to the understanding of local segregation processes that affect grains of different densities. Techniques used and results ob- tained can be applied to studies of bedding in mod- ern sediments and to the interpretation of bedding in ancient deposits. Further, observations made in these flume studies of modes of segregation, trans- port, and accumulation of heavy minerals should help in future research on and exploration for eco- nomically valuable placer deposits. This program was completed under a cooperative arrangement between the US. Geological Survey, University of Kansas, and Colorado State Uni- versity. The data contained herein are essentially the same as those contained in a dissertation by Brady (1971). The data were collected under the general supervision of the second author. Special thanks are due the dissertation committee members, W. M. Merrill, E. C. Pogge, M. E. Bick— ford, A. J. Powell, and J. D. Winslow, of the Uni- versity of Kansas, for advice and counsel during the research. THEORETICAL CONSIDERATIONS RELATIVE VELOCITIES OF WATER-TRANSPORTED PARTICLES WITH DIFFERING DENSITIES An analysis of the forces acting on discrete parti- cles in a few idealized situations can provide the SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS basis for estimates of their effects in the natural environment. Actual values for the velocities and forces involved in the grain movement would be very difficult to determine experimentally. By mak- ing certain assumptions to allow for direct com- parisons between grains with different densities, however, approximations of the relative velocities of grains can be developed. For immersed particles moving along a bed, the five principal for‘ces important in determining the movement of the particle are the (1) gravity forces related to the immersed weight of the particle, the (2) drag and (3) lift forces that result from pres- sure and frictional effects of the fluid on the particle, (4) frictional forces that result from contact be- tween the grain and bed, and (5) forces resulting from interaction of moving grains. If one assumes an individual sphere moves With- out interference from adjacent moving grains, four principal forces can be defined. The gravity force, F9, is the resultant force acting on the particle that is dependent on the immersed weight of the particle and the gravitational constant, 9. The gravity force is defined as 7rd3 FG=—"(P8_P)g (1) 6 where d = diameter of the particle, p, = mass density of the particle, and p = mass density of the fluid. (All symbols used in the text are listed in appendix A.) The hydrodynamic forces acting on a body are discussed in any standard fluid mechanics text, as for example that of Daily and Harleman (1966, p. 376—394). The hydrodynamic drag force, FD, that acts on a particle is dependent on the frictional drag: resulting from surface shear between the grain and the fluid and on the form resistance that is related to shape of the grain and results from pres- sure drag on the particle. It is customary to define a total drag coeflicient, CD, to include both frictional and form drag. Some researchers have directly measured the drag and lift forces acting on regular shaped objects such as spheres (Watters and Rao, 1971; Coleman, 1967; and Ippen and Verma, 1955) and hemispheres (El-Sammi, 1949) in laboratory flumes. The drag force is defined as V02 7Td2 FD=CDA,p 2 =01; 8 P(Vf—‘Vs)2 (2) where A, = projected area of the sphere, V0 = HEAVY-MINERAL SEGREGATION relative velocity of the flow past the sphere, V, = velocity of the flow at some representative distance above the bed, and V, = velocity of translation of the particle. Lift forces on the body are due to a difference in pressure between the upper and lower sides of the particle. The increased velocity resulting from fluid acceleration around the upper side of a particle causes a local reduction in pressure, while the pres- sure on the lower side of the grain surface at or near the bed approaches the static pressure of the fluid. The lift force, FL, is defined as V02 'fl'dz FL=CLA8p 2 =CL?P (VI—Vs)2 (3) where CL = coefficient of lift. The frictional force acting on a moving particle is difficult to determine. The frictional force is dis- cussed in most basic physics or mechanics texts, such as that of Sears and Zemansky (1963, p. 35). Ippen and Verma (1955, p. 921—987) have also dis- cussed the frictional force. Bagnold (1966, p. 5) states that the friction coefficient for grains is of the same order as the static coefficient, not only when the grains are at rest but also when they are in motion. For the purposes of this study, the fric- tional force was assumed to be equal to the coeffi- cient of kinetic friction, CF, times the normal force between the particle and the bed, FN. The frictional force, FF, is defined as FF=CFFN=CF(FgCOS0—FL) (4) where 0 = angle between the bed surface and hori- zontal. A positive value of 0 indicates that the bed surface is rising in a downstream direction, as the surface does on the stoss slope of a ripple or dune. Although the coefficient of kinetic friction for sediment particles is very difficult to determine, one would suspect that it is closely related to the coeffi- cient of static resistance, CR, of a particular parti- cle resting on a given bed configuration. For a rigid spherical particle of diameter d," resting on a bed of rigid spherical particles of diameter dB arranged in a prescribed manner, it is a simple matter to determine the coefficient of static resist- ance, CR. For example, if the bed spheres are arranged in a close packed rectangular pattern and are resting on a horizontal plane, it can be easily shown that the centrally applied horizontal force required to move a sphere of diameter d... in the direction of K3 least resistance is CR F'N, where CR is given by the relation 1 OR = —— (5) flea + 2k —_ 1 and k is defined as the ratio of dm to d3. Likewise, if the bed spheres are arranged in a rhombic pat- tern, the value of CR, corresponding to movement in the direction of least resistance is given by 1 CE = (6) 2 ./k2 + 2k — (1'73) ' It is seen that the resistance of a particle to motion is a function of both the size of the moving particle and the size of the bed particles. In order to determine the effect of particle size on the resistance to motion, the resistance ratio is defined as the ratio of OR at any value of k to the value of CR with k=1. The relation of the resistance ratio to k is shown in figure 1. The curves approach infinity at a value of k for which a small moving particle could fall between the interstices of the larger bed particles. Figure 1 illustrates that the resistance to motion of a small particle resting on 10,0 1.0 RESISTANCE RATIO 0 Rhombic arrangement A Rectangular arrangement 0.1 1.0 10.0 d DIAMETER RATIO (k=dl) B FIGURE 1.—Resistance of a particle to motion as a function of the ratio of its size to the size of the bed material. K4 a bed of large particles can be quite large. It is not presumed that the values given in figure 1 can be applied directly to field situations; however it is suggested that the trend is qualitatively correct. The four forces as they are applied to a spherical particle are shown schematically in figure 2. The gravitational force can either oppose or supplement the drag force depending on the sine of 6. By use of the four fundamental equations 1—4, a general equation of motion for particles can be derived. Direct comparisons between grains of different densities can then be made by establishing ratios of the translating motion of the grain of greater density to that of the grain of lesser density and reducing the equations to a form that expresses the relative difference in the velocities of the tw0 grain types for the same flow conditions. For a particle moving at a uniform velocity, the general translation-motion equation for the particle can be expressed as FF=FD'—‘F(;Sin0 (7) By dividing the frictional force on one particle by the frictional force on a particle of different density, the following ratio can be established using equations 4 and 7: F, Fr1 FD —~F(; Sing CF (Fa COSQ—FL) (8) FIJI—Fa. sin 6 —CF1(FGICOSt9”‘FL1)' The subscript 1 is used to denote the forces and coefl‘icients affecting the sphere of the lower density. By substituting equations 1, 2, and 3 into equa- F\ow direction FIGURE 2.——Schematic diagram of forces acting on a discretel moving particle in a fluid. SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS tion 8, and simplifying terms, the following equa- tion can be developed: 3pCD (Vf—V8) 2 ~ 4dg (p8—p) sin 6 3pCDl(V11—Val)2 * 4dlg(ps1—p) Sin 0 CF [4dg(ps—p) COS l9 — 3CLP(Vf—‘Vs) 2] CF1[4d19 (P‘l -— p) COS 0—3CL10(Vr1—-Vn)2] (9) By considering 0 = 0, equation 9 can be simpli- fied to CD(Vr—Vs)2 CDI(V’1‘V'1)2 CF[4dg (pg—p)—3CLp(Vf—Vs) 2] CF1[4dig(P51~P)—‘3CL10(Vf1—V51)2] (10) Equation 10 can be used to determine the relative velocities of rolling spheres with different densities. Assuming the two spheres have equal diameters and therefore equal drag coefficients and equal lift coefficients and assuming equal coefficients of fric- tion, equation 10 reduces to (Vr—Vs) 2 (Vf—V‘l) 2 ( 8—“) (Pu—p) By applying densities of materials of interest in this study: 5.0 g/cm3 (gram per cubic centimeter) for 9,, 2.65 g/cm3 for p81, and 1.0 g/crn3 for p, equation 11 can be expressed in dimensionless form as V, VI, ’1 —— = 1.56 — 0.56 —— V'1 Vf (12) A graph of equation 12 is shown in figure 3. The relative velocities of spheres of the two dif- ferent densities are clearly shown in figure 3. The velocity of the denser sphere, V,, is always less than that of the lighter sphere, an, unless both are equal to the fluid velocity,V,, a condition where there is no frictional force. This condition could occur when both particles are suspended. As the velocity of the lighter particle becomes progressively smaller, the relation V,/Vs1 also becomes progressively smaller until a point is reached where movement of the denser sphere ceases. At this point—the point of HEAVY-MINERAL SEGREGATION 1.0 i Vs= Velocity of sphere with 95 = 5.0 g/cm3 Vs: Velocity of sphere with p5 = 2.65 g/cm3 I I V, = Velocity of fluid 0.36 FIGURE 3.—Velocity ratios for spheres of equal size but of different densities. incipient motion of the denser particle—the velocity of the low-density particle is 0.36 times the fluid velocity. A second situation for which the relative velocity can be approximated is that of two spherical parti- cles that have equal submerged weight but different densities. Substituting values for the densities of the spherical particles of 5.0 g/cm3 and 2.65 g/cm3, the ratio of diameters required to obtain equal sub- merged weights is 1:1.34. However, in order to derive a general velocity formula such as equation 12 the following additional conditions must be as- sumed: 1. For the drag force equation, a drag coefficient ratio (Co/CD1) of 1.2:1 is stipulated. Drag coefficients of the two spheres will differ be- cause the spheres are of different size. The value of 1.2:1 was approximated from the CD versus Re diagram in the US. Inter-Agency Committee on Water Resources Report 12 (1957, p. 20) by using grain sizes similar to the experimental runs (0.12 mm (millimeter) for the heavy grain and 0.163 mm for the light grains). 2. The lift forces for this situation are ignored. 3. Two relationships for friction will be considered. First, the coefficient of static friction is con- K5 sidered to be the same for both spherical par- ticles (Cr, = On). Second, the ratio of the two coefficients of friction is assumed to be equal to the resistance ratio given in figure 1. It will be assumed that the bed is composed of particles of a size equal to that of the larger particles and that these particles are ar- ranged in a rhombic pattern. From figure 1 the value of Cr/Crl is found to be 1.25. 4. An assumption is made for this analysis that the increase in fluid velocity with distance from the bed is linear, at least up to a point where the characteristic velocity is deter- mined, as it is in the sublayer of laminar flow. The fluid velocity is assumed to be zero at the bed surface. The fluid velocity then at the point of drag force application of the small sphere would be 0.746 of the value of the fluid velocity at the corresponding point on the larger sphere. Accepting these assumptions, the basic equation 10 can be reduced to V: V'l -1 .— = 1.23 —— 0.65 —) (13) V11 f for equal friction coefficients and V: V'l -1 __ = 1.54 — 1.06 < ———> (14) V.1 Vr for a resistance ratio determined from figure 1. Equations 13 and 14 are plotted in figure 4. For the development of equations 10—14, the bed surface was considered horizontal; but the rela- tions shown in figures 3 and 4 should be qualitatively similar for any given bed-form slope. The basic difference in forces affecting the grains when a slope factor is introduced is related to the effect of grain weight on the grain movement. A gravity force component parallel to the bed will act against the drag force if the local bed surface is inclined in a direction opposite to the energy slope or the stream gradient. Such restraining pull is present in grain movement up the stoss side of a dune or rip- ple (fig. 2). When the local bed surface is inclined in the direction of the energy slope or stream gradi- ent, as it is on a flat bed or the lee slope of a dune, the particle weight then becomes additive to the 1.0 l Vs: Velocity of sphere wnh ps= 5.0 g/cm3 Vs: Velocity of sphere with p s = 2.65 glamJ I I Vf=Velocity of fluid 0.65 V_s V 0.5 '— Equal friction coefficients Friction coefficient ratio from figure 1 FIGURE 4.—Velocity ratios of spheres that have equal sub- merged weight but different densities. drag force in influencing grain movement down- stream. In addition to the effect of gravity, frictional forces resulting from differences between size of moving particle and size of particles at the bed sur- face will have marked effect on the grain velocity. A coarser sand bed will provide a higher coefficient of friction than a finer sand bed for a given size of grain in movement. The above analysis of grain movement assumes that the grains of interest are not so large or heavy that they tend to displace the underlying grains and sink into the bed during the flow. For grains that do, and they occasionally occur in the field, different methods of analysis would be required. Grains moving along the surface of a sediment bed are continually being deposited and reentrained at a rate dependent on the local conditions of the flow. Light and heavy grains are most likely to be segregated when their velocities differ greatly. As grains of different densities slow to velocities that are much less than the fluid velocity, high-density grains will be deposited first. Before high-density grains are yet in motion, low-density grains will be entrained and moved much more readily. This type of selective deposition provides for efficient segre- gation by causing the accumulation of high-density grains in areas where the flow is not readily capa- ble of transporting all the material supplied to the SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS area. In other words, if a mixture of particles is supplied to an area where the flow is incapable of transporting the total load, the heavy particles will be selectively deposited first. These mathematical relationships establish in a semiquantitative but simplified manner what has long been observed, that small dense grains are more resistant to surface movement than are larger low- density grains. Graphs similar to figures 3 and 4 can be constructed for natural materials of any density. Then, the graphs can be used to help ex- plain why some of the bedding features observed in sediments in the natural alluvial environment are formed of materials of a particular density. SHEAR STRESS AS A DENSITY-SEGREGATION PARAMETER Consideration of critical shear stress, 1,, which is the stress exerted by the flow on the bed that is just capable of initiating grain movement, adds in- sight into the segregation of grains of varying densi- ties. Shields (1936) plotted experimental results of the beginning of particle motion based on a dimen- sionless shear stress, 7*, and a particle Reynolds number, R , where I (15a) and (15b) _ with y, equal to the specific weight of the sediment grains, y the specific weight of the fluid, d, the grain diameter, U. is the shear velocity or y???) with p the fluid density, v is the kinematic viscosity of the fluid, and To is the average shear stress at the bed. Additional data and refinement of this plot by later workers has resulted in‘the generally accepted Shields diagram shown in figure 5 (A.S.C.E. Task Committee on PreparatiOn of Sedimentation Man- ual, 1966, p. 297). From Shields curve (fig. 5), one can develop the relation of critical shear to grain size for grains of different densities. Grigg and HEAVY-MINERAL SEGREGATION K7 llllllll l llllllll l l’lllllll llllllll 'Vsling/I:m3 0 Amber ............... 1.06 O Lignile ............... 1.27 (Shields) 0 Granite .............. 2.7 ‘5’ ,3}? I) Barite ............... 4.25 I .4" Fully developed turbulent velocity profile * Sand (Casey) ............ 2.65 L. “0 : + Sand (Kramer) ............ 2.65 : ua‘ — x Sand (us. was) ........... 2.65 _ U) —- _ '3; _ A Sand (Gilbert) ........... 2.65 _ 5 0.5 — I Sand (White) ............ 2.61 _ (ft _ \ Turbulent boundary layer ‘3 Sand in air (White) ......... 2.10 Lu ' .......... 2F, \ A Steel shot (White) 7.9 _ U, \ 3 \ _. _ \ _ Z o \ a \ Z \ Lu 5 I 5 °" _ l D : _ * : 0.05 — x * _ 0,02 Illlllll l llllllll l llllllll llllllll 0.2 0.5 1.0 5 10 50 100 500 1000 U d5 BOUNDARY REYNOLDS NUMBER, Rfi y a FIGURE 5.—-Shields diagram showing sediment entrainment as a function of the particle Reynolds number (adapted from A.S.G.E. Task Committee on preparation of Sedimentation Manual, 1966, p. 297). Rathbun (1969) have developed such a series of curves that show on a theoretical basis that grains of different density but equal fall velocity require dilferent shear stress for initiation of movement. For a grain diameter below 0.1 mm, Grigg and Rathbun (1969, p. 79) show that critical shear is a function only of grain density, but for a grain diameter above 0.1 mm, they show that the critical shear becomes a function of size as well. The experimental conditions under which the Shields diagram was developed were quite different from the natural conditions that exist in an allu- vial channel. Data used to develop the Shields curve were obtained from artificially flattened surfaces of sand beds that consisted of uniformly sized grains, and they were collected under fully de- veloped turbulent flows in which shear at the bed was just large enough to initiate movement of a few grains. In contrast, large amounts of sediment are in transport at relatively high velocities on streambeds when segregation occurs, and the size distribution of the bed material is seldom uniform. Even though Shields’ (1936) work was developed to explain very small amounts of sediment mo- tion, it gives insight into relations among moving grains. During a given flow, grains are continually being deposited and then reentrained into the flow; that is, there are always some grains at the inter— face that are continually subject to conditions near incipient motion. One can see, at least qualitatively, from Shields’ work that the denser grains will require a much larger shear stress for movement than lighter grains of the same size. A part of the threshold of motion problem is to determine how much sediment is in transport along the bed surface. Best known among the bed-load equations is the Einstein bed-load function (Ein- stein, 1950). Einstein’s bed-load equations express a relation between the intensity of shear on a parr ticle, 5b, and intensity of transport, Q, where K8 QB [< y 1 V” )<—>l Ya Y's—’7 gdsa and (”W d”) ¢= —— (16b) )1 R’S where (13 is the rate of transport of the bed load, in weight of total bed load per unit time and width, g is the gravitational constant, d, is the grain diam- eter, S is the energy slope, and R’ is the hydraulic radius with respect to the particles. (R’ is based on the resistance to flow due to particle resistance as opposed to that due to the bed or streambank configuration.) The shear intensity parameter, rlx, of Einstein is essentially the reciprocal of Shields’ SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS dimensionless shear stress, 7., and is important in determining the total transport rate of the bed load, qB. The fact that the transport rate is a function of 5!; lends credence to the importance of Shields’ parameter in situations other than the initiation of motion of uniformly sized grains on flattened beds. BED FORMS PRODUCED BY FLOW IN AN ALLUVIAL CHANNEL Shortly following initiation of movement of the bed material, bed forms start to develop. These initial forms are described by Kennedy (1963, p. 522) as “the result of scour and deposition due to the perturbation velocities induced by any protu- berance on the bed.” Flows in alluvial channels are classified into two flow regimes, upper and lower, Water surface 8 Dunes and superposed ripples Boil D Washed-out dunes or transition ‘ Water surface F Anlrdune standing waves G Antidune breaking wave H Chute and pool FIGURE 6.—Idealized diagram of bed forms in an alluvial channel (from Simons and Richardson, 1966, p. J5). HEAVY-MINERAL SEGREGATION K9 TABLE"1.’—Classification of flow regimes [Adapted from Simona, Richardson, and Nordin (19653, p. 36). ppm, parts per million] Bed material Phase relation Flow regime Bed form concentrations Mode of sedi- Type of roughness between bed and (ppm) ment transport water surface Lower regime ___ Ripples ___________ 10—200 Discrete steps __ Form roughness predominates -__ Out of phase. Ripples on dunes ___ 100—1,200 __-do ____________ do __________________________ Do. Dunes ____________ ZOO—2,000 ___do _____________ do __________________________ Do. Transition ______ Washed-out dunes__ 1,000—3,000 ________________ Variable _______________________ Upper regime __ Plane beds ________ 2,000—6,000 Continuous _____ Grain roughness predominates ___ In phase. Antidunes ________ €2,000 ___do ____________ do __________________________ Do. Chutes and pools -_ §2,000 -__do _____________ do __________________________ Do. with a transition zone between. These regimes are based on the bed configuration, mode of sediment transport, process of energy dissipation, and phase relation between the bed and water surfaces (Si- mons and Richardson, 1963). Relations of bed forms within these two regimes are shown in table 1, and the bed forms are shown in figure 6. The A.S.C.E. Task Force on Bed Forms in Allu- vial Channels (1966, p. 53) defines m’pples as bed forms with wave lengths less than approximately 1 foot and heights less than 0.1 foot. Dunes are bed forms larger than ripples and out of phase with any water-surface gravity waves that accompany them. A flat bed is a surface devoid of form. Anti- dunes and chutes-and-pools develop within the upper portion of the upper flow regime but were not stud- ied in this series of experiments. These features are described by Simons, Richardson, and Nordin (1965a, p. 40—42). Bed forms within the lower flow regime include ripples, ripples superimposed on dunes, and dunes. In the lower regime the water-surface waves and undulations are out of phase with the bed undula- tions. In general, resistance to flow is high, and sediment transport is small. In natural streams, dunes, or dunes with superimposed ripples are the most common bed forms (Simons and Richardson, 1966, p. J11). Within the transition flow the bed configuration is very erratic and may include forms common to both the upper and lower regimes. Dunes present in the transition zone will often decrease in ampli- tude and increase in length before the bed becomes flat (washed-out dunes) (Simons and Richardson, 1966, p. J11). In the upper flow regime the usual bed forms are flat beds (plane beds) or antidunes. Resistance to flow is small, and sediment transport is large. Water- surface waves in this regime are in phase with the bed surface except during the breaking of an anti- dune (Simons and Richardson, 1966, p. J11). Bed forms produced by the four different experi- mental runs in this study were dunes in the lower flow regime, long profile dunes in the transition zone, and a flat bed in the upper flow regime. Ter- minology used in this report for the different sur- face features of dunes and the bedding structures associated with the dunes is shown in figure 7. RELATION 0F GRAIN ENTRAINMENT TO TURBULENCE The effect of turbulence in a given flow is an important flow characteristic in grain entrainment. Local boundary shear stress must be determined from the velocity gradient at the bed and cannot be determined from the slope-depth relationship alone. The apparent shear stress, -r, in turbulent flow is expressed by Streeter (1966, p. 226) as dU 1’ = (1‘ + 77) —— (17) dY in which ,u is the dynamic viscosity, 77 is the eddy viscosity that depends on the state of the turbulent motion, and dU/dY is the velocity gradient normal to the bed. Intensity of turbulence is important, be- cause high turbulence is indicative of large velocity fluctuations and usually indicates large velocity gradients. McQuivey and Keefer (1969) studied the segre- gation of magnetite grains from quartz grains on the stoss side of ripples in a small flume and found much larger turbulent intensities over the trough area than over the crestal region of a ripple. Tur- bulent intensity also decreased with distance from the bed. Measurements were made with a hot-film anemometer. Differences in turbulent shear stress from ripple trough to crest and differences in shear stress required for movement of grains of different densities were considered by McQuivey and Keefer K10 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS FLOW Stoss slope Brink point Brinkline in plan view Summit point Cresfline in plan View . Trough point Troughline in plan View \ \ \ \ \\\ \\ \ \ \\\ Foreset masks \\‘ Bottomser beds \\\ \ / Sliptace / FIGURE 7.—-Dune profile showing dune terminology used in report (X 4 vertical exaggeration). Location terminology adapted from Allen (1968, p. 62). as important factors in heavy-mineral segregation. Similar results of turbulence measurements are described by Raudkivi (1967, p. 206—207) for experi- ments conducted by Sheen (1964). Raudkivi states that turbulent intensities are greatest just down- stream from the point of separation (brinkline) on a ripple, that turbulence is intense in the trough area, and that its intensity rapidly decreases down- stream. Velocity and turbulence profiles were deter- mined by McQuivey at selected locations for each of the runs of this study. These data are contained in a dissertation by Brady (1971). SUMMARY Theoretical conisderations of transport of grains with different densities lead to the conclusions that small dense grains are more resistant to tractive movement than larger low—density grains and that boundary shear is an important parameter in deter- mining the rate of sediment transport. Difi'erent bed forms are produced under different flow conditions with such common bed forms as ripples and dunes formed in the lower flow regime, flat beds formed in an upper flow regime, and washed-out dunes formed in the transition phase. The turbulent intensity of the flow is large near the bed and decreases with distance from the bed. Much larger turbulent intensities occur in the trough regions of dune beds than on the crestal areas, and the intensity decreases rapidly downstream from the trough area toward the brinkline of a dune. Intensity of turbulence is important because high turbulent intensities are indicative of large velocity fluctuations and usually indicate large velocity gra- dients. The amount of local boundary shear stress is dependent on the local velocity gradient. EXPERIMENTAL RUNS AND RESULTS OF SEDIMENT ANALYSIS A large recirculating.water-sediment flume of rec- tangular cross section and dimensions of 61 meters in length, 2.44 meters in width, and 1.22 meters in depth (fig. 8) was used for the series of four experi- ments. The large size of the flume permits the estab- lishment of flow conditions that approximate those in a natural channel and eliminates many of the boundary effects that are associated with smaller fiumes. The slope of the flume can be changed by use of adjustable screwjacks, and water-sediment discharge can be increased to a maximum of ap- proximately 2.5 cubic meters per second. The in- terior of the flume is surfaced with aluminum having an epoxy coating. A transparent plexiglass section 21.95 meters long is located midway along the left wall of the flume to allow observations to be made of sediment movement. HYDRAULIC MEASUREMENTS Near equilibrium conditions were established for each of the flows before sediment and hydraulic HEAVY-MINERAL SEGREGATION data were taken. Equilibrium flow is defined as flow that has established a bed configuration and slope consistent with the fluid, flow, and bed-material characteristics over the working reach of the bed (Simons and Richardson, 1966, p. 3). After equi- librium flow was established for a given experiment, measurements were made of sediment discharge, water-sediment discharge, slope of the water sur- face and energy grade line, depth, and water tem- perature. Additional hydraulic parameters were cal- culated from these basic data. Mean values of sig- nificant hydraulic variables are shown in table 2. Water-surface elevations were measured every 1.52 m (meters) along the centerline of the flume for several profiles. For each profile a line was fitted to the water-surface-elevation measurements and their corresponding flume stations by the method of least squares and its slope determine-d. The mean value of the calculated slopes was taken to be the water-surface slope for the run. By adding the local velocity head, Q2/29(WD)2, where Q is dis- charge, W is channel width, D is water depth, and g is the gravitational constant, to the water-surface elevation at a given measurement point, the eleva- tion of the energy grade line was obtained. The slope Adjustable tailgate K11 TABLE 2.—Hydraulic variables and parameters of runs Water Energy Mean discharge Run Bed form slope depth (cu m (X 10'“) (cm) per sec) 1 ____ Dunes _________ 1.02 32.9 0.48 2 ____ Dunes _________ 1.06 58.5 1.38 3 __-_ Transition _____ 1.22 33.7 .73 4 ____ Flat bed _______ 1.79 52.8 2.08 Shear Tempera- Mean stress Run Bed form ture velocity (dynes 1°C) (cm per per Froude sec) cm 2) No. 1 ____ Dunes ________ 20.8 60 33 0.34 2 ____ Dunes ________ 20.9 97 61 .40 3 ____ Transition ____ 20.7 89 40 .49 4 __-_ Flat bed ______ 21.0 161 93 .71 of the energy line was determined in much the same way as the slope of the water surface. Profiles of the bed and water surfaces along the flume centerline were recorded on chart paper by use of a sonic sounder; and from these sounder pro- files, the depth of flow was determined. The mean depth of flow (table 2) for the run was determined by averaging the depth values obtained every 1.52 m along each profile. 61.0". Head box 10.457m ID pipe 1] ' L a Return 0.660m ID pipe pipes \L 0.838m ID pipe / 4“] 120 HP pump r 6 Adjustable screwiacks r / ///// /// / /// Side contracted orifices 4 V ._.._. LONGITUDINAL SECTION 2.44m 1.22m Adiustable screwjacks V // /¢ Motor / // CROSS SECTION Note: Not to scale FIGURE 8.—Schematic diagram of the fiume used in the four experimental runs. K12 Water discharge was determined by use of water- air manometers that were connected to calibrated orifice meters located in the three return-flow pipes. Mean discharge for each run was determined from an average of four to 20 individual readings. Water temperature was held as constant as possible by use of steam and cold water. The temperature for each run had a fluctuation of less than i 1°C (Celsius). Mean velocity ((7) was calculated by use of the continuity equation (9 —. (18) D X W _ Q U=—= A Any error in the mean velocity reported would be primarily due to an error in mean depth readings. The shear stress at the bed, 70, and Froude num— ber, F, are both calculated from the above measured variables. The shear stress is defined for a large area as To = yDS (19) where y is specific weight of water and S is the energy slope. The Froude number value is a meas- ure of the effect of gravity on the flow pattern and is defined as (20) For a Froude number less than one, a flow is de- fined as tranquil, because the average velocity of the flow is less than the velocity of propagation of small surface waves on the fluid. For a Froude number greater than one, the flow is defined as rapid, for the fluid velocity exceeds the velocity of movement of the small surface waves. SEDIMENT ANALYSIS SEDIMENT CHARACTERISTICS Sand used in the experiments was obtained from a conveyance channel of the Rio Grande near Ber— nardo, N. Mex. An arkosic sand, it contains approxi- mately 60 percent quartz, 36 percent feldspars, 3 percent rock fragments, and 1 percent accessory minerals. Heavy minerals (specific gravity >295) SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS constitute 1.13 percent of the weight and 0.72 per- cent of the volume of the total bed-material sample. Dark opaque grains, mainly ilmenite and magnetite, amount to 0.38 percent of the bed-material sample by volume. Other heavy minerals included amphi- boles, pyroxenes, garnet, zircon, tourmaline, limon- ite, and hematite. Within this report, sediments referred to as opaque heavy minerals consist of ilmenite and magnetite, and those referred to as light minerals consist of the remainder of the mineral grain-s. These two groupings provided for maximum efliciency in recognition and description of the segregation char- acteristics and conditions. SIZE ANALYSES—TOTAL BED MATERIAL Samples for the bed-material analyses (fig. 9) were obtained from a composite sample of 10 ver- tical cores of the bed. Samples were taken at ran- dom locations in the flume after the water had been drained. Median size, as determined by fall diam- eter using visual accumulation tube (U.S. Inter- Agency Committee on Water Resources, 1958), was 0.286 mm with a geometric standard deviation, 0, (A.S.C.E. Task Committee, 1962, p. 98) of 1.59, where 1 (dso £184) a = — + . 2 dis d50 A geometric standard deviation, hereafter referred to as sorting, with a value of 1.0 refers to a per- fectly size-sorted sand, while a value of 3.5 or larger refers to a poorly size sorted sand. Sieve analysis of the bed material showed a median size of 0.285 mm and a sorting, 0', of 1.58, while direct measure- ment of grains with conversion to the weighted sieve size (see appendix B for a discussion of techniques) showed a median size of 0.287 and a sorting of 1.56. Weighted median size of the opaque heavy min- erals as determined by microscope measurement in the bed material was 0.144 mm with a sorting of 1.49 (appendix C, table 5). The total sediment discharge was determined from a width-depth integrated sample of the water- sediment mixture collected at the lower end of the flume. Size and gradation of the collected sediment was determined by use of the visual accumulation tube after each sample was dried and split to a workable size. (21) HEAVY-MINERAL SEGREGATION Weighted direct I measurement / /’/ Sieveanalvsis 95 -— 1’ _ li< / Visual accumulation / tube analysis _ PERCENTAGE OF PARTICLES FINER THAN INDICATED SIZE 111111 1 1 l | 1 1 1 0-1 0.5 1.0 GRAIN SIZE, IN MILLIMETERS 0.1 FIGURE 9.—-Size-distribution curves for sand used in the flume. Curves plotted from analyses by visual-accumula- tion (VA) tube, sieves, and weighted direct measurement are shown. SIZE ANALYSES—SUSPENDED SEDIMENT Suspended-load samples were collected by a siphon with an inside diameter of 0.95 cm (centimeter). Inlet velocity at the siphon nozzle was adjusted to equal the local fluid velocity by changing the total head on the siphon. Local velocities were determined by a modified Ott velocity meter. For dune runs 1 and 2, sediment concentration (in milligram per liter) profiles were determined at the trough, brink point, and high on the dune stoss side. Two sedi- ment concentration profiles were measured for the transition run—one in the plane-bed reach and one high on the stoss side of one dune. One concentration profile was taken during the flat-bed run. Ap- pendix D contains the concentration and size analyses for all suspended sediments analyzed. Opaque-heavy-mineral grains were present in the suspended-sediment samples from each vertical pro- file in each of the four runs. Only run 2 had a volume percentage of dark opaque grains approach- ing that of the bed material. Each of the suspended- sediment samples from the runs show the opaque K13 heavy minerals to be distinctly smaller than those of the bed-material samples. Median size of the suspended opaque-heavy- mineral grains in each run falls below the 20th percentile size determined for the corresponding bed-material sample of opaque heavy minerals. A more complete analysis of the suspended- sediment samples has been given by Brady (1971). SIZE ANALYSES—CORE SAMPLES Opaque heavy minerals and light minerals ob- tained from cores were studied to determine whether differences in, size and sorting existed among sedi- ments in the different runs. Studies of the opaque- heavy-mineral grains were concentrated on the dark- mineral laminations of runs 2—4. Only minor accu- mulations of opaque heavy minerals were present in run 1, and those were insignificant in. thickness and areal distribution compared with heavy-mineral accumulations of runs 2-4. In addition to vertical cores mentioned previously, horizontal core samples were taken from at least two networks across and along the bed following each run. For each network, samples were obtained from the flume centerline and from 0.61 meter from each wall at 1.22 meter intervals along the flume. Total length of each sample network was selected to include the entire length of at least one bed form (average length of the networks was 6.1 meters). Small pits were dug to obtain the samples. Along the wall of each pit a can 6.5 cm in diameter and 12.7 cm in length was inserted horizontally to obtain the horizontal cores. Similar core samples were ob- tained from large areas of heavy-mineral segrega- tion that were missed in the network samples. Inasmuch as heavy-mineral accumulations de- veloped only near the upper surfaces of the bed, it was necessary that the surface sediments be in- cluded in the sampling. Therefore, most of these samples were taken in such a way that a small space remained above the sediment surface in the can. Plaster of Paris was poured into this open area, and moisture was allowed to evaporate. A chemical soil grout (AM—9, American Cyanamid Co.) was poured into the sample and allowed to harden. Adhesive strength of the grout was controlled to permit easy removal of sand grains from selected areas. The groute-d samples were sawed to remove disturbed portions of the core, and the sedimentary structures and segregation of minerals were studied in the position that they were deposited. K14 Selection of cores for analysis was based on the presence of and the location in them of segregated beds of opaque heavy minerals. The method of preparation and a description of the mounting of grains from a lamina within a core sample is de- scribed in appendix B. Complete analyses of size, shape, and sorting are shown in appendix C, table 5. In run 2, opaque-heavy-mineral samples were ob- tained from topset and foreset beds and from the brinklines of dunes. Samples from run 3 were db- tained from topset and foreset beds, and one sample was taken from the flat-bed region. Samples from run 4 were obtained from dark—opaque laminae lo- cated at the base of and within the flatabed region. Grain size and sorting for samples shown in table 5 (appendix C) were obtained from direct measure- ment of 200 individual grains per sample mount. Size and sorting analyses were determined from grain mounts of light minerals obtained either from light-mineral laminae adjacent to or from light minerals present within opaqvue-heavy-mineral laminae. Analysis of variance tests were conducted for the median size, sorting, and shape factor of opaque- heavy-mineral grains obtained from core samples from runs 2, 3, and 4. These statistical tests are used to determine whether two or more sample means could have been obtained from populations with the same parametric mean with respect to a given variable, or whether the sample means were drawn from different populations (Sokal and Rohlf, 1969, p. 175). In this study the analysis of variance tests were conducted to determine if size and sort- ing of the opaque heavy minerals in the segregated layers of each run were significantly different in each run. Since the same sediment was used for each run, any significant differences in the data must be due to the effect of the different flows on the grains. Data used for the analysis of variance tests were obtained from laminae of dark opaque minerals in the core samples (appendix C, table 5). A more com- plete presentation of these results has been given by Brady, (1971, p. 44). The results of the tests on the median grain diameter and the grain-shape factor of opaque- heavy-mineral grains showed no differences among runs at the 5 percent level of significance. A signifi- cant difference, however, did exist in the sorting among runs at the 1 percent level. An a posteriori SNK test (Sokal and Rohlf, 1969, p. 239-246) of the sorting means of the three runs was conducted to determine Which run was significantly different from the others. Results of the SNK show that the SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS mean sorting value of the opaque-heavy-mineral samples in run 4 is significantly larger than the sorting values are for the other two runs at the 1 percent significance level. The median diameter and sorting for light-mineral samples that were obtained adjacent to and Within the opaque-heavy-mineral laminae also were tested by analysis of variance tests (sorting and median diameter values of the samples are listed in appen- dix C, table 6). The tests show that no difference in sorting of light minerals existed between runs 2—4; but, a significant difference did exist at the 5 per- cent level between the median diameter of the sam- ples. Results of these tests should indicate whether a given flow had an effect on the properties of light- mineral grains that were closely associated with opaque-heavy-mineral grains that differed signifi- cantly from the effects that other flows had. A SNK test of the mean of the sample median grain sizes for each of the three runs showed that no significant difference existed between the three runs. However, a SNK test for uneven sample sizes, such as was used for runs 2—4, does not provide sufficient sensitivity to determine which run differed significantly from the other two in its effect on sample median size. EXPERIMENTAL RESULTS SUMMARY OF BED FORM AND OPAQUE-HEAVY-MINERAL SEGREGATING CHARACTERISTICS Four different flow runs were observed in this study (table 2) ; based on the terminology of Simons and Richardson (1966) , two runs were made in the lower flow regime, one run was made in the upper flow regime, and one run in the transition regime. The bed configuration consisted of dunes (lower flow regime) in runs 1 and 2. Transition bed forms were long profile dunes and a near flat-bed condi- tion in run 3. Run 4 consisted entirely of a flat bed formed in the upper flow regime. Average lengths (L) and heights (H), measured from sonic sounder charts, and length/height ratios for the dunes of different runs are given in table 3. DUNE BED FORMS (RUN l) Dunes in run 1 were formed by flow that pro- duced a low shear stress at the bed surface (table 2). In profile the dunes were generally triangular in shape, with the crestline coinciding with the dune brinkline. Topset beds occurred on only a few dunes. HEAVY-MINERAL SEGREGATION A K15 B FIGURE 10.—Dune bed configuration and opaque-heavy-mineral accumulations at the bed surface following run 1. A, Dune- bed configuration B, Stoss slopes of dunes showing small areas of accumulated opaque heavy minerals (length of rule is 30.5 cm). TABLE 3.—Mea,n dune size (with standard deviations) meas- ured by sonic sounder Number Run of dunes Height1 Length” Length/height measured ( cm ) (meters ) ratio 115 10.2 i 4.9 1.63 i 0.66 18.2 -_|- 8.7 28 30.0 i 13.2 7.24 i 4.67 26.3 i 15.0 46 12.3 i 6.8 5.66 i- 2.48 46.6 i 29.6 I~D1.me height, H, determined by maximum vertical distance between the trough point and the summit point of the dune as measured along center line of the flume. aDune length, L, was determined from the low trough point between dunes to the next trough point downstream as measured along the center- line of the flume. The average angle of inclination of the foreset beds in run 1 was 32.4°, with a standard deviation of 23°. Configuration of the dunes forming the bed surface (fig. 10A) can best be described as linguoid. Rates of movement of the dunes ranged from 0.6 to 1.0 meter per hour. Opaque heavy minerals associated with the dunes were limited to small very thin ripple-form accu- mulations on the stoss slopes of the dunes (fig. 103). The small thin accumulations of opaque heavy min- erals appear to develop just downstream from the reattachment point (the location where the flow im- pedes on the back of the downstream dune after it has passed over the upstream dune front) and migrate up the dune stoss slope. No accumulations of opaque heavy minerals were observed in the foreset beds. DUNE BED FORMS (RUN 2) Dunes formed by flow conditions in run 2 (table 2) were longer and higher than dunes produced by K16 S‘EDIMENT TRANSPORT IN ALLUVIAL CHANNELS the other runs. Distance between brinkline and crest- line commonly ranged from 25 to 110 cm and aver- aged 60 cm. Topset beds, which are generally com- posed of rather fine material, were present on most dunes; they reached a total thickness of as much as 3 cm. Foreset beds in run 2 showed an average dip of 292° and a standard deviation of 3.1°. Generally the inclination angles of the foreset beds ranged from 28° to 32°, but some low bed angles of 21° to 23° indicate unstable hydraulic flow during dune development. Dune fronts in run 2 were sinuous across the width of the flume (figs. 11, 12), and rams of movement of the dunes down the fiume (based on successive brinkline locations) ranged from 1.5 to 3.4 meters per hour. Accumulations of opaque heavy minerals asso- FIGURE 12.—Accumu1ations of dark opaque heavy minerals ciated With the dunes (fig. 13) were present com- on the upstream sides of dunes (run 2). Location of cut- m on] as‘ away view of dune (fig. 14) is shown by the line near the 1 0y ' h . rals n the dune stos le es flume wall on left side of photograph. The ripple surface ' Raque eaVy mme . 0. S D that is shown on the dune is due to abrupt changes in In the form 0f thln ripple accumU-lfitlons 01' hydraulicflow thatoccurred when the flume was shut down very thin almost sheetlike accumulations. The at the end of the run. Segregation of the heavy minerals thin ripple accumulations, which resembled was not formed by shutdown of the flume- those shown in figure 103, were very common. They appear to have originated on the lower part of the dune stoss slope and to have mi- grated up the dune slope. Thin sheetlike accu- mulations of the opaque heavy minerals like those shown in figure 12 were present on many dune stoss slopes. 2. Thick accumulations of opaque heavy minerals associated with the dune crest area. These accumulations formed the thickest beds of opaque heavy minerals observed, and the beds were nearly 100 percent opaque heavy min- erals. Observations made through the plexi- glass wall of the flume during the flow showed that the opaque-heavy-mineral accumulations formed on the highest portion of the dune (in dune profile). The accumulation as a whole moved downstream at a rate approximately equal to the rate of movement of the dune. Scour occurred periodically both upstream and downstream from the heavy-mineral area. If degradation immediately downstream reached approximately 1-2 cm below the high point of the accumulation, large amounts of the heavy minerals were transported from the accumulation by suspended and tractive move- ment and redeposited as a heavy-mineral lamina along the lee slope. 3. Accumulations of opaque heavy minerals that were deposited between the dune crestline and the brinkline. These deposits, derived from the thick crest area accumulation of opaque heavy minerals, formed part of the topset beds of’ the dune. An example of numerous opaque- heavy—mineral laminae in the topset beds is FIGURE 11.—Dune bed configuration (view upstream) of run 2. Figure 12 is a close view of the large dune (center of the . photograph) on which the white square is located. shown in figure 14B. HEAVY-MINERAL SEGREGATION \\\ K17 \ \\\\ Foreset beds \/_\\ FIGURE 13.——Generalized view and cut-away of a dune showing structures and locations of different types of opaque- heavy-mineral accumulations: a, thin ripple-form accumulations on stoss slope; b, crestal region accumulation; 6, region between the crestline and brinkline where accumulations occur; d, accumulations in foreset beds_(x 3 Ver- tical exaggeration). 4. Accum‘ulations of opaque heavy minerals de- posited at the brink point and on the slipface of the dune. These deposits formed dark lami- nae in the foreset beds like those shown in figure 11A. The concentrated opaque-heavy- mineral layers did not extend down the foreset beds more than 8 cm (total slipface length on the dunes commonly was 20—30 cm), and con- centration of heavy minerals decreased with increased distance down the bedding plane from the brinkline. Opaque heavy minerals were lost from the topset beds by tractive and suspended transport over the brink point. TRANSITION BED FORMS (RUN 3) During the run the bed forms alternated between large dunes (fig. 15A and B) and a near flatdbed condition (very long profile dune). The near flat- bed condition of the run differed from a true flat bed in that it did not at any time extend over the entire length of the flume. In addition, the near flat-bed condition difiered from the flat bed of run 4 by having a slipface on its downstream edge as well as slight form irregularities on its surface. Dunes associated with run 3 had a much larger length-to-height ratio than the dunes of runs 1 and 2. The distance from the crestline to the brinkline for the dunes of run 3 commonly ranged from 15 to 85 em, but for some dunes the distance was as much as 2.5 meters; the mean distance was 53 cm. Topset beds of fine material were present on virtually all the dunes. Dune fronts were sinuous across the flume as shown in figure 15A and B. Angles of inclination of foreset beds averaged 28.6° with a standard deviation of 32°. Several foreset dip values of 21° to 23° indicated locally unstable depo- sition. Rates of movement of the dune fronts ranged from 2.7 to 4 meters per hour. Opaque-heavy-mineral accumulations commonly associated with the transition bed forms can be classified as follows: 1. Thin but widespread accumulations near the base of flat beds, just above foresets formed with or as part of dunes deposited earlier. 2. Thin laminae of concentrated opaque heavy min- erals within the flat beds. These laminae were usually thinner than the opaque-heavy-mineral beds at the base of the flat-bedded sediments. 3. Accumulations associated with the dune phase of the transition bed forms. They were basic- ally the same as those associated with the dunes of run 2, namely: a. Thin accumulations in ripple-form and sheetlike accumulations that advance up the stoss side of dunes. b. Thick accumulations that were commonly present along the crestal region of the dune (fig. 16A and B). c. Accumulations that extended downstream from the crestline to the brinkline (fig. 17A and B). In several dunes opaque- heavy-mineral segregation was observed in the foreset beds (fig. 17A). (1. Thick accumulations were often present in the topset beds. These deposits resulted from burial of surface accumulations. BED FORMS OF MOVING FLAT—BED CONDITIONS (RUN 4) The flow that produced the flat beds of run 4 had K18 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS B FIGURE 14.—Opaque—heavy-mineral accumulations in foreset and topset beds of dunes formed in run 2. A, Cut-away part of dune shown in figure 12 showing accumulation of opaque heavy minerals (dark beds) in the foreset beds (can diam- eter is 6.5 cm); B, Segregation of opaque-heavy-mineral grains in topset laminations. HEAVY-MINERAL SEGREGATION A K19 B FIGURE 15.——Bed configuration and opaque-heavy-mineral accumulation at the bed surface formed during run 3. A, Dune region of transition flow; 3, Close-up view of dunes showing opaque-heavy-mineral segregation on the dune stoss slopes. Ripples present on the dunes were not present during the run but were formed as the result of abrupt changes in flow conditions during flume shutdown. the highest shear stress and Froude number of any flow during the four runs. Under equilibrium flow the sediment bed had an essentially featureless sur- face (fig. 18) , the bed elevation at any point depart- ing only a few centimeters from the mean eleva- tion. A study of bed—surface-elevation fluctuations at one location during the equilibrium flow showed a maximum fluctuation of only 1.8 cm during a 12 hour period. Studies by Guy, Simons, and Richard- son (1966, p. 24, 29) show vertical fluctuations with time of flat-bed surfaces during several runs as ranging from 1 to 3 cm. Bedding structures were all flat lying and covered preexisting bed forms. Gen- erally the material in the flat lying deposits was finer than the material in the preexisting foreset beds. Total thickness of the flat beds in the run was usually less than 3 cm. Of the four runs studied in detail, total sediment concentrations in the total-load and suspended-load samples were by far the largest in run 4. Opaque—heavy—mineral accumulations were com- mon in the flat-bed run, and accumulations of the heavy minerals were present at the base of and within the flat beds over virtually the entire flume area (fig. 19). The individual beds, however, tended to lense out within a few meters. Accumulations were often the thickest and most widespread at or near the base of the flat beds. In run 4 no opaque- heavy-mineral accumulations were present at bed surface. RELATION 0F FALL VELOCITIES 0F DARK OPAQUE AND LIGHT-DENSITY GRAINS Samples of light minerals obtained from laminae adjacent to or within laminae having a high con- K20 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS FIGURE 16.—Accumulations of opaque heavy minerals formed along the crestal region of a dune (run 3). A, Accumulation on the crestal region of a long dune in the transition flow; B, Exposed topset beds (located at the right side of the 71-cm rule in top photograph) showing the thick accumulation. HEAVY-MINERAL SEGREGATION K21 B FIGURE 17.—Opaque-heavy—mineral accumulations formed in topset and foreset beds during run 3. A, Opaque heavy minerals in dark laminae of topset beds near the brinkline and in the foreset beds in laminae composed of the grains that have passed over the brink point; B, Foreset beds have very few opaque heavy minerals present, but a large amount of opaque heavy minerals are present in the thin topset beds. K22 FIGURE 18.—F1at-bed surface formed by run 4. Ripples at the surface were due to shutdown of the flume. centration of opaque heavy minerals were studied to examine the role fall velocities play in the associa- tion of light- and heavy-mineral grains. To do so, a graph (fig. 20) relating sieve size to fall velocity for grains with a shape factor of 0.7 and with specific gravities of 2.65 and 5.0 was plotted from data reported by the US Inter-Agency Committee on Water Resources (1957). Values of fall velocities for the dm, dw, and d84 grain sizes were determined from figure 20 by using the samples described in tables 5 and 6 (appendix C). These fall-velocity values have been tabulated by Brady (1971, p. 112). Fall-velocity relations between opaque—heavy-mineral grains and light-mineral grains of the bed-material sample and the average of all the core samples are shown in figure 20. If one averages the range between the 16th and 84th percentiles of the opaque-heavy-mineral grains and the light-mineral grains for the sampled laminae in the core samples, 78 percent of the light mineral grains have fall velocities within the same range as 80 percent of the opaque-heavy-mineral grains. For the bed-material samples, 74 percent of the light- mineral grains had fall velocities equal to 78 per— cent of the opaque-heavy-mineral grains. Median fall-velocity values of the opaque heavy minerals and the median fall velocities of light minerals sampled adjacent to (18 samples) or SEDIMENT TRANSPORT IN AL‘LUVIAL CHANNELS within (five samples) the opaque-heavy—mineral laminae have a correlation coefficient of 0.369 (fig. 21) , a value that suggests no correlation exists. The lack of correlation for medians of fall velocities between the two mineral groups shows that the median fall velocity of one group is not a predictor of the median fall velocity of the other group despite the fact that a large number of grains have equiva- lent fall velocities in adjacent laminae. The lack of correlation for mean fall velocities of the opaque heavy minerals and light minerals, therefore, sug- gests that other grain properties were much more important for local sorting. RELATION OF GRAIN ENTRAINMENT TO CRITICAL SHEAR STRESS AND GRAIN SIZE By using Shields diagram (fig. 5), one can develop the relation of critical shear to grain size for grains of different densities. Such a series of curves was developed by Grigg and Rathbun (1969, p. B79). TWO curves similar to those constructed by Grigg and Rathbun are plotted in figure 22 for grains of 5.0 and 2.65 specific gravi- ties. The range between the 16th and 84th per- centiles of the opaque-heavy-mineral grains and the light-mineral grains of the bed material and the average values for the sampled laminae in the core samples from runs 2, 3, and 4 are plotted in figure 22 to show the relation between the critical shear stress of the two mineral groups. The large differ- ence in critical shear indicates that quartz and feld- spar grains would be entrained from sands in this study much more readily than magnetite and ilmen- ite grains. Figure 22 is based directly on Shields diagram. The data on which the Shields diagram was based were obtained by laboratory experiments in which particles moved over a bed that consists of particles of the same size. How differences in size affect the moving and stationary particles has been discussed on 'pages 3 and 4. By use of figure 1, one can qualitatively adjust figure 22 so that it is more applicable to the flume situation. For example, fig- ure 1 indicates that the resistance of a 0.1 mm particle resting on a bed of 0.2 mm particles is underestimated in figure 22 by as much as a factor of 3. Once a small magnetite or ilmenite grain is deposited on a bed of large quartz and feldspar grains, it is extremely difficult for the flow to move it again. The resistance of a 0.4 mm particle resting on a bed composed of 0.2 mm particles is overestimated HEAVY-MINERAL SEGREGATION K23 FIGURE 19.——Flat—bed flow deposits showing opaque-heavy-mineral layers (dark beds) within the flat-lying beds. Lower dark-mineral bed directly overlies foreset beds of an earlier run. Wavy appearance of the dark laminae in the photo- graph i-s due to an irregular cross-section cut. The rule is 71 cm in length. in figure 22 by perhaps a factor of 2. The flow will quickly remove a large quartz or feldspar particle from a bed which is composed of small dense grains. In addition, distinct differences in physical size between grains also leads to a “hiding factor,” or a shielding of the smaller grains from the flow by the larger grains. Einstein and Chien (1953) dis- cussed the “hiding factor.” To test whether the slope of the lines in figure 22 may actually be negative when the bed is composed of a poorly sorted material in the size range of interest here, an experiment was conducted to deter- mine what efl’ect the sorting of the bed material might have on a particle’s resistance to motion. A flat bed of quartz sand (d50 = 0.280 mm, 0' = 1.50) was placed over a 94-cm section of a flume 20 cm deep, 20 cm wide, and 10 meters long. The bed roughness for a section 6 meters long upstream from the sand bed was similar to that of the sand bed. The flow was started at a velocity insufficient to move any of the bed material, and the velocity was gradually increased. During the velocity in— crease the water depth was held constant at 3.5 cm, while the slope of the water surface remained parallel to that of the bed. The velocity was in- creased slightly each 24 hours for 6 days. The total material transported from the test section during each day (run) was collected and sieved. Results of this experiment (table 4) show that little sediment was eroded during the first five runs. During the last run, ripples developed, and a con- siderable amount of sediment was eroded, mainly producing a few isolated scour holes several milli- meters deep. The selectivity with which the flow transported a particular size fraction of the bed material can be determined by computing the ratio of the percent of that size fraction in the material transported out of the test section to the percent of the size fraction which was available for transport. This ratio will be called the transport ratio. Transport ratios which are greater than one indicate size fractions which are readily transported or which have a low resist- ance to motion. If a particle’s resistance to motion were correctly represented by figure 22, one would expect the transport ratio to decrease continuously with increasing particle size. By assuming that a representative sample of the bed material was available for transport on the bed surface at the beginning of run A, the transport ratios for each size class and run were computed from the data given in table 4. Except for run A, which did not transport any sediment larger than 0.707 mm, the transport ratios were larger than one for all grain sizes greater than 0.35 mm. The increase in the value of the transport ratio indicates a decrease in resistance to motion with increase in grain size in the range 0.25 to 1.0 mm, a relation- ship opposite to that indicated in figure 22. It is suspected that some sorting of the bed ma- terial occurred at the bed surface as a result of the placement of the bed and that this sorting affected the resulting transport ratios of the smaller grain sizes during the first five runs. Therefore, no signifi- cance is attached to the transport ratios of the finer sizes for the first five runs. Ripples were developing during run F, and a few scour holes were eroded several millimeters deep. K24 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS TABLE 4.—Results of a resistance-to-motion experiment using a poorly sorted quartz bed material Size, in millimeters 0— 0.062— 0.125— 0.177— 0.250— 0.350— 0.500-— 0.707— Run 0.062 0.125 0.177 0.250 0.350 0.500 0.707 00 Total Weight (in grams) of material eroded during the run A __________ 0.0006 0.0089 0.0126 0.0132 0.0157 0.0285 0.0010 0 0.0805 B ___________ .0007 .0067 .0100 .0089 .0098 .0180 .0109 .0010 .0660 C ___________ .0016 .0110 .0147 .0109 .0075 .0136 .0146 .0017 .0756 D ___________ .0013 .0104 .0235 .0387 .0528 .0784 .0554 .0012 .2617 E ___________ .0016 .0111 .0133 .0236 .0827 .2505 .2033 .0051 .5912 F ___________ .000 .019 .594 3.221 8.106 11.106 4.085 .057 27.188 Total _______ .006 .067 .668 3.316 8.275 11.495 4.370 .066 28.263 Percent of total eroded material 0.02 0.24 2.37 11.7 29.3 40.6 15.5 0.23 Percent of bed material 0.2 4.9 11.0 22.8 33.2 22.2 5.6 0.05 Ratio (percent eroded/percent in bed) 0.1 0.05 0.22 0.52 0.88 1.8 2.8 5 Because of this erosion pattern, it is believed that the size distribution of the material which was avail- able for transport was nearly the same as the size distribution of the total bed material and that the computed transport ratios for run F accurately rep- resent the resistance to motion of the particles. The transport ratios for run F increased con- sistently with particle size throughout the entire range of particle sizes. Therefore, it is concluded that the resistance to motion of sand grains de- creases with increasing grain size when the trans- port is occurring over a poorly sorted bed. T‘here obviously must be some maximum size above which this relation is no longer true. The data presented in table 4 indicate that this maximum size is larger than 0.1 mm. These results indicate, as the plot of figure 1 sug- gests, that figure 22 does not correctly depict the resistance to motion for particles for material being transported over a poorly sorted bed material. The resistance to motion should decrease, rather than increase, with increasing particle size for particle sizes within the range of 0.05 to 1.0 mm. The median size of the total load transported in these small fiume experimental runs made at the point of initiation of grain movement was larger than the median size of the bed material, whereas the median size of the total-transport—load samples from the large flume runs was smaller than that of the bed material. In natural streams, total—load sam- ples almost always have smaller median sizes than does the bed material of the stream (Carl F. Nordin, oral commun., April, 1971). Smaller particles are, of course, more easily en- trained and carried in suspension by the flow, and the suspended load always has a smaller median size than does the total load. It is usually impossible to determine the size distribution of the entire sus- pended load so that the true size distribution of the bed load is seldom known either in the field or in the laboratory. In addition, the median size of the bed material tends to increase with distance below the mean bed elevation for fully developed bed forms. As a con- sequence the coarser particles tend not to be ex- posed to the flow and are not available for transport as frequently as the finer particles deposited at higher elevations in the bed. Their availability would tend to account for a higher transport rate of small particles even though their resistance to motion along the bed is greater than that of larger particles. The small flume experiment shows that a marked “hiding effect” does exist for a poorly sorted be-d material, and this result is consistent with flume and field data. When small grains form only a small part of the surface material as the small opaque- mineral grains did in this study prior to their con- centration, the selective removal by the flow of larger less dense grains can play an important part in their segregation. HEAVY-MINERAL HEAVY-MINERAL TRANSPORT AND DEPOSITION IN A FLAT—BED FLOW Accum‘ulations of dark opaque minerals were widespread in the flatbed runs (run 4). The acou- mulations of opaque heavy minerals at the base of the flat-bedded sands suggested that the heavy min- erals were concentrated at the base of the tractive load during degradation and were the first deposited during aggradation. To test this hypothesis, a study was made of the transport of heavy minerals rela- tive to time under equilibrium‘hydraulic conditions. The small recirculating water-sediment flume (20 cm deep, 20 cm Wide, and 10 m long) was used in the experiment with a sand bed of the same Rio Grande sand that was used in the large flume runs. The sand bed was thoroughly mixed after the flow was started. Mixing of the sand provided maximum possible exposure of heavy minerals to the flow. The run, which lasted for 47 hours, was started just after the mixing of the sand. Hydraulic conditions necessary to form the flat bed were held as constant as possible throughout the run. Average discharge for the run was 10.98 liters per second with an average water depth of 7.36 cm. Water-surface slope was 0.0045, and the average temperature was 16.9°C. Total-load samples containing 80—135 grams of sediment were collected at close time intervals (15 min) early in the study and at increasingly longer time intervals (up to m __ m 0.5 — _ Lu )— uJ — _. E _J :‘ — __ E Z ui _ _ E ”’ E» E /? Bed-material sample _. d U) 50 Core samp|e average 0'1 b' / Shape factor : 0.7 ’ \ . /"3 d" Temperature : 20.8”C 0.05 l l l l l l l l i l 1.0 5.0 10.0, 30.0 FALL VELOCITY, IN CENTIMETERS PER SECOND FIGURE 20.—Fall-velocity relationship of light-mineral grains to opaque-heavy-mineral grains obtained from the bed-ma- terial sample and core samples of runs 2, 3, and 4. SEGREGATION K25 5° l l 7 0 Run 2 A Run 3 I Run 4 2.0 — .. — MEDIAN FALL VELOCITY OF OPAOUE MINERALS, IN CENTIMETERS PER SECOND o 1 l 1 1 0 1.0 2.0 3.0 4.0 5.0 MEDIAN FALL VELOCITY OF LIGHT MINERALS, IN CENTIMETERS PER SECOND FIGURE 21.—Plot of median fall velocities of opaque-heavy- mineral grains and light-mineral grains. 7 hr) as the study progressed. Total-load concentra- tions for the study averaged 2,699 mg/l. Sediment from the total-load sample that passed the 60 mesh (0.25 mm) sieve was retained for mag- netite separation. Magnetite less than 0.25 mm was used in this study as the marker mineral because of the ease of separation of magnetite and because 88 percent of the dark-opaque-minerals of the bed- material sample were finer than 0.25 mm. A strong hand magnet was used to separate the magnetite grains from the sample. The percentage of magnet- ite in the sand that passed the 60 mesh sieve was calculated, and the results of these percentage plots relative to time (fig. 23) confirm the hypothesis that in a flat-bed flow under equilibrium conditions there is a decreasing volume of transport of heavy min- erals with increasing time of transport. DISCUSSION OF DATA RELATIONS AMONG SEDIMENT SAMPLES Analysis of variance tests of median sizes and shape factors of opaque-heavy-mineral grains ob- tained from laminae having high concentrations of opaque heavy minerals show no significant variance at the 5 percent level among sediment samples taken from each of runs 24. There was, however, a sig- nificant difference at the 1 percent level in sorting K26 ‘°'° _ T l I | — 9 Bed—material sample _ 5 Core sample average U) Q — u.I u.I EEW— 0 a E u) — If E 5 E _ a?” 5 2 8-6/ \ _| I: \ ‘15" < Z dis 0 8 _ Es 0 l3- 5'9‘ dlb 1.0 l l I | l l l l l l l l l 0.05 0.10 0.50 1.0 GRAIN SIZE, 'IN MILLIMETERS FIGURE 22.-—-Critical shear relationship of light minerals to opaque heavy minerals for the bed-material and core samples. among the three runs. Among the light minerals from runs 2—4 sampled from laminae adjacent to the opaque-mineral laminae, a significant difference existed in the median size at the 5 percent level, and no significant difference (ES-percent level) existed for the sorting values. Sorting values determined for opaque-heavy- mineral samples from run 4 were much larger than for those from other runs. Sorting values for opaque— heavy-mineral samples of run 4 were close to those for dark opaque grains in the bed-material sam- ples. This correlation indicates that all sizes of the high-density material in run 4 were being moved by the flow, whereas sorting of opaque heavy min- erals towards finer sizes was occurring in runs 2 and 3. Sorting is the grain distribution parameter most affected by the different hydraulic conditions. In the flat-bed flow (run 4), segregation apparently oc- curred first at the base of the bed load and formed a widespread layer of opaque-heavy-mineral grains. As local erosion of the bed occurred, the opaque minerals became concentrated at the base of the flow, and subsequent deposition allowed preserva- tion of the dark laminae. For such a concentrating mechanism, the sorting would have a wide range of values and would depend on the ability of the local flow to sort the sample as to size. The smaller sort- ing values obtained for the dune flows shows that sorting as to size is accomplished more efficiently in the lower flow regimen. Analysis of the critical shear stress for grain movement indicates that the larger low-density grains of the bed material require a much smaller SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS shear for movement than the smaller, more dense grains. Relations of velocities of heavy minerals and light-density minerals (figs. 3, 4) and the criti- cal shear relationship of opaque heavy minerals in the bed-material (figs. 1, 22) all seem to support the idea that the less dense grains are much more readily entrained and moved. In addition, the difference in size between the low-density grains and the high- density grains leads to a “hiding effect” that can effectively shield the smaller grains from the flow. A large percentage of the light-mineral grains and opaque-heavy—mineral grains in adjacent lami- nae had fall velocities in the same range. However, comparison of fall velocities of median Sizes of the dark-opaque-mineral samples and light-mineral sam- ples from the core samples showed that no correla- tion exists (correlation coefficient of 0.369) for the median values of these two groups. The light-mineral samples were obtained from within (five samples) and adjacent to (18 samples) the opaque-heavy- mineral laminae. All the light-mineral samples ex- amined were taken from positions within 2 mm of the sampled heavy-mineral laminae. The lack of correlation and the presence of distinct segregated laminae, even though an adequate supply of both mineral groups having equal fall velocities was available, suggest that factors other than grain fall velocity were important to the occurrence of local sorting. Gross transfer of the sediment load, however, may be related to the fall velocities, for the fall velocities of 78 percent of the opaque-heavy-mineral grains in the bed-material samples overlap those of 74 percent of the light-mineral grains in the size dis- tribution range between the 16th and 84th percen- tiles. Turbulence is more intense in the trough region than on the higher portions of the stoss side or near the brink point of the dune; and, in general, turbu- lence is more intense near the bed. A large shear stress at the bed, caused by the turbulent eddies, is probably important in the initiating movement of the opaque heavy minerals, especially in the region of the reattachment point. Intermittency of turbulence was not studied quan- titatively, but strong turbulent eddies passing over the crestal region were observed in the flow and strong intermittent turbulence is suggested by the presence of opaque-heavy-mineral laminae in the topset beds. Strong turbulence which increases the local shear could cause a rapid movement of the opaque-heavy-mineral grains from the crestline toward the brinkline—and the low-density material could then move rapidly over the dense grains or be HEAVY-MINERAL SEGREGATION carried temporarily in suspension. With a decrease in turbulence, the heavy minerals would be de- posited before the light minerals. BED FORMS AND HYDRAULIC VARIABLES Observations of the four runs in this study and other experimental runs made in the large flume, as well as field observations, indicate that the bed con- figuration is the most important single factor affect- ing the opaque-heavy-mineral segregation. Bed con— figuration, however, is not an independent variable but is dependent on a large number of hydraulic variables as shown by Simons and Richardson (1966, p. J 13—J 16). The most important variables affecting the bed forms are the energy slope, depth of flow, physical properties of the bed material, and velocity of flow. In flume studies, flow velocity is considered to be dependent on the energy slope and depth of flow; however, in field relations, velocity is the inde- pendent variable, and depth of flow is probably the dependent variable. Under the flow conditions of this study there appears to have been three fundamental types of heavy-mineral segregation. 1. Thin accumulations of opaque heavy minerals covering small areas, associated with dunes without topset beds and the stoss slope of large dunes with topset beds. 2. Accumulations of opaque heavy minerals asso- ciated with topset deposits of large dunes. 3. Accumulations of opaque heavy minerals that were associated with flat-bed movement of the sediment. The small areas of thin accumulations of opaque heavy minerals were found in association with rip- ples and small dunes. On larger dunes small areas of heavy-mineral accumulations formed on the dune stoss slope, commonly in the areas just downstream from the reattachment point of the flow (the loca- tion where the flow impedes on the bed after it passes over the upstream dune front). The accumu- lations of opaque heavy minerals moved up the stoss side of the dune as units, and additional grains were added to the migrating areas during their move- ment. Dark opaque-heavy-mineral accumulations generally moved as very thin ripples having very large length to height ratios (fig. 103). The buildup and movement of these accumulations may be described somewhat as follows. The intense turbulence associated with the reattachment point supplies both heavy and light material to the section just downstream from the reattachment point. Be— K27 fore segregation occurs, the bed at this section con- sists primarily of rather coarse foreset material. This coarse bed material serves as an effective trap for the small dense particles supplied to the area (figs. 1, 22). As more and more of the dense parti- cles are trapped and segregated at this location, a small area of the bed will become covered. Once cov- ered, the area becomes more resistant to erosion (fig. 22), and the erosion of the light particles around the heavy-mineral area tends to expose the accumu- lation to increasingly stronger flow conditions. Finally the segregated accumulation starts to move up the stoss slope of the dune as the dense particles are eroded from the upstream edge of the accumu— lation, move across the relatively smooth surface of the heavy mineral area, and are deposited at the downstream edge of accumulation. All during this process large quantities of the larger less dense par- ticles are transported over the smooth surface of the accumulation. Large areas of opaque-heavy-mineral accumula- tions often were associated with topset deposits that occurred on large dunes and transition bed forms. The greatest thicknesses of accumulations of dark opaque-mineral grains were associated with this type of deposit. Three different situations associated with the topset accumulations of opaque-heavy- mineral grains were as follows: (1) Accumulations that occurred along the crestal region of the dunes. These opaque-heavy-mineral accumulations moved downstream with the dune if the dune maintained approximately the same shape and height. Losses from the crestal region were offset by additions of heavy minerals from upstream areas. (2) Laminae of opaque heavy minerals that occurred downstream from the crestline were found both upon and within °~‘6 I I I I l . Sample 9 75 l l .0 o on .0 o a PERCENT MAGNETITE IN TRANSPORT O ,_ O (D a; N 5 U to SI- 48 TIME, IN HOURS FIGURE 23.—Relation of magnetite in transport to time in 20-cm flume and under flat-bed conditions. K28 the topset beds. These heavy-mineral deposits were derived from a crestal accumulation. (3) Foreset laminae of opaque-heavy-mineral grains. The segre- gated opaque—heavy-mineral laminae in the foreset could be traced up slope in many cases into the top- set beds. The foreset accumulations were caused by ' conditions similar to those that deposited the opaque- heavy-mineral laminae in the topset beds except that the heavy-mineral grains were transported in suffi- cient quantities past the brink point to allow some to slide down the lee slope and form the concen- trated laminae in the foreset beds. A decrease in degree of concentration of opaque-heavy-mineral grains within laminae with distance down the fore- set indicates a diluting of the opaque heavy min- erals with low density grains or a decrease in the proportions of opaque heavy minerals transported to that point. When accumulations of opaque heavy minerals are deposited just past the brinkline in the foreset beds, a periodicity of transport is indicated by the alternate layers of light and heavy minerals in the foreset sequence (fig. 14A). The most plausible explanation of this alternation is that strong inter- mittent turbulent eddies increased motion of the high-density grains and moved them past the brink point of the dune and that most of the lower density material was either carried into suspension by the increased turbulence or moved rapidly over the small, high-density grains. The bed-surface elevation of flat-bed flow under equilibrium conditions varied randomly with time but by only a few centimeters from a mean eleva- tion at any location. Therefore, for thick laminae of opaque heavy minerals to form in a flat-bed flow it is important that a flow condition produce a deep scour (in this study, a transition flow) prior to the fiat-Abed flow. Such erosion is necessary in order to expose the heavy minerals in a thick section of bed material to the flat-bed flow. During the flat-bed run, accumulations of opaque heavy minerals occurred near the base of the trac- tive load. Other accumulations of opaque heavy min- erals that were present within the flat beds probably also represent heavy minerals deposited in the same way as those at the base of the flat beds but subse- quent to depo‘sitionx’of the basal accumulations. Re- sults of the 20-cm flume experiment show a decrease with time in the evolume of heavy-mineral grains transported in a flat-bed flow at near equilibrium conditions. This decrease in heavy-mineral transport indicates that a large percentage of the heavy min- erals were deposited early during the flow and that the heavy minerals either remained at rest or were SEDIMENT TRANSPORT IN ALILUVIAL CHANNELS reentrained at a rate that was less than the rate of deposition. On dunes, the thickest accumulations of opaque heavy minerals occurred in the topset bed area near the crest of the dune. Runs 2 and 3 had large dunes that had a fairly large crest-to-brink distance and topset beds that had large areas of thick heavy- mineral accumulation associated with them, While dunes of run 1 had a crestline corresponding to the brinkline, and no topset beds or large areas of con- centrated heavy minerals. In order to determine why the opaque heavy min- erals form large accumulations near the crest of dunes, consider the expression for the rate of sedi- ment transport as given by Simons, Richardson, and Nordin (1965b) by 1 Mb .._. + _ at 1—/\ am where y = elevation of the bed surface, t = time, A = porosity of the sand bed, q» : bed-load trans- port rate in volume per unit time per unit width, and x = distance along the bed surface in the direc- tion of the flow. This equation states that the rate of change of bed elevation with time (that is, the rate of deposition or erosion) is proportional to the rate of change of bed-load transport with respect to distance. From the negative ratio obtained by apply- ing this equation to the area upstream from the crest of a dune, it is apparent that this is a region of erosion. Erosion is needed in order to keep the thin accumulations on the stoss slope of the dunes ex- posed to the flow so that they continue to move. How- ’ ever, downstream from the crest of the dune by/ at is positive, indicating that this is generally a region of deposition. Because of their large resist- ance to motion, dark opaque minerals are selectively deposited from the moving bed load after it passes over the crest. The net result is that the thin accu- mulations move up the StOSS slope of the dune and are deposited just downstream from the crest. At this point the heavy minerals accumulate to rather large thicknesses, for the material is transported out of the region only by occasional bursts of ex- treme turbulence. Thick accumulations probably could not build up in run 1 because the crestline and brinkline were coincident; the brink point is a place where the grains can be lost to suspension and to the foreset material. Topset beds were deposited with a small dip angle in the downstream direction (generally 4°—6°) be- tween the crestline and the brinkline. In general ) = 0 (22) HEAVY-MINERAL SEGREGATION appearance the topset beds resembled planar beds of a flat-bed run. The topset beds are generally composed of ma terial which is finer than the bed material. At first, this appears to be paradoxical since, as can be seen from equation 22, the crestal region represents the region of the flow where the transport capacity of the flow is greatest. The topset material must be selectively deposited from the moving load that passes the crest. The particles with the greatest resistance to motion should be deposited first. Thus, the segregation by the flow, that is deposit of the finer material in the topset beds and transport of the coarse material on to the brink point, indicates that the trend of the resistance to motion with in- creasing sieve size is opposite to that indicated in figure 22. This reverse trend can be predicted by qualitatively adjusting figure 22 using the informa- tion provided in figure 1 and the experimental re- sults presented in table 4. Results of field experi- ments by Rathbun, Kennedy, and Culbertson (1971, p. I43—I45) show that up to a limiting size, the coarser material in a flat-bed flow has greater velocities than the central sizes of the grain dis- tribution. CONCLUSIONS 1. The type of bed configuration appears to be the most important factor affecting local segre- gation of heavy minerals in an open channel flow. Bed configuration, however, is not an independent variable but is dependent on a large number of hydraulic variables, the most important being energy slope, depth of flow, velocity of flow, and the physical properties of the bed material. 2. Three fundamental types of heavy-mineral ac- cumulations were observed in this study. a. Small areas of thin accumulations of opaque heavy minerals that were associated with the stoss side of dunes. They move as thin ripples and commonly originate in the area just downstream from the reattach- ment point. b. Accumulations of opaque-heavy-mineral grains that were associated with the top- set deposits of large dunes. These accu- mulations often formed thick deposits along and adjacent to the crestal area of the dune. Opaque-heavy-mineral segrega- tions were also present within the topset beds, at the surface between the crestline K29 and brinkline, and some formed deposits in the foreset beds. The segregated layers in the foreset beds were probably due to mass transport of heavy minerals from the topset area past the brinkline by strong turbulent motion. c. Accumulations of opaque heavy minerals that were associated with the flat-bed flows. The thickest and most widespread of the flat-bed segregations of heavy min- erals generally occurred at the base of the flat beds, but additional laminations of heavy minerals were present in the flat beds. 3. Among the sediment properties of size, sorting, and shape obtained for opaque heavy minerals from core samples taken from the bed, the only significant variance that occurred be- tween runs 2, 3, and 4 was a difference in the sorting of the opaque-heavy-mineral grains. 4. Theoretical considerations indicate a distinct difference exists in the transport rates of spheres of different densities moving as bed load. The initiation of motion of grains is illustrated by the Shields diagram (fig. 5). Based on the Shields criteria, curves can be developed to show the relationship between critical shear and grain size for materials of different densities. The curves constructed clearly show that the opaque heavy minerals are much more resistant to motion than the light minerals. 5. Theoretical analysis and experimental results illustrate that the size of the particle in trans- port as well as the size of the bed material affects the resistance of a particle to tractive motion. For the particle sizes of interest in this study, it is found that a particle’s resist- ance to tractive motion over a poorly sorted bed material decreases with increasing parti- cle size at least in the size range studied. 6. Fall velocity values for median sizes of opaque- heavy-mineral grains and associated light minerals from laminae adjacent to or Within the opaque-mineral laminae are not correlated. This lack of correlation and the presence of distinct segregated laminae, suggests that fall velocity alone has little or no effect on the local sorting of heavy minerals. REFERENCES Allen, J. R. L., 1968, Current ripples—their relation to pat- terns of water and sediment motion: Amsterdam, North- Holland Publishing Co., 433 p. 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Hydraulic Re- search Cong., 12th, Proc., Fort Collins, Colo. U.S.A., v. 3, p. 185—192. Corey, A. T., 1949, Influence of shape on the fall velocity of sand grains: M.S. thesis, Fort Collins, 0010., Colorado State Univ., 102 p. Daily, J. W., and Harleman, D. R. F., 1966, Fluid dynamics: Reading, Mass., Addison-Wesley Publishing Co., 454 p. Einstein, H. A., 1950, The bed load function for sediment transportation in open channel flows: U.S. Dept. Agri- culture Tech. Bull. 1026, 70 p. Einstein, H. A., and Chien, N., 1953, Transport of sediment mixtures with large ranges of grain sizes: Berkeley, Calif., Univ. California Inst. Engineering Research, 49 p. El-Sammi, E. A., 1949, Hydrodynamic forces on particles in the surface of a stream bed: Ph.D. dissert., Berkeley, Calif. Univ. California. Grigg, N. S., and Rathbun, R. E., 1969, Hydraulic equival- ence of minerals with consideration of the reentrain- ment process, in Geological Survey research 1969; U.S. Geol. Survey Prof. Paper 650—B, p. B77—B80. Guy, H. P., Simons, D. B., and Richardson, E. V., 1966, Sum- mary of alluvial channel data from flume experiments: U.S. Geol. Survey Prof. Paper 462—1, 96 p. Henderson, F. M., 1966, Open channel flow: New York, The MacMillan Co., 522 p. Ippen, A. T., and Verma, R. P., 1955, Motion of particles on bed of a turbulent stream: Am. Soc. Civil Engineers Trans., v. 120, p. 921—939. Kennedy, J. F., 1963, The mechanics of dunes and antidunes in erodible-bed channels: Fluid Mechanics Jour., v. 16, p. 521—544. ' Lane, E. W., 1947, Report of the Subcommittee on Sediment Terminology: American Geophysical Union Trans., v. 28, p. 936—938. McQuivey, R. S., and Keefer, T. N., 1969, The relation of magnetite over ripples in Geological Survey research 1969: U.S. Geol. Survey Prof. Paper 650-D, p. D244— D247. Rathbun, R. E., Kennedy, V. C., and Culbertson, J. K., 1971, Transport and dispersion of fluorescent trace-r particles SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS for the flat-bed condition, Rio Grande Conveyance Chan- nel, near Bernardo, New Mexico: U.S. Geol. Survey Prof. Paper 562—1, 56 p. Raudkivi, A. J., 1967, Loose boundary hydraulics: Oxford, Pergamon Press, 331 p. Richardson, E. V., and McQuivey, R. S., 1968, Measurement of turbulence in water: Am. Soc. Civil Engineers Proc., v. 94, no. HY2, p. 411—430. Rittenhouse, G., 1943, Transportation and deposition of heavy minerals: Geol. Soc. American Bull., v. 54, p. 1725—1780. Rubey, W. W., 1933, The size distribution of heavy minerals within a waterlaid sandstone: Jour. Sed. Petrology, v. 3, p. 3—29. Schultz, E. F., Wilde, R. H., and Albertson, M. L., 1954, In- fluence of shape on the fall velocity of sedimentary par— ticles: U.S. Army Corps of Engineers, Missouri River Div., Sediment Ser., no. 5, 161 p. Sears, F. W., and Zemansky, M. W., 1963, University physics, [3d ed.], pt. 1: Reading, Mass., Addison-Wesley Pub- lishing Co., 548 p. Sheen, S. J., 1964, Turbulence over a sand ripple: M.S. thesis, New Zealand, Univ. Auckland. Shields, A., 1936, Anwendung der Ahnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung: Mitteilungen der Press. Versuch anst. f. Wasserbau u. Schifl‘bau., Berlin, no. 26, 26 p.; Application of similarity principles and turbulence research to bed load move- ment—translated to English by W. P. Ott and J. C. van Uchelen, U.S. Dept. Agriculture, Soil Conservation Service Coop Lab., Calif. Inst. Technology, Pasadena, 21 p. Simons, D. B., and Richardson, E. V., 1963, Forms of bed roughness in alluvial channels: Am. Soc. Civil Engi- neers Trans., v. 128, p. 284—302. 1966, Resistance to flow in alluvial channels: U.S. Geol. Survey Prof. Paper 422—J, 61 p. Simons, D. B., Richardson, E. V., and Nordin, C. F., Jr., 1965a, Forms generated by flow in alluvial channels: Soc. Econ. Paleontologists and Mineralogists Spec. Pub. 12, p. 34—52. 1965b, Bed load equations for ripples and dunes: U.S. Geol. Survey Prof. Paper 462—H, 9 p. Sokal, R. R., and Rohlf, F. J., 1969, Biometry: San Fran- cisco, W. H. Freeman and Co., 776 p. Streeter, V. L., 1966, Fluid Mechanics, 4th ed.: New York, McGraw-Hill Book Co., 705 p. Tourtelot, H. A., 1968, Hydraulic equivalence of grains of quartz and heavier minerals, and implications for the study of placers: U.S. Geol. Survey Prof. Paper 594—F, 13 p. U.S. Inter-Agency Committee on Water Resources, 1957, Some fundamentals of particle size analysis, Report 12 of A study of methods used in measurement and analysis of sediment loads in streams: Washington, U.S. Govt. Printing Oflioe, 55 p. 1958, Operator’s manual 6n the visual-accumula- tion-tube method for sedimentation analysis of sands, Report K of A study of methods used in measurement and analysis of sediment loads in streams: 30 p. Watters, G. Z., and Rao, M. V. P., 1971, Hydrodynamic effects of seepage on bed particles: Am. Soc. Civil Engineers Proc., v. 97, no. HY3, p. 421—439. APPENDIX K32 Symbol A A. Cr CL Ca dn d: F17 Fr F0 F1. as '11:: b?“ R* SEDIMENT TRANSPORT A. SYMBOLS AND NOMENCLATURE Definition Area, such as the cross-sectional area of the flume. Projected area of a sphere. Longest diameter of a grain with three mutually perpendicular axes. Intermediate diameter of a grain with three mutual- ly perpendicular axes. Coefficient of drag for a sediment particle. The coeffi- cient of drag varies with the particle geometry, relation of particle shape to flow, and the Reynolds number of the flow. Coefficient of friction for a sediment particle. The coefficient of friction depends primarily on the nature of the particle surface and the surface of the material with which it is in contact. Coefl'icient of lift for a sediment particle. The coeffi- cient of lift depends on the shape of the particle, relation of particle shape to flow, and the Reynolds number of the flow. Coefficient of static resistance of a sediment particle. The coefficient of static resistance depends on the shape and size of the particle and the arrange- ment, size, and shape of the bed particles. Shortest diameter of a grain with three mutually perpendicular axes. Flow depth. Diameter of a spherical particle. Diameter of spheres making up bed material. Diameter of a sphere resting on the bed. Diameter of a grain—equal to sieve diameter or approximately equal to b diameter of a particle. Hydrodynamic drag force—force exerted by the flow on the particle parallel to the relative motion of the flow. Frictional force—resistance to motion between two bodies in contact. Gravity force. Hydrodynamic lift force-—the force component pro- duced by the flow on a particle that is perpendicu- lar to the direction of the flow and opposite to the gravity force. Resultant force normal to the bed surface. Froude number = (7/ VW—a ratio of inertial forces to gravitational forces. Gravitational constant (980 cm per sec?) . Dune height—vertical distance from trough point to crest point. Ratio dm 170 dB. Dune length—measured from trough of a given dune to trough point of the next dune upstream. Number count of a given size in grain—size analysis. Fluid discharge (cubic meter per sec). Bed-load discharge—weight of sediment carried in bed load per unit width‘per unit of time. Bed-load discharge—volume per unit width per unit time. UD Reynolds number = — —a ratio of inertial forces U to viscous forces for the mean flow. Particle Reynolds number : U d/v—a ratio of in- C IN ALLUVIAL CHANNELS Ci C2-C1“m a 51 <5 QQNQRE as D: To To .‘I Symbol De finit-ion ertial forces to viscous forces relative to a par- ticle. Hydraulic radius a channel would have if the re- sistance to flow were limited to grain roughness (no resistance due to bed-form or streambank roughness). This term can be stated in terms of the average flow depth, D, with corrections for bed-form roughness. Energy slope of the fluid. Time. Fluid velocity. Mean fluid velocity. Shear velocity = \/ To/P. The shear velocity is not a real velocity but is related to the real velocity which would give rise to shear stress To (Hender- son, 1966, p. 412). Velocity of flow at a representative distance from the bed. Relative velocity of flow past a body. Velocity of translation of a particle. Channel width. Distance along bed surface. Elevation of the bed surface. Height above the bed surface. Specific weight of water. Specific weight of a sediment grain. Eddy viscosity that depends on the state of tur- bulent motion. Angle between the bed and horizontal line. Porosity of the bed. Dynamic viscosity of the fluid. a Kinematic viscosity of the fluid : —— —a ratio of p viscosity to mass density. Mass density of water. Mass density of a particle. Geometric standard deviation of a sediment size dso distribution. 1 d3. _ + __ 2 d1. duo Shear stress in the fluid. For turbulent flow dU T = (,u + n) —— dY a: and for laminar flow dU 'r:il.— dY Average shear stress at the bed : 'yDS—force per unit area acting on the bed in the direction of flow. Critical shear stress for sediment particles—the minimum amount of shear stress necessary to start movement of particles at the bed. Dimensionless shear stress (Shields entrainment function) = To (VI-“1) dc Einstein’s intensity of bed-load transport. Einstein’s intensity of shear on a particle. HEAVY-MINERAL SEGREGATION B. GRAIN-MOUNT PREPARATION AND RELATIONSHIP OF DIRECT GRAIN MEASUREMENTS To SIEVE-SIZE EQUIVALENTS Preparation of grain mounts—Grain mounts for size analyses were prepared for the bed-material sample, core samples and many of the suspended- sediment samples studied. Where loose sample grains were used, as they were from the bed-material sam- ple, the sample was reduced by a microsplitter to the desired size. For samples of opaque-heavy— mineral grains and light-mineral grains that were obtained from selected laminations or areas of a grouted core, the material was removed by use of a blunted dissecting needle. Both types of samples were prepared by distributing the grains as evenly as possible onto a petrographic slide that had pre- viously been covered with alcohol. The grains, in settling through the alcohol, oriented themselves with their shortest axis (0 axis) perpendicular to the slide. Measurement of 500 grains for shape factor analysis showed that this orientation oc- curred for 88 percent of the grains. Those grains with the c axis lying parallel to the slide usually had a c axis length very similar to the intermediate axis (b axis) length. When the alcohol evaporated, a residue remained that caused the grains to adhere to the slide. After grain shape studies were made, Lakeside 70 and a cover glass were applied for permanent mounting and grain-size measurement. Sieve-analysis equivalent of direct measurement— Mounted mineral grains were measured directly by use of a petrographic microscope with a calibrated eyepiece that was divided into units of 12.1 microns. For most samples, intermediate axes (b axis) were measured in units of 200 grains per slide. Where more than 200 measurements were used for a given sample, additional slides were made. If an abundance of material was available, as it was for the bed-material sample, grains were se- lected by an equal-interval point—count method. A pattern of evenly spaced intervals was made by use of a modified stage micrometer mounted on the microscope. If a grain was present under the stage stop, that grain was measured. A stage interval was selected that was large enough to prevent repetition of individual grain measurements. Slides made from samples with limited amounts of material (samples from grouted cores) were analyzed by a line-measurement technique. In the line method, horizontal traverses were made over K33 the slide at equal intervals and the b axis was measured for each grain of the particular mineral being studied that the line crossed. The probability that a grain will be measured by the point method is in direct proportion to its pro- jected area on the slide, and the probability that a grain will be “hit” by the line method is in direct proportion to its diameter as measured perpendicu- lar to the traverse line. Neither of these ‘methods, however, allows for differences in the thickness of the grains perpendicular to the slide. Opaque heavy minerals and light minerals were studied separately, and both groups had mean shape factors (appendix C) of near equant shape (0.68— 0.75 shape factor); therefore, a relation between measured size and sieve equivalence was determined. In order to make the direct measurements equiva- lent to the size equivalents determined by sieving, a common measuring factor was used. The best common standard for such a relation was the nomi- nal grain diameter defined as the diameter of a sphere that has the same volume as the particle (Lane, 1947, p. 937). The U.S. Inter-Agency Com- mittee on Water Resources (1957, p. 31, 33—35) developed graphs from extensive studies that show the relation of the intermediate axes of grains to their nominal diameters and the sieve-size equiva- lents of grains to their nominal diameters for vari- ous shape factors. Based on the graphs of the U.S. Inter-Agency Committee on Water Resources (1957, figs. 4, 5), the sieve diameter equivalent of the grains is 0.85 times the value of the direct inter- mediate axis measurement (using a shape factor of 0.7) for the grain sizes in this study. Besides adjustments to convert b axis to sieve- size measurement, other factors had to be consid- ered in conversion of direct measurement to the weight frequencies of a sieve analysis; these factors include adjusting for different grain thicknesses and assuring that a certain size grain occurred in the measurement in its correct proportion relative to the total grain-size population. Differences in grain thicknesses were corrected by multiplying the b size frequency count by the b-axis diameter. To compute a weight frequency distribution from di- rect measurement, the following manipulations of the direct b-axis measurements were made. 1. For the line method, the size frequency was de— termined by taking the percentage of each size from the sum of the sizes determined by 272192, where n is the b-axis frequency and b is the b-axis size. 2. For the point-count method, the size frequency K34 SEDIMENT TRANS-PORT was determined by taking the percentage of each size from the sum of the sizes determined by Enb. Cumulative curves were plotted with the weighted percentages as the ordinate and with the b-axis values multiplied by 0.85, the correction factor, on the abscissa. A check of the 0.85 conversion factor was made by using the bed-material sample. The results showed close agreement to a sieve analysis of the same material except on the large-grain-size end (fig. 9). Direct measurement of the b axis of 1,000 grains showed a weighted median value of 0.338 mm and a sorting (a) of 1.56. A sieved sample of the same bed material gave a median value of 0.285 mm and a sorting of 1.58. The sorting values of the sieved sample and of the weighted direct measurements were similar. Applying the correc- tion factor of 0.85 to the median diameter of 0.338 mm determined by direct measurement gives a cor- rected value of 0.289 mm, which is in good agree- ment with the median diameter of 0.285 mm deter- mined from sieve data. Values stated in the text of this study for a given grain-size measurement are the sieve-size equivalent values determined by the method just described and by the use of 0.85 as the size conversion factor. C. ANALYSES OF OPAQUE-HEAVY-MINERAL GRAINS AND LIGHT-MINERAL GRAINS FROM CORE SAMPLES (RUNS 2—4) Data on size and sorting shown for each of the samples in tables 5 and 6 were determined from direct measurement of 200 individual grains using techniques described in appendix B. The bed- material size analyses, however, were based on 1,000 measurements. Twenty grain measurements per sample were made for determination of mean shape factor. The shape factor used in this report was originally de- fined by Corey (1949) as C S.F. _ ‘/ab for three mutually perpendicular axes of the grains, where IN ALLUVIAL CHANNELS a = maximum diameter of the grain, b = intermediate diameter of the grain, and c = smallest diameter of the grain. One advantage in the use of the Corey shape factor over other shape factors is the extensive experimental data available on sediment analysis by Schultz, Wilde, and Albertson (1954) and a sum- marization by the U.S. Inter—Agency Committee on Water Resources (1957) of the work in which the Corey shape factor was used. Discussion of the (Text continues on p. 37.) FIGURE 24.—Sections of core samples showing opaque-heavy- mineral beds. A, Run 2—topset beds (sample B—47—X was obtained from a crestal accumulation); B, Run 2—foreset beds; C, Run 3—topset beds; D, Run 3—foreset beds (sam- ple B—48—B) and flat bed area (samples B—48—3, 10, and 12) ; E, Run 4—within the flat bed deposits; F, Run 4—at the base of the flat beds. HEAVY-MINERAL SEGREGATION K35 TABLE 5.—Size analyses of opaque heavy minerals from core samples Median Sample (150 die Sorting Shape Description of location in bed1 (mm) (mm) (mm) (a) factor Representative sample of bed material Bed Material _____ 0.144 0.099 0.220 1.49 0.684 Run 2 B—47—B—1 ________ 0.140 0.098 0.180 1.36 0.735 Foreset, 2—mm dark-mineral streak with interspersed light- density minerals (sta. 86, 1.06 m right of centerline). B—47—X—1 ________ .133 .104 .158 1.23 .747 Topset, 7-mm dark-mineral zone near surface (sta. 176, 1.00 m left of centerline). B—47—36—1 ________ .105 .083 .150 1.34 .715 Topset, dark-mineral zone (0.5 mm), 3 mm below the sur- face (sta. 100, 0.61 m right of centerline). B—47—37—1 ________ .115 .081 .155 1.39 .711 Topset, dark—mineral zone (1 mm), 1.5 mm below the sur- face (sta. 96, 0.61 m left of centerline). B—47—46—1 ________ .132 .103 .162 1.25 .711 Brink point, dark-mineral zone (1 mm), 4.5 mm below the surface (sta. 85, 0.61 m left of centerline) . B—47~46—2 ________ .140 .107 .176 1.28 .718 Foreset, downstream from B—47—46—1, same dark-mineral streak but with light-density minerals interspersed (sta. 85, 0.61 m left of centerline). B—47—47—1 ________ .112 .087 .138 1.26 .698 Topset, dark-mineral zone (3 mm), 5 mm below the sur- face (sta. 85, on centerline). Average ____ .125 .095 .160 1.30 .719 Run 3 B—48—A—1 ________ .126 .101 .154 1.23 .754 Topset, thickest laminae in zone, 1.5 mm thick of several thin dark-mineral laminations; 5 mm from surface (sta. 98, 1.07 m right of centerline). B~48—B—1 ________ .154 .102 .198 1.40 .744 Topset (near brink point), dark-mineral zone (1 mm) at base of topset 3 mm from surface (sta. 114, 0.79 m left of centerline). B—48—B—2 ________ .150 .115 .192 1.29 .769 Foreset, 2-mm dark-mineral zone with interspersed light- density minerals (sta. 114.2, 0.79 m left of centerline). B—48—10—1 ________ .087 .063 .111 1.33 .724 Flat Bed, dark-mineral zone (0.5 mm) 35 mm from the surface (sta. 18, 0.61 m left of centerline). B~48—37—1 ________ .124 .099 .161 1.28 .721 Topset, thick dark-mineral zone (4 mm) at the surface (sta. 94, 0.61 m left of centerline) . B—48—40—1 ________ .122 .088 .154 1.32 .723 Topset, uppermost dark-mineral laminae (0.5 mm) in dark-mineral zone 17 mm from surface (sta. 90, 0.61 In left of centerline) . B—48—52—1 ________ .110 .082 .145 1.33 .751 Topset, dark-mineral zone (0.5—1 mm) 4 mm below the surface (sta. 74, 0.61 m left of centerline). Average ____ .125 .093 .159 1.31 .741 Run 4 B—46—5—1 _________ .144 .102 .218 1.46 .744 Dark-mineral zone (1.5 mm) at base of flat-bed sands, 6 mm from surface (sta. 176, on centerline) . B—46—12—1 ________ .100 .076 .120 1.26 .715 Dark-mineral zone (1 mm) at base of flat-lying sand, 8 mm from surface (sta. 168, 0.61 m right of centerline). B—46—20—1 ________ .135 .095 .173 1.35 .693 Dark-mineral zone (0.5 mm) interbedded with light-den- sity, fiat-lying sand, 11 mm from surface (sta. 110, on centerline). B—46—20—2 ________ .103 .070 .150 1.47 .748 Mixed dark-mineral and light-density minerals zone (1.5 mm) just below sample B—46—20—1. Taken 20 mm above base of flat-bed sand (sta. 110, on centerline). B—46—26—1 ________ .147 .095 .201 1.46 .758 Dark-mineral zone (1 mm) 6.5 mm from surface, overlain and underlain by light-density sand, 22 mm above base of flat-bedded material (sta. 102, on centerline). B—46—52—1 ________ .150 .082 .205 1.59 .781 Zone of dark minerals with interspersed light-density minerals (1 mm), 16 mm below surface, 35 mm above base of flat-bedded sands (sta. 130, on centerline). K36 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS TABLE 5,—Size analyses of opaque heavy minerals from core samples—Continued Median Sample dso die (is; Sorting Shape Description of location in bed1 (mm) (mm) (mm) (a) factor Run 4—Continued B—46—55—1 ________ .135 .086 .173 1.43 .757 Dark-mineral zone with interbedded light-density grains (zone is 2.5 mm thick) at. base of flat-bedded material, 15 mm from surface (sta. 155, on centerline). Average _..__ .131 .087 .177 1.43 .742 Runs 2—4 Average ____ .127 .091 .165 1.35 .735 1Stations along the flume are designated in feet (1 ft = 0.3048 m) downstream from the headbox. (Example: the distance between sta. 100 and 51:3. 110 is 10 ft (3.05 m).) TABLE 6.—Size analyses of light minerals associated with opaque heavy minerals in the core sample Median dso the (134 Sorting Description of location in bed1 Sample (mm) (mm) (mm) (a) Representative sample of bed material Bed material _____ 0.287 0.190 0.462 1.56 Run 2 B—47—B—2 ________ 0.201 0.150 0.247 1.29 Foreset, light—mineral zone (2 mm) underlying dark-mineral zone sample in B—47—B—1 (sta. 86, 1.06 m right of centerline). B—47-X—2 ________ .219 .155 .276 1.33 Topset, light-mineral zone (1.5 mm) underlying dark-mineral zone sampled in B—47—X—1 (sta. 176, 1.00 m left of centerline). B—47—36—2 ________ .176 .131 .244 1.37 Topset, light-mineral zone (2 mm) overlying dark-mineral zone sampled in B—47—36—1 (sta. 100, 0.61 m right of centerline). B—47—36—3 _______ .167 .121 .229 1.38 Topset, light-mineral zone (2 mm) underlying the dark-mineral zone sampled in B—47—36—1 (sta. 100, 0.61 m right of centerline). B—47—37—2 ________ .180 .136 .248 1.35 Topset, light-mineral zone (1.5 mm) underlying dark zone sampled in B—47—37—1 (sta. 96, 0.61 m left of centerline). B—47—46—2 ________ .222 .150 .315 1.45 Foreset below brink point, light-density grains within the dark- lminfral zone sampled in B—47—46—2 (sta. 85, 0.61 m left of center- me . B—47—46—3 ________ .236 .168 .349 1.44 Brink point, light-mineral zone (2 mm) overlying the dark-mineral ‘ zone sampled in B—47—46—2 (sta. 85, 0.61 m left of centerline). B-47-47—2 _______ .188 .138 .268 1.39 Topset, light-mineral zone (2 mm) overlying dark-mineral zone sampled in B-47—47—1 (sta. 85, on centerline). B—47—47—3 ________ .207 .150 .266 1.33 Topset (low angle), light-mineral zone (2 mm) underlying dark- mineral zone sampled in B—47—47—1 (sta. 85, on centerline). Average ____ .200 .144 .271 1.37 Run 3 B—48—A—2 ________ 0.236 0.170 0.309 1.35 Topset, light-mineral zone (2 mm) underlying the dark-mineral zone sampled in B—48—A—1 (sta. 98, 1.07 m right of centerline). B—48—B—2 ________ .254 .183 .343 1.37 Foreset, light-density minerals from within the zone where dark minerals were sampled in B—48—B—2 (sta. 114, 0.79 m left ofi centerlin‘e) . B—48—B—3 ________ .290 196 .388 1-41 Foreset, light-mineral zone (2 mm) overlying the dark mineral foreset in B—48—B—2 (sta. 114, 0.79 m left of centerline) . B—4S—B-4 ———————— 212 ~151 280 1'35 Topset (near brink point), light-mineral zone (1.5 mm) overlying the dark-mineral zone sampled in B-48—B—1 (sta. 114, 0.79 m left of centerline). HEAVY-MINERAL SEGREGATION K37 TABLE 6.——Size analyses of light minerals associated with opaque heavy minerals in the core sample—Continued Median dao dm (154 Sorting Description of location in bed1 Sample (mm) (mm) (mm) (0) Run 3—Continued B-48—10—2 ________ .243 .173 .305 1.33 Flat Bed, light-mineral zone (2 mm) overlying dark-mineral zone sampled in B—48—10—1 (sta. 18, 0.61 m left of centerline). B—48—37—2 ________ .199 .155 .260 1.30 Topset, light-mineral zone (2 mm) underlying dark-mineral zone sampled in B—48—37—1 (sta. 94, 0.61 m left of centerline). . B—48—40—2 ________ .232 .159 .299 1.37 Topset, light-mineral zone (2 mm) overlying the dark-mineral zone sampled in B—48—40—1 (sta. 90, 0.61 m left of centerllne). B—48—52—2 ________ .200 .141 .332 1.54 Topset, light-mineral zone (2 mm) overlying the dark-mineral zone sampled in B—48—52—1 (sta. 74, 0.61 m left of centerline). B—48-52—3 ________ .220 .169 .285 1.30 Topset, light-mineral zone (2 mm) underlying the dark-mineral zone sampled in B—48—52—1 (sta. 74, 0.61 m left of centerllne). Average __.._ .232 .166 .311 1.37 Run 4 B—46—5—2 _________ 0.258 0.167 0.360 1.47 Light-mineral zone (2 mm) overlying the dark-mineral zone sam- pled in B—46—5—1 (sta. 176, on centerline). B—46—12—2 ________ .218 .162 .285 1.33 Light-mineral zone (2 mm) overlying the dark—mineral zone sam- pled in B—46—12—1 (sta. 168, 0.61 m right of centerline). B—46—20—2 ________ .201 .134 .286 1.46 Light—density minerals within dark-mineral zone sampled in B—46— 20—2 (sta. 110, on centerline). B—46—52—1 ________ .218 .152 .301 1.40 Light-minerals directly overlying and within the dark-mineral zone sampled in B-46—52—1 (sta. 130, on centerline). B—46—55—1 ________ .227 .136 .362 1.63 Light-mineral zone within the zone where dark minerals were sam- pled (B—46—55—1). Light minerals separating the very thin dark- mineral laminations (sta. 155, on centerline) . Average __-_ .224 .150 .319 1.46 Runs 2-4 Average ____ 0.218 0.154 0.297 1.40 1Stations along the flume are expressed in feet (0.3048 m) in a downstream direction. Corey shape factor’s relation to other shape factors is presented by Tourtelot (1968, p. F4-F7). Measurements of the shape factor determined for the bed-material sample of opaque heavy minerals and of light minerals were each based on 60 shape factor measurements, 20 measurements on each of three grain mount slides. For identifying the numbers in tables 5 and 6, the following criteria should be used: B — 47 — B — 1 (1) (2) (3) (4) 1. The “B” refers to a “bed” sample as opposed to a “S” for suspended sample (appendix D). 2. The “47” refers to a continuous fl‘ume experiment series run number. The following numbers are the designated run numbers for this study: 45 = Run 1 47 = Run 2 48 Run 3 46 Run 4 3. The “B” used in the example is a selected core sample. All letters in the third position desig- nate selected samples, while numbers indi- cate core samples obtained in the established sample network. Numbers and letters used are usually consecutive except for “X” used in run 2. 4. The “1” in the fourth position designates the grain mount number made from the particu- lar core sample. ll Examples of horizontal core samples obtained from the bed including the cores from which the bed sample of light mineral and opaque heavy mineral grains were obtained are shown in figure 24. (See p. 34.) K38 SEDIMENT TRANSPORT IN ALL-UVIAL CHANNELS D. SEDIMENT CONCENTRATION AND SIZE ANALYSES OF SUSPENDED-SEDIMENT SAMPLES TABLE 7.—Size analyses and concentration of suspended-sediment samples Size 1 Height Concentration Sorting Run Location above bed (mg/1) dso dm du (47) (cm) (mm) (mm) (mm) 1 ______ Trough _____________ 33.6 122 0.146 0.116 0.184 1.26 18.3 236 .186 .154 .225 1.21 9.2 475 .172 .132 .215 1.28 3.1 501 .172 .134 .217 1.28 Brink point _________ 24.4 66 .158 .127 .200 1.25 18.3 130 .143 .108 .179 1.25 9.2 117 .148 .116 .187 1.27 3.1 290 .165 .128 .212 1.29 Stoss side __________ 18.3 291 .174 .140 .207 1.22 9.2 234 .174 .140 .216 1.24 3.1 343 .177 .146 .224 1.24 2 ______ Trough _____________ 42.7 458 .138 .104 .172 1.29 30.5 2304 .187 .146 .230 1.26 24.4 1554 .173 .123 .209 1.31 9.2 2022 .186 .128 .244 1.38 Brink point _________ 36.6 176 .127 .092 .157 1.31 18.3 256 .138 .101 .184 1.35 12.2 345 .140 .103 .183 1.33 3.1 551 .145 .110 .184 1.29 Stoss side __________ 33.6 391 .140 .107 .176 1.28 21.4 513 .157 .116 .205 1.33 9.2 569 .146 .107 .190 1.33 3.1 763 .150 .120 .188 1.25 3 ______ Stoss side ___________ 33.6 59 .130 .102 .165 1.27 18.3 328 .155 .117 .212 1.35 9.2 279 .144 .112 .184 1.28 3.1 618 .146 .115 .184 1.26 Flat bed ____________ 27.5 25 .116 .090 .159 1.33 21.4 39 .119 .096 .150 1.25 12.2 218 .134 .105 .160 1.24 7.6 974 .172 .133 .220 1.29 4 ______ Flat bed ____________ 33.6 512 .123 .088 .156 1.33 21.4 940 .136 .099 .168 1.30 9.2 2103 .151 .110 .195 1.33 3.1 6477 .183 .133 .226 1.31 1 Size determined by VA-tube sedimentation analysis.