DEPARTMENT OF THE ARMY CORPS OF ENGINEERS BEACH EROSION BOARD OFFICE OF THE CHIEF OF ENGINEERS LABORATORY STUDY OF THE GENERATION OF WIND WAVES IN SHALLOW WATER TECHNICAL MEMORANDUM NO. 72 T-arig rinmi mL m- vir ,1 I t X B ILLINOIS GEOLOGICAL SUi. VE < /_,_ R v ^ FEB 20 1972 9 LABORATORY STUDY OF THE GENERATION OF WIND WAVES IN SHALLOW WATER TECHNICAL MEMORANDUM NO. 72 BEACH EROSION BOARD CORPS OF ENGINEERS MARCH 1955 FOREWORD The prediction of wave characteristics in shallow water is of great importance along much of the Gulf Coast of the United States, as well as for many inland water areas (as Lake Okeechobee, Florida). This has been difficult in the past as the effect of the shallow bottom is considerable, particularly in reducing the wave height from what would be expected by use of the deep water wave prediction methods. This report gives the results of some laboratory studies of wave generation in shallow water in a small enclosed wind-wave tank. This report was prepared at the University of California in Berkeley in pursuance of contract DA-U9-05>5-eng-31 with the Beach Erosion Board which provides in part for research and investigation on wave generation in shallow water. The author, Osvald Sibul, is a Research Engineer at that institution working primarily in the Wave Research Laboratory. The work done on this study was supported jointly by the Jacksonville District, Corps of Engineers, and the Beach Erosion Board. The funds were allotted from the Civil Works Investigation Program of the Office, Chief of Engineers under projects CW 166 and CW 167, "Study of Waves and Wind Tides in Shallow Water". Views and conclusions stated in this report are not necessarily those of the Beach Erosion Board. This report is published under authority of Public Law 166, 79th Congress, approved July 31 , 19U5>. TABLE OF CONTENTS Page No , Abstract . 1 Introduction . 1 Definitions . 3 Laboratory Equipment and Procedure . i; Procedure . b Evaluation of the Data . 7 Results and Discussion . lb Wave Heights . lb Wave Periods in Shallow Water . 20 Wave Statistics. 25 Conclusions . 33 Acknowledgments . 3b References . 3b Digitized by the Internet Archive in 2019 with funding from University of Illinois Urbana-Champaign Alternates https://archive.org/details/laboratorystudyoOOsibu LABORATORY STUDY OF THE GENERATION OF WIND WAVES IN SHALLOW WATER by Osvald Sibul University of California ABSTRACT Wind waves in shallow water were studied in a laboratory channel. The experiments were conducted with smooth and rough bottom conditions, and with strips of cheese cloth in the channel to simulate the rough¬ ness effects of vegetation in nature. The data indicate that the Sverdrup-Munk-Bretschneider curves may be used to predict the wave heights and periods for relatively deep water. In shallow water the wave heights may be considerably lower than predicted by the curves, depending upon the relative depth of water. The experiments indicate that the depth starts to affect the wave heights at approximately d/H 0 < The wave periods are also affected by the depth, but not as much as are the wave heights. The reduction in period can be noticed when d/L 0 < 0.2; the period continues to decrease with decreasing depth. Further, it was found that the maximum wave height for a group of 100 waves is 1.34 times that of the significant wave height and 1.93 times that of mean wave height, H mean *» The a verage period of the significant waves (T^q/ 3 ) and the maximum waves (T^ m ax ) was found to be of the same magnitude and equal to 1.10 times tne mean wave period T mean . The maximum wave period almost never coincided with the maximum wave height. The maximum wave period T maX was found to be 1.2£ times that of significant wave period T^/ 3 , and 1.42 times that of mean wave period, T mean . INTRODUCTION When the wind is blowing over the water surface it generates waves, the heights and periods of which are a function of wind intensity and duration, fetch, and water depth. The characteristics of the ocean or of lake surfaces are of interest to those concerned with the problems of coastal engineering or shipping. Some of these problems are: design of harbors and shore protection works such as levees, dams, and break¬ waters; loading and unloading of ships; and the operation of seaplanes. During the past half century, data on wind waves have been taken by several observers and under a great variety of conditions. Many of these data were obtained from visual observations with the wind speeds being estimated either from scattered observations or from weather maps. Sverdrup and Munk(l)* developed in the early "40’s" (published 19b?) a semi-empirical theory relating the wave heights, periods, and steepnesses to the intensity and duration of the wind and the length of the fetch. •a-Numbers in parentheses refer to references on pages 34 and 35* In their treatment several numerical coefficients were obtained from observations of wind and waves at sea. The data were insufficient to check the theory for a wide range of conditions. Since these results were published, many new data have been made available. These include laboratory investigations by Flinsch(2) and Johnson and Rice(3) i n the United States; and Francis(^) in England. Field measurements have been made by Johnson (5,6) on relatively small bodies of water with limited fetches at both Clear Lake, California and Abbotts Lagoon, California. The new data, as well as the original data of Sverdrup and Munk were analyzed by Bretschneiderw ) and the curves revised to fit all the available data. The scatter of the data is considerable. The Sverdrup-Munk-Bretschneider curves give satisfactory results for deep water. For shallow water there exists an additional variable, the depth of water, which limits the maximum wave height and period and is expected to alter also the statistical distribution of wave heights and periods. Observations indicate that the wave heights are smaller in shallow water than under similar deep water conditions, but insofar as it is known, there were no comprehensive laboratory studies available for the characteristics of waves in shallow water although Keulegan has gathered considerable, as yet unpublished, laboratory data at the Bureau of Standards. The primary concern of this study was to investigate wind-tides and the characteristics of wind-generated waves in shallow water. The experiments were made with several water depths, each combined with five different wind velocities. To investigate the bottom roughness effect, the experiments were made in three sets: (a) smooth bottom, (b) rough bottom, and (c) rough bottom and strips of cheese-cloth in a channel to simulate the roughness effects of vegetation in nature. Besides the comprehensive wave measurements, the position of the mean water level and the vertical wind velocity distribution, measured by the use of a Pitot tube, were obtained for each run. All of the re¬ sults concerning the wave characteristics are given in this report; the rest of the data, such as the water-surface roughness and the wind setup are presented in separate reports (8,9). 2 DEFINITIONS The definitions used in this report are as followsj C d d ( F 6 ^maan H l/3 ^■max h ^mean 1*1/3 I*max “o WTL SWL ^iiiean T l/3 T ■“•max T H ■Tie an T Hl/3 T Hmax t wave velocity C = L/T,in ft/sec. still-water depth (bottom to SWL),in ft. the depth of water at the location the wave measurements were made (bottom to MWL),in ft. the fetch, defined as the distance parallel to the Wind direction measured from the equilibrium shoreline,(when the body of water is under wind action) to the point wave measurements were made,in ft. thfe acceleration of gravity ( g = 32.17 ft/sec 2 ). the mean wave height, defined as the arithmetic average of qll the waves in a group of 100 waves. 'Aie single wave height is defined as the vertical distance between crest and preceding trough,in feet. the significant wave height - the arithmetic average of the highest one- third of the waves,in feet. the maximum wave height of a group of 100 waves,in feet. the wind setup, the vertical distance between SWL and MWL,in feet. the average wave length for a group of 100 waves. Wave length is the horizontal distance between successive wave crests measured perpendicular to the crest, in feet. the average length of the longest one-third of the waves, the maximum wave length of a group of 100 waves. the subscript "o" refers to the deep water conditions (such as H 0 , L 0 , T 0 , when d/L>0.5). the mean water level. the still-water level; the surface of the water if all wave and wind action were to cease. the average of all the wave periods of a group of 100 waves. the average of the longest one-third of the periods in a group of 100 waves. the longest period in a group of 100 waves. the average wave period to the mean wave height (T^ = ^mean) the average period of the highest one-third of the waves T1/3) the period of the highest wave in a group of 100 waves (Tg^ < T max ). duration of wind in seconds. the average wind velocity (ft/sec), defined as the total discharge of air per second divided by the area between MWL and the top of the channel. 3 LABORATORY EQUIPMENT AND PROCEDURE Experiments were performed in a channel 1.0 foot wide, 60 feet long and 1.28 feet deep as shown in Figure 2a. The channel was constructed of wood, with one side made of plate-glass for observation purposes. The wind was generated by a blower mounted at one end of the channel, driven by an A.C. motor. The wind velocities could be varied from zero to approximately $0 ft/sec. by varying the air intake area at the blower. To straighten the wind flow upon entering the channel, a honey-comb was set between the blower and the channel. To guide the wind gradually on and off the water surface, a sloping beach (slope approximately i;i0) was set at the beginning and the end of the channel, as shown in Figure ?a. The downwind (leeward) beach served also to make the waves break and dissipate their energy and reduce the effect of wave reflections. The discharge of air was measured by a Venturi meter mounted as shown in Figure 2a. This Venturi meter was used to obtain approximately the desired wind velocity. Final wind velocity measurements were made, however, by using a Pitot tube mounted on a point gage. The wave heights and periods were measured at four locations, as indicated in Figure 2a, by double-wire resistance elements connected to Brush recorders. A sample wave record is given in Figure 3. Piezometer openings were installed on the top and the bottom of the channel at five locations along the centerline. The piezometer open¬ ings were connected to micro-manometers as shown in Figure 2b. This arrangement was made so that the nanometers could be read against the inside pressure (the actual MWL) and against the atmospheric pressure. The difference between these two readings indicated the inside pressure, and therefore the pressure drop between successive manometers could be determined and corrections applied where necessary. To check this latter measurement, three draft gages were connected to the piezometer openings on the top of the channel at the locations of manometers 1, 3, and as shown in Figure 2a. Pressure readings were made simultaneously with those of the manometers. These two always agreed very closely. Any difference indicated a faulty connection or a clogging of the piezometer openings and corrections could be made at once. Procedure The desired wind velocity was obtained by adjusting the air inlet of the blower to proper size. The blower then was shut off and the ends of the channel were closed so that no draft could occur along the channel. When the water surface had calmed completely, the SWL was determined at the location of each of the five manometers. Then the blower was started and the wave recorder started at once, so that the initial generation of waves and the gradual change of water surface elevation under wind action could be studied. Zero time was considered 4 c 4> E Q> o c o 4 - t/> v> a> .. d) CD *- cr> j o * cr> qj 3 o o $ Q a> .a 3 tn O QC o 5 FIGURE 2 • GENERAL LABORATORY SET-UP FOR STUDY OF WIND WAVES IN SHALLOW WATER to be the moment the blower was started and was marked accordingly on the surface elevation-time history records. The initial record was taken from zero to two minutes, the following record in intervals at: 5 min,, 10 min., l£ min., 30 min., and the last after 1 hour from the beginning of the experiment. The length of each interval was at least the time necessary for 100 waves to pass a fixed point, but was usually somewhat longer. The wind velocities were measured at three different locations along the centerline of the channel (PI, Pi*, and P$a in Figure 2a), Observations indicated a slight increase in velocity towards the leeward end of the channel. The increase was due to the set-up of the MWL and to increased wave heights at the end of the channel which reduced the wind passage area. This phenomenon was the most pronounced for deep water depths. However, the difference in average wind velocities at the opposite channel ends never exceeded 5> or6 per cent and the average for the channel was always very closely represented by the average velocity at Pi*. For shallower water depths and lower wind velocities it was found that the average velocities were almost unchanged along the centerline of the channel. As a conclusion of this investiga¬ tion the velocity profiles in later experiments were obtained only at Pi*, which meant a considerable saving in time. For each run a continuous wind velocity profile between the wave crests and the top of the channel was observed. When the surface elevation-time records indicated that the equilibrium condition between the wind and gravitational forces were reached, the position of MWL was measured by the use of micro¬ manometers at locations as indicated in Figure 2a. The wave motion was damped in the line to the micro-manometer so that the reading was the MWL directly. Additional measurements made for each run included the horizontal retreat of windward shore line and advance of leeward shore line under wind action, the distance from windward shore to the first ripples on the water surface, the barometric pressure, and the dry-and wet-bulb temperatures of a sling psychrometer. The barometric pressure did not show any appreciable changes during a set of experiments. The range of pressures for all the experiments during the seven months period was between 29.876 and 30.59L inches of mercury with an average value very close to 30.000 inches. The sling psychrometer measurements were taken outside the channel just before the air entered the channel. The computed unit weight of the air did not undergo any appreciable changes. The average value was approximately 0.076 lb/ft^ with a range between 0.071*2 and 0.0781* lb/ft3 for the seven-month test period. The complete data is given in Reference 9, Table I,under the proper run numbers. The fetch F was measured from the windward shore line to the point where the waves were measured, as indicated in Figure 1. To study the effect of bottom roughness, the experiments were made with: (a) a smooth bottom with seven different still-water depths, (b) a rough bottom (bed roughened by means of expanded metal lath) with five different still-water depths, and ( c) a rough bottom and strips of cheese cloth in the channel at 1-foot intervals to simulate the roughness effects of vegetation in nature. This bottom condition was combined with four different still-water depths. 6 EVALUATION O F THE DATA A sample wave record is shown in Figure 3* First it was decided to evaluate the mean, significant, and maximum wave heights and periods as a function of wind duration, t. Difficulties arose, however, in selecting the proper wave groups to be analyzed. The characteristics of the waves under laboratory conditions change very rapidly during the first few minutes of the experiment, and so the standard group of 100 waves could not be considered for, say, t = 10 ; 20 ; 30 etc. seconds. To get at least some estimate of the wave characteristics, groups of l£ waves were analyzed, and the time when the center of the group passed the point of measurement was taken as the representative time for the whole group. A sample of such data is given in Figure k for the wave heights. Scatter was usually considerable, especially for small values of t where the length of the evaluated wave groups was the shortest and the changes in wave characteristics the most drastic. For larger t values, longer wave groups could be evaluated and the results scattered less than with the shorter groups. Using the method as just described to analyze the data for various water depths and wind velocities, it was establ ished that the waves obtained a more or less constant characteristic for t > l£ minutes. It was decided, therefore, to analyze only this portion of the data for the remaining experiments where the duration of the wind was long enough to allow an equilibrium condition to be established between the wind intensity, mean water-surface, and the waves. The data given in this report, therefore, pertain to a wind duration of at least one-half hour and a wave group of 100 waves, unless otherwise stated. The group of 100 waves in the laboratory compares favorably with the data obtained in the ocean from a continuous 20 -minute wave record. On the Pacific Coast of the United States, the average wave period is approximately 12 seconds, hence a 20 -minute record contains about 100 waves. On the Atlantic Coast and the Great Lakes, the average period of the waves may be considerably shorter and so the 20 -minute record may include 1*00 or more waves. Hence, to standardize the method of evaluation, it seems to be reasonable to use always a certain number of waves rather than a specified time interval. The group of 100 waves was chosen so as to be a fair representative of the total record, including both high and low waves. A wave was de¬ fined as that condition where a definite crest and trough occurred, re¬ gardless of its height or length. All the single crests in a given group were numbered from 0 to 99 and the wave heights and periods measured as shown in Figure 3 and tabulated in Table I. The mean wave height, ^mean ,anc * P er i°dj T raean , were found as the arithmetic average of the group. Next,the 33 highest waves in the group were marked and the arithmetic averages found for these waves. These values were called the significant wave height, and the period corresponding to this significant wave height, THi/ 3 . H max was the highest wave present in the given group and and Tp max the period corresponding to the maximum wave height. The wave periods also were considered individually by selecting the 33 longest 7 8 FIGURE 3 TIME HISTORY FOR SURFACE ELEVATION AT FOUR POINTS ALONG & OF CHANNEL SAMPLE OF RUN 102 «/> ■O c 8 V CO 9 FIGURE 4 • WAVE HEIGHT AS A FUNCTION OF WIND DURATION TABLE I WIND WAVE MEASUREMENTS IN THE LABORATORY WAVE CHANNEL OEPTH AVERAGE WINO VELOCITY FETCH WAVE HEIGHT WAVE PERIOD AND^SIGfPw )DS FOR MAX. ftVE HEIGHTS Ji_ ■ HORIZONTAL HORIZONTAL DI9TANCE RUN BOTTOM Of WATER F MEAN SIGN MAX MEAN SIGN. MAX ii H. M l T # WINDWARD LEEWARO SHORE TO FIRST NO. ROUGHN <9 (ft) u« ( ft./MC ) (ft) Hmeoo (ft) Hi (ft) HfTWK (ft) ^m*on (••c.) Tx (»tc) ImO T H l/^lSEC) h max. (ft.) H. H. (*fC) T. ■a SHORELINE (ft.) SHORELINE (ft.) RIPPLES (ft) 1 C 3 4 0 e 7 6 9 10 ll 12 13 14 15 16 17 18 19 20 21 22 23 It • mooth 0.370 10.05 12 85 VERY SM A L 0 370 22.72 0.005 0 009 0017 0 15 0.19 0 22 0. 1 8 0 20 7.27 0.024 0.370 15.416 0.370 35 38 0.020 0.026 0 032 0.21 0.25 0.30 0.23 0.23 11 32 0.030 0 868 12.333 0 32 0 78 0 708 0,370 48 25 0.030 0 031 0.038 0 28 0 34 0.48 0.29 0.30 15 44 0 034 0.910 10.880 0 35 0.97 0 592 13 • 0 370 14.10 13 02 0.003 0 006 0.010 0 12 0 17 0 20 0.14 0.1 8 2 00 0.028 0 214 13.214 0 370 22 89 0.017 0.039 0 049 0 22 0.27 0 35 0.24 0.28 3 66 0035 1 114 10.571 0.370 35.55 0 042 0.057 0.075 0.31 0.36 0 42 0.32 0.30 5 69 0.043 1 325 0 604 0 37 0 97 0 520 0 370 48 42 0.044 0 068 0.090 0.37 0 46 0 55 0.39 0.36 7.75 0.049 1 390 7 551 0 40 1 .15 0 451 14 0.370 19.25 13.03 0.011 0 019 0.023 0 19 0.24 0 30 0.21 0.23 1.13 0.039 0 487 9 487 0.370 22 92 0.038 0.061 0 090 0 29 0 36 0.50 0.30 0.32 1 99 0 051 1 196 7 254 0.370 3538 0.060 0.088 0.124 0.37 0.43 0 50 0.38 0.40 3.09 0.061 1 442 6 065 0.44 0.97 0.372 0.375 48.45 0.038 0.083 0.1 10 0.44 0.53 0.70 0.46 0.47 4.21 0.070 1 185 5 357 0 48 1.10 0 318 15 • 0.363 2560 12.70 0.029 0 044 0 057 0.27 0 32 0.40 0.29 0.30 0 62 0.055 0 800 6 636 1.50 0.370 22.37 0.066 0.094 0.126 0 37 0.43 0 50 0.37 0.40 1 .11 0.069 1 362 5.362 0.373 35.23 0.072 0.102 0.140 0.41 0.51 0 GO 0.46 0.40 1 73 0.084 1 1 214 4 464 0 52 0 98 0.271 0.383 48.10 0 079 0.109 0.158 0 55 0.66 0 90 0.53 0.60 2 36 0.096 1.135 4010 0 56 1 .17 0 239 It . 0.350 33.40 12.30 0.036 0 048 0.064 0.31 0.37 0.43 0.31 0.30 0.35 0.073 0.657 4 794 0,67 1 .40 0.90 0 360 22.17 0.063 0.101 0.128 0 37 0.49 0.55 0.44 0.45 0.64 0.094 1 074 i 029 0 380 34 83 0.087 0.1 16 0.128 0.49 0.63 0.75 0.58 0.60 ; 1.00 0.114 1 .017 3.333 0.61 1 .03 0.199 0.393 47.70 0.100 0.144 0.175 0.38 0 77 0.94 0.64 0.65 1.37 0.130 1.107 3 038 0 65 1.18 0 182 17 • 0.285 330 11.75 0.028 0.044 0.062 0.28 0.34 0 42 0.31 0.30 0.35 0.071 0.619 4.014 o.sr* 1.13 1 ■ 10 0.290 21.62 0.061 0.083 0.118 0.40 0 45 0.53 0.41 0.40 0.64 0.091 0,912 3 186 0.310 “ 34.28 0.033 0 083 0.120 0 42 0 59 0 70 0.54 0.40 1.01 0.112 0.758 2 767 0 60 0 90 0 168 0.320 47,13 0.114 0.137 0.155 0 66 0.78 0B5 0.72 0.48 1.39 0.129 1 .062 2.480 0 66 1.18 0.143 It . 0.290 23.20 12.03 0.022 0 031 0.041 0.23 0.28 0.36 0.26 0.20 0.61 0.053 0.584 5.471 0.15 0.58 1 .40 0.300 21.90 0,043 0.068 0.083 0.34 0.4| 0 50 0.35 0.38 l.ll 0.067 1 .014 4.477 0.303 3436 0.059 0.094 0.120 0.37 0.47 0.50 0.42 0.30 1.75 0.003 1.132 3.674 0.52 0.90 0.220 0.310 47.53 0.057 0.091 0.130 0 44 0.56 0 70 0.50 0.43 ! 2.41 0.095 0.957 3.263 0 56 1.00 0 192 It . 0.293 20.30 12 05 0.010 0.015 0.021 0.17 0 21 0.30 0.20 0. 20 1 0.94 0.041 0.365 7.195 0.16 0.45 £.30 0.300 21.92 0.031 0.049 0.070 0.29 0.33 0.43 0.30 0.30 i 1.71 0.053 0 924 5660 0.300 3458 0.041 0.059 0085 0.37 0.44 0.52 0.40 0.43 ! e.7o 0.064 0.921 4 607 0 46 0.95 0 276 0.305 47.43 0.043 0.072 0.103 0.40 0 49 0 60 0.45 0.45 3.71 0 074 0.972 4.121 0 49 1 00 0.248 eo • 0.300 16.30 12.20 0.004 0.006 0 008 0 12 0 16 0.25 0.13 0.1 3 1 48 0.032 0.187 9.375 0.300 22.07 0019 0.029 0043 0.22 0 26 0.30 0.24 0.24 2.67 0.041 0.707 7.317 0.300 34,73 0.039 0.059 0.076 0.30 0.35 0.40 0.32 0.33 4.20 0 050 1 .100 6.000 0.40 0.87 0 366 0.300 47.60 0.039 0.056 0.085 0.39 0.46 0.66 0.39 0.40 5.76 0 060 0 933 5.000 0.44 1 04 0 302 ei • 0.300 II ,20 12.20 VERY SM A LL 3.12 0.021 14 285 0 03 0.08 7.00 0.300 22.07 0.004 0 005 0008 0.17 0.21 0.25 0.17 0.1 6 5.65 0.027 0.185 1 III 1 0.300 34.73 0.016 0.025 0.030 0.23 0.20 0 40 0.25 0.23 8 89 0.033 0,757 9 090 0.33 0.84 0.537 0.300 4760 0.032 0 043 0 036 0.30 0 32 0.40 0.29 0.30 12.19 0 038 1 131 7.094 0.36 0 88 0 450 £2 - 0.230 31.20 1120 0.034 0.050 0.068 0.28 0.32 0.40 0.31 0.30 0.37 0.064 0.781 3.593 0.45 1.30 0.00 0.240 21.07 0.063 0.090 0.106 0.38 0.45 0.52 0.37 0.33 0.70 0.085 1.058 2 823 0.255 33.73 0.064 0.090 0.104 0.44 0.58 0 66 0.51 0.45 1 .1 1 0.103 0 873 2 475 0.58 1 00 0.148 0.270 46.60 0.094 0.130 0 168 0.60 0.76 0 90 0.64 0.44 1.54 0,120 1.003 2 250 0.62 1 .22 0.137 C3 • 0.240 23.0 1 1.50 0.021 0 039 0.046 0.23 0.31 0.35 0.25 0.27 0.59 o'.osi 0 764 4.705 0.23 0.70 1.50 0.230 21.37 0,044 0.068 0.091 0.34 0 42 0.48 0.36 0.31 1 10 0.066 1 030 3.787 0,230 34.03 0.058 0.000 0.098 0.42 0.52 0.60 0.43 0.42 1.75 0.080 1.000 3.125 0.51 1.01 0.107 0.260 46 90 0.058 0 086 0.102 0.42 0.55 0.63 0.47 0.48 2 42 0.093 0 924 2.795 0.55 1.00 0.168 84 . 0 245 20.40 11.52 OOIO 0.015 0.019 0.20 0 23 0.28 0.21 0.22 0.89 0.040 0.375 6.125 0.13 0.40 2 35 0.250 21.39 0 034 0.044 0.052 0 28 0.32 0.36 0.29 0.30 1 65 0.053 0 830 4.716 0.250 34.03 0.046 0 068 0 084 0 36 0.40 0.49 0.36 0.32 2 63 0.065 1 ,046 3846 0.46 0 86 0 230 0.233 46.92 0.048 0.070 0.082 0.40 0.48 0.58 • 0.42 0.45 3.63 •0.074 0 945 3 445 0.49 0.97 0.207 85 • 0.230 15.20 11.60 0 006 0012 0.014 0.12 0.16 0 19 0.13 0.1 3 1.6! 0.029 0.413 8.621 0.08 0.16 3.60 0.250 81.47 0.024 0.030 0.037 0.22 0 28 0.34 0.24 0.22 2 99 0.038 0.789 6.578 0,230 34.13 0.038 0.034 0.067 0.31 0.37 0 40 , 0.31 0.32 4,75 0.046 1.173 5.434 0.39 0 94 0.321 0 250 4700 0.042 0.059 0.070 0.37 0.42 0.55 ■ 0.37 0.38 6.54 0.053 1 ..113 4.716 0.41 1.02 0 290 8t • 0.250 II .10 11.67 VERY SM A LL 3 05 0.020 12.500 6.40 0.250 21.54 0.004 0.007 0.013 0.16 0.21 0.25 0.17 0.20 5 62 0.026 0 269 9 615 0 250 34 20 0021 0.030 0.037 0.22 0.27 0.30 0.23 0.24 0.93 0.033 0.909 7.575 0.33 0.81 0.448 0 250 47.07 0.027 0.036 0.045 0.28 0 32 0.40 0.28 0.25 12 29 0.038 0.947 6 578 0.35 ' 0.91 0.400 87 • 0.200 10.70 11.15 VERY SMA LL 3.13 0.019 10 526 0.08 0.05 6.50 0.200 21.02 0.003 0005 0.007 0.13 0.16 0.25 , 0.13 0.13 5.91 0.025 0.200 8000 0.200 33.68 0.010 0.018 0.024 0.19 0.24 0.31 0.21 0.22 9 46 0.031 0.500 6.451 0.32 0.75 0.383 0.200 46.55 0.021 0.030 0.038 0.28 0.31 0.40 0.27 0.27 13 08 0.034 0 882 5 082 0.35 0 88 0.320 8t . 0.195 1500 1 1.18 0.004 0 006 0 009 0.14 0.19 0 26 : 0.15 0.14 1 44 0.029 0.206 6.724 0.02 0.14 350 0.200 21.05 0.038 0.055 0.073 0.23 0 28 0.40 0.26 0.30 2.71 0 039 1.410 5.128 0.200 33.71 0.033 0.054 0.073 0.30 0.37 0.47 0.31 0. 33 4,35 0.048 1.125 4 166 0 39 0.94 0.257 0.203 46 58 0.041 0055 0.070 0.39 0 45 0.55 0.39 0.33 6.00 0.055 1.000 3.727 0 42 1.07 0.227 89 0.190 20.0 11 .03 0,019 0.030 0.044 0.18 0.21 0 30 0.19 0.1 8 0.09 0,039 0.769 4.871 0.17 0.22 2.25 0.200 20.90 0.032 0.047 0.062 0 30 0.34 0.45 0.30 0.30 1.68 0.051 0.921 3.921 0.200 33.36 0.029 0.043 0 066 0.35 0 43 0.55 0.37 0.40 2.70 0062 0.693 3.225 0.45 0.95 0.193 0.210 46.43 0.033 0.049 0.074 0 42 0.53 0.65 0.45 0. 40 3.73 0 068 0.720 3088 0 48 1.10 0.176 10 TABLE I (CONT.) RUN NO BOTTOM ROUGHN DEPTH OF WATER (ft) AVERAGE WIND VELOCITY Uov 1 2 3 4 9 6 7 • 9 10 II 12 13 14 15 16 17 IB 19 20 21 22 23 30 smooth 0 190 24 30 10 97 0 020 0 030 0.045 0 24 0 28 0 30 0.24 0.30 0.60 0.048 0 625 3 958 0 22 0 42 1 15 0 200 2084 0 046 0 067 0 090 0 35 041 0 50 0.37 0.40 1.14 0 064 1 046 3 125 0 200 33 50 0 046 0 068 0 090 0 39 0 49 0 60 0.42 0.41 1 83 0 079 0 060 2 531 0 51 0 96 0 150 0 210 46 37 0 042 0 062 0 080 0.44 0 55 0 66 0.48 0.43 2 53 0 090 0 680 2 333 0 54 1 01 0 140 31 . 0 180 30 50 10 67 0 025 0 036 0 050 029 0 35 0 40 0.30 0.32 0 37 0 061 0 590 2 950 0.190 20 54 0 056 0 077 0 100 0 38 0 45 0 50 0.40 0.45 0 71 0 001 0.950 2 345 0 210 33 20 0 054 0 081 OHO 0 42 0.54 0.70 0.49 0.55 1.15 0 101 0.801 2 079 0 58 0 93 0 122 0 225 46 07 0.071 0.103 0.130 0 44 0 60 0.77 0.49 0.34 1 59 0 116 0 887 1.939 0 62 0 96 0 114 32 - 0 130 28 70 10.10 0 022 0 034 0 047 0 26 0 31 0 40 0.29 0.26 0.39 0 056 0 607 2 321 0 65 100 0 65 0.145 19.97 0 038 0 060 0.072 0 35 0 43 0 55 0.39 0.40 0 78 0.074 0 010 1 959 0 165 32 63 0 046 0 068 0 090 0 40 0.51 0 70 0. 46 0.44 1 .27 0.092 0 739 1 793 0 55 0 92 0 106 0.1 BO 45 50 0 055 0 084 0.1 10 0 44 0 60 0 01 0.52 0.61 1 77 0.100 0 777 1 666 0 59 1.01 0 101 33 . 0.140 240 10 45 0 019 0 029 0 042 0.24 0 28 0 36 0.25 0.22 0 58 0.047 0,617 2 978 0.22 0.55 0 90 0.130 2032 0 032 0 050 0.072 0 30 0 36 0 45 0.32 0.40 1 .13 0 063 0 793 2.380 0 160 32 98 0 035 0 054 0 080 0 37 0 48 0.60 0.40 0.40 1 04 0.077 0 701 2 077. 0.50 0 96 0 125 0.165 45 85 0 026 0.042 0.053 0 36 0 48 0 75 0.40 0.37 2.56 0 088 0 477 1.875 0 54 0 88 0 HO 34 ■ 0 140 2050 10.53 0 009 0 014 0 021 0 19 0.22 0 30 0.20 0.20 0.81 0 039 0 350 3 509 0 09 0.27 2.80 0 150 2040 0 029 0 042 0 052 0 28 0 34 0 63 0.30 0.27 1.56 0 052 0.807 2 804 0.155 3306 0 038 0 055 0 072 0 37 0.43 0 52 0.38 0.40 2.53 0 064 0 859 2 42 I 0.46 093 0 142 0 160 4593 0 030 0 049 0 078 0 36 0 47 0 60 0.43 0.40 3 51 0.073 0.671 2.191 0 48 0 97 0.135 33 • 0 145 1530 1060 VERY SMA L 1 42 0.028 5.178 0.02 0 22 3.70 0 150 2047 0 020 0 030 0 047 0.20 0 23 0 32 0.21 0.23 2 74 0 037 0.810 4 054 0 150 33.13 0 029 0.048 0 083 0 29 0 33 0.44 0.29 0.28 4.44 0 046 1 043 3 260 0.38 0 86 0 203 0.155 4600 0 031 0 047 0.076 0 36 0 44 0 75 0.38 0.37 6.16 0.054 0.070 2 870 0.41 1.07 0.180 M . 0.130 10.90 10.62 VERY SMA LL 2 88 0.019 7894 0 02 0.07 5.40 0 150 2049 0 004 0 006 0 010 0 13 0 16 0 20 0.14 0.17 3.55 0.025 0 240 6 000 0.150 33.15 0 012 0.018 0.024 0 20 0 26 0.30 0.21 0.20 8 90 0 031 0.580 4 838 0 32 0.8 1 0 287 0 i50 46.02 0 016 0025 0.033 0 27 0.31 0.40 0.27 0.28 12.46 0.036 0 694 4.166 0.35 0 88 0 240 37 • 0 060 31 50 760 0 010 0.014 0 020 021 0.26 0.32 0.23 0.22 0 25 0.056 0 250 1 071 2.56 1 45 0.30 * 0.090 17.47 0.011 0 020 0.028 0 20 0.32 0.37 0.24 0.37 0 57 0 080 0.250 1 125 0.120 30.13 0 037 0 054 0.070 0 37 0 46 0.54 0.4 1 0.40 0 98 0.099 0 545 1.212 0.50 0 79 0 069 0.150 4300 0 040 0 064 0 085 ■ 0 37 0.50 0 60 0.43 0.46 1 39 0 117 0.547 1 282 0.62 0 80 0 076 36 • 0 083 2440 9 85 0 011 0 016 0.019 020 0 24 0.30 0.22 0.24 0.53 0 046 0 347 1 847 0.22 0 43 1.00 0.100 19.72 0.021 0 031 0 042 0 27 0.34 0 40 0.31 0.30 1 .06 0 063 0 492 1 507 0.11 0 32 60 0 029 0 046 0 062 0 36 0 43 0.50 0.39 0.41 1.76 0.070 0 589 1.410 0.50 0 86 0.085 0.120 4525 0 032 0.046 0.060 0 37 0 40 0 64 0.41 042 2 44 0 089 0.516 1 348 0 54 0 80 0 080 39 . 0.090 20.40 9.96 0006 0.012 0.016 0 19 0.22 0.28 0.20 0.22 0.77 0 038 0.315 2 368 0.13 0.27 1.90 0.100 19.83 0.016 0.023 0.035 0.26 0.30 0.42 0.28 0.28 1 .53 0.050 0 460 2000 0.110 32 71 0.017 0.028 0 038 0 30 0.38 0.40 0.33 0.32 2 53 0 063 0.444 1 746 0.46 0.82 0 101 0.113 45 36 0 020 0 035 0 056 0 31 0 44 0 50 0.41 0.42 3.51 0.072 0.486 1 597 0.48 0 91 0.097 40 . 0 093 15.00 1010 0.002 0.003 0.005 0.12 0.15 0.19 0. 13 0.1 4 1.30 0 029 0 103 3 275 0 02 0.18 4,00 0.100 19.97 0.014 0 022 0.029 0.21 0.25 0.37 0.23 0.22 2.57 0 030 0.578 2.631 0 105 3205 0.017 0.027 0.040 029 0 35 0,40 0.30 0.34 4 23 0 047 0 574 2 234 0.39 0.89 0.134 0.110 4550 0 021 0 033 0.040 0 32 039 0.46 0.35 0.30 3 86 0.054 0.61 1 2.037 0 42 0 92 0.122 41 . 0.100 1140 10.10 0 0009 0.0013 0.0023 0 1 1 0.13 0.17 0. 1 1 0.15 2 50 0.019 0 069 5.263 0.01 0.03 6 00 0 100 19.93 0 003 0 005 0 008 0.14 0.17 0.22 0. 15 0. 15 4 93 0.026 0.193 3 846 0 100 3285 0010 0.014 0021 0 18 0 23 0.30 0.21 0.22 8 13 0.033 0.424 3.030 0 33 0 69 0.179 0.100 45.50 0.014 0.022 0.030 026 0 30 0.38 0.26 0.26 11.26 0.038 0 578 2 631 0.36 0 83 0.150 42 0 30.30 NO WAV S 17 00 1.02 0 40 0.020 3.17 VERY SMA LL 0.11 o.oeo 15.23 0.013 0.023 0.030 0 22 0 29 0.26 0.25 0.33 0.071 0 323 1 .126 0.49 0.59 0.065 0 110 28 10 0.023 0.039 0.060 0.27 0.37 0 44 0.35 0.38 0 98 0.093 0.419 1182 0.56 0 66 0 068 43 . 0.015 23 90 200 VERY SMA lL 0.1 1 0.025 0 600 7.63 0.47 1.20 0 050 1 187 0 006 0.009 0.012 0 16 0.22 0.30 0.1 8 0.20 0 67 0 048 0 187 1 041 0.070 24 53 0.012 0 018 0036 0.26 0.31 0.35 0.29 0.2 7 1.38 0 067 0.268 1 044 0 47 0.65 0.061 0 065 3740 0 008 0015 0.025 024 0.35 0.52 0.31 0.33 2.1 1. 0.080 0.187 1.062 0.51 0 68 0.063 44 • 0.030 19 90 7.50 VERY SMA -L 0.61 0.033 2.13 0 37 2.40 0.030 17.37 0 007 0010 0.013 0 17 0 20 0 26 0.1 9 0.1 8 1 41 0.047 0.212 1.063 0.065 3003 001 1 0.017 0 024 0 24 0.29 0.33 0.2 6 0.2 2 2 44 0.039 0.288 1101 0.44 0.65 0.065 0 075 42.90 0 006 0 01 1 0.020 0 19 0 30 0 40 0.27 0.30 3 48 0.069 0 159 1 086 0.47 0.63 0.066 43 , 0.040 160 949 VERY SMAl L 1.19 0 028 1.428 0.16 0.18 5 00 0.050 19 36 0 004 0 006 0.010 0.15 0.18 0.20 0.1 6 0.1 2 2.*»o 0.038 0.157 1 .315 0.060 32.02 0.006 0.010 0.015 0 19 0 22 0.30 0.20 0.20 4 02 0.048 0 208 1.250 0.39 0 56 0.077 0 065 4489 0.0 II 0.016 0 020 0 23 0 27 0.30 0.26 0.28 3 64 0 060 0.266 1 .083 042 0 64 0.072 46 0.045 II.20 9 58 VERY SMA LL . 2 46 0.0 19 2 360 0.06 0.03 12 50 0 050 1945 VERY SMA LL 0 1 1 0.14 0 17 4 99 0.025 2.000 0.055 321 1 0 003 0 004 0006 0 16 0 19 0 20 0.1 7 0.1 8 0.23 0.032 0.125 1.718 0.33 0 57 0 090 0.060 4490 VERY SMA LL 11.53 0.037 1 621 0.35 | 0 096 ' . TABLE I (CONT) RUN NO SOTTOM ROUGHN DEPTH Of WATER d g (H.) A/E RAGE WIND VELOCITY U« (II /»«c ) FETCH F (II.) WA YE HE GHT — WAVE PERIOD WAVE PERIODS FOR MAX. AND SIGN. WAVE HEIGHTS 4 u r H . (II ) H 1 «. ^L H * T . MAX ^moi (ID m£an T m*on (MCj 5KJN \ (••c.) MAX (MC) t h (SEC) Th ma X ( sec) 1 1 9 4 6 • r • 0 10 II 12 13 14 15 16 17 18 19 20 101 fouflh 0.30S 3270 12 35 0 046 0 063 0 000 0 34 0 39 0 48 0.35 0.35 0.37 0071 0 09 500 050 0.76 0 277 0 365 2243 0081 0 109 0 138 '0 43 0 51 0 58 0.47 0.48 0 68 0 092 1 10 3 97 0 56 0 91 0 *77 0 380 34 88 0 087 0 132 0 173 0 47 0 63 0.72 0.58 0.50 1 05 0 III 1.19 3 42 0 61 1 03 0 199 0 395 47 75 0 118 0 160 0 190 0 50 0 75 0 90 0.67 0.76 1 44 0 127 1 26 3.11 0 65 1.18 0 182 102 . 0 365 26 30 12 77 0 029 0 041 0047 0 28 0 33 0 46 0.29 0.28 0 59 0 056 0 74 6 52 0 44 0 75 0 369 0 370 22 85 0 049 0 074 0 110 0 37 041 052 0.38 a 40 1 06 0 072 1 03 5 15 0 49 0 84 0 301 0 375 35 30 0 055 0 089 0 132 0 40 0 53 084 0.45 0.48 1 64 0 088 1 01 4 26 0 53 1 00 0 260 0 380 48.17 0 069 0 107 0 150 0 46 061 0 00 0.56 0.62 2 24 0 100 1.07 3 00 057 1 07 0 226 103 . 0 365 21 60 12 85 0016 0 021 0 027 023 0 26 0 32 0.24 0.24 0 89 0 045 0 46 8 1 1 0 39 0 67 0 468 0 370 22 93 0 040 0 055 0 076 0 32 0 37 0 52 0.32 0.28 1 50 0 058 0 95 6 38 0 44 0 04 0 374 0.370 35 38 0 053 0 080 0 104 0 39 0 46 0 64 0.39 0.38 244 0 070 114 6 29 0 40 0 96 0 314 0.375 48 25 0 060 0 009 0 125 0 45 0 54 0 64 0.46 0.46 3 33 0 080 1 1 1 4 69 O.SI 1 06 0 282 104 . 0 370 16 65 12 93 0 004 0 007 0 010 0 15 0 10 0 24 0.17 0.18 1.50 0 034 0 20 10 09 0 33 0 55 0 661 0.370 2301 0 023 0 033 0 040 0 25 0 28 0 36 0.26 0.26 267 0 043 0 76 8 60 0 38 0.74 0 500 0 370 35 46 0 048 0 062 0 075 0 34 0 39 046 0.34 0.34 4 12 0 052 1 20 7 12 04! 0 95 0 430 0.370 48 33 0051 0 077 0 094 0 40 047 0 62 0.39 a 34 5.61 0 060 1 27 6 17 0 44 1 07 0 374 105 • 0370 12 00 12 97 VER^j SM A L 0 14 0 19 0 30 290 0023 1609 0.27 0 70 1 000 0 370 2305 0 009 0014 0024 0 21 0 24 0 32 0.20 0.22 5 15 0.030 0 47 12.33 0 31 0.77 0 755 0 370 35 50 0 026 0 037 0 046 0 27 0 30 0 34 0.28 0.26 7 93 0 036 1 02 10 27 0 35 066 0 588 0.370 48.37 0 035 0 040 0 057 0 34 0 38 0 48 0.33 0.36 1081 0 041 1 17 9 02 0 37 1 03 0 529 106 . 0.060 32 40 4 80 0 0022 0 0035 0 0055 0 17 0 22 0 28 0.1 8 0.20 0 15 0 047 0 07 1 28 0 43 0.51 0 063 0 100 1488 0015 0 024 0042 0 24 0 30 0 34 0.27 0.29 0 46 0 076 0 32 1 32 0.51 0 59 0 075 0 130 2733 0 032 0051 0 068 0 34 0 43 0 64 0.38 0.43 0 84 0 099 0 52 1 31 0 57 0 75 0 078 0 155 4020 0 049 0 068 0 089 0 47 0.60 0 83 0.52 0.54 1 23 0 l 18 0 50 1 31 0 62 0 97 0 079 10? . 0 085 2520 9.80 0 010 0015 0 022 0 22 0 27 0 34 0.23 0.25 0 50 0 048 0.31 1 77 0 41 0 66 0 099 0.095 19 88 0.015 0 022 0.032 0 29 0 35 0.44 0.32 0.36 101 0 065 0 34 1 46 0.46 0 76 0 087 0 110 32.33 0 024 0 035 0 040 0.36 0 43 0 50 0.36 0.40 1 64 0080 0 44 1 38 051 0 84 0.063 0.120 4 5.20 0 020 0 030 0 045 038 0.45 0 57 0.40 0.42 2 29 0 092 0 33 1.31 0 55 0.02 0 077 106 . 0090 20 70 9 94 0008 0012 0 018 0 19 0 23 039 0.20 0.22 0 75 0 038 0 32 2 37 0 36 0.64 0.136 0.100 20.02 0016 0 024 0030 0 27 0 32 0 38 0.29 0.28 1 30 0 052 0 46 1 92 041 0 70 0.116 0.105 3247 0015 0 025 0.036 0 34 041 051 0.35 0.37 2 44 0 064 0 39 1 64 0 46 0 89 0 096 0.115 45 34 0.017 0 026 0 035 0 37 044 0 54 0.38 0.38 341 0 074 0 35 1 56 0.49 0 90 0 093 109 . 0.095 16 20 1009 0 0013 0 0025 00060 0 15 0 20 0 28 0.1 6 0.17 1 24 0'029 0 09 3 20 0.31 0 65 0.194 0 100 20 17 0.013 0019 0 025 0.23 0.27 0 33 0.24 0.24 2 47 0.039 0 49 2 57 0 36 0,75 0.152 0.105 32 62 0.015 0.024 0.033 0.29 0 34 0 42 . 0.31 0.30 4 00 0 049 0 49 2 14 0 40 0 85 0 (20 0.11 45 49 0.018 0 026 0 037 0 34 0 38 0 45 0.34 0.35 5 58 0056 0 46 1 97 0 43 0 80 0 1 16 no . 0 100 11.30 10.17 VERY SMA .L 2 56 0019 5 26 0 25 0 313 0.100 20 25 0 003 0 006 0008 0 16 0 20 0 28 0.1 8 0.1 8 5 10 0026 0 23 3.85 0 29 0 69 0 232 0 100 32.70 0.012 0.017 0 020 0 24 0 27 0 35 0.23 0.23 824 0 033 0.52 303 0 33 0 82 0.179 0.105 43.5? 0015 0 022 0.029 0 29 0 32 047 0.29 0.26 II 48 0 037 0.59 2 84 0 36 0 89 0 159 m . 0 180 31.20 10.67 0 027 0 044 0 077 0 26 0 32 0 40 0.29 0.30 0 35 0 063 0.70 2 86 0 47 0 68 0.159 0.195 2075 0 042 0 062 0 083 037 0 47 0 56 0.4 1 0.40 0.69 0 083 0.75 2 35 0.53 0 89 0 135 0.210 3320 0 06b 0 100 0 117 0 43 0 55 0 65 0.48 0.48 1 10 0 103 0 97 2 04 0 58 0 95 0.122 0.225 4607 0 070 0 100 0 133 0 45 0 63 0 88 0.58 0.72 1 52 0 118 0 92 1 91 0.63 1 00 0.111 112 . 0 190 25 30 10.96 0 021 0 032 0.042 0 24 029 0 40 0.24 0.30 0 55 0 050 0.64 3 80 0.41 0 71 0 221 0.200 21.04 0 030 0 040 0 060 0 32 0 39 0.53 0.34 0.38 1 06 0 067 0 72 2 99 0.47 0 83 0 177 0205 33 49 0 057 0 083 0.1 15 0 39 0 50 064 0.40 0.45 1 68 0 082 1 01 2 50 052 096 0 147 0.210 46 36 0040 0 065 0 093 0.42 056 0 65 0.49 0.50 2 33 0 094 069 2 24 0.55 1 .02 0 136 113 . 0.195 2090 11.05 0 009 0.015 0 026 0 20 0 24 0 33 0.2 1 0.20 0 81 0 041 0.37 4 75 0 39 0.62 0.250 0200 21 13 0 033 0 049 0 070 0 28 0 33 0 40 0.30 0.30 1.56 0 053 0 92 3 78 0.42 0 79 0.222 0 205 33 58 0.047 0 066 0 098 0 36 0 43 0.50 0.38 0.40 2 47 0 066 1 00 3 1 1 0 46 0 94 0 180 0210 4645 0 037 0 055 0 070 0 40 0 50 0 62 0.44 0.40 3 42 0 076 0 72 2 77 0 50 1 00 0.164 114 - 0 195 1600 II 13 VERY SMA L 0 15 0.19 022 1 27 0 032 6. 10 0.32 0.59 0 375 0 200 21 21 0 026 0038 0047 0.25 0 29 0.32 0.26 0.28 2 42 0 042 090 4 77 0 37 0 78 0 286 0.200 3366 0 041 0 060 0084 0 32 0 39 0 45 0.34 0.40 3 84 0 051 1 18 3 92 041 0 95 0 233 0205 4653 0 037 0 055 0 068 0.39 0 47 0 55 039 0.31 5 30 0.059 0 93 3 40 0 44 1 07 0 207 IIS . 0.200 II 50 MIS 0 0020 0.0040 0 0075 0 13 0 17 0 30 0.1 3 0.13 2 71 0.021 0 23 9 52 0 26 0 65 0 572 0.200 21 23 0 006 0010 0013 0 19 0 22 0.26 0.1 9 0.20 5.16 0.027 0 35 7 41 0 30 0 73 0 435 0.200 336e 0 022 0032 0 046 0 26 0.31 0 34 0.27 0.27 8 19 0033 0 99 6 06 0 33 0 94 0 357 . 0200 4653 0031 0 044 0 060 0 33 0.36 040 0.32 0.30 II 32 0 039 1 12 5 13 0 36 1.00 0 303 lie . 0 3125 NO WAV ES 0 0 075 1 1.83 0 017 d o 0 050 0 23 0 29 0.36 0.25 0.34 0 39 0 066 0 42 1 14 0 48 0 60 0 064 0 105 24 70 0032 0 047 0064 0 35 0 43 030 0.38 0.42 061 0091 0.52 1 15 0 55 0 70 0 068 117 . 0 2490 N 0 WAV E S i 0 045 6 88 0.006 0 009 0.013 0 16 0 20 0 26 0.1 8 0.22 0 36 0 040 0 23 1 13 0 38 0 53 0 061 0 070 19 33 0 020 0 029 0 037 0 26 0 32 0 38 0.28 0.28 1 00 0.063 0 47 III 0 45 0.71 0 067 0.090 32.20 0017 0 026 0 038 0 32 0 40 0 52 0.34 0.34 1 67 0 079 0 33 1 15 0 51 0 70 0.068 116 . 0 025 20 90 2 70 VERY SMA LL 0 20 0 022 1 14 0 29 0 050 0 050 12 70 0 008 0012 0 016 0 18 0 22 0 40 0.19 0.22 0 94 0 043 0 27 1 16 0.38 0 56 0.066 0.065 25.23 0.017 0 023 0.027 0.26 0.31 0 48 0.28 0.27 1 86 0 058 0 39 1.12 0 44 0 70 0 066 0 080 30 10 0 015 0 022 0 028 0 30 0 37 0.42 0.33 0.26 2 81 0 069 0.31 1.16 0*8 0 77 0 068 119 . 0.040 16 20 7.43 VERY SMA LL 0.91 0 026 1 54 0.29 0 093 0.045 17 51 0 006 0010 0 014 0 17 0 21 0.28 0.1 9 0.20 2 15 0 037 0 26 1 22 0 35 0 60 0 071 0055 2996' 0.011 0 017 0 020 0 22 0 27 0.34 0.24 0.25 3 67 0 047 0 36 1.17 0 39 0 69 0.071 0065 4203 0 007 0 012 0.016 0 24 0 31 0 40 0.25 0.24 5.25 0 035 0 22 1.18 0 42 0 74 0 072 120 • 0 045 11.80 9 54 VERY SMA LL 2 28 0.020 2.25 0.25 0.141 0.050 19.62 0.020 0 050 0 13 0.17 0.24 4 69 0.027 0.74 1.85 0 30 0 57 0 109 0.055 3207 0.007 0 010 0.014 0 17 0 19 0 24 0. 1 8 0.20 7 66 0 033 0.31 1.67 0 33 0 58 0 098 0.055 44 94 0000 0 013 0.017 0.20 0 24 0 32 0.22 0.23 10.74 0.038 0.34 1.45 0.36 0.67 0 083 12 TABLE I (CONT) RUM NO BOTTOM ROUQMN DEPTH OF WATER d g (N ) AVERAGE WIND VELOCITY Uov (W/aac) FETCH F 3 x 10^ gH 0 /U 2 s const, a 0.25 (3) and H 0 = 7.8 x 10**3 u 2 . (U) In deep water the maximum wave height is controlled by the wave steepness. Studies by Michell(lO), Stokes (ll)> Havelock (12), and others, on the problem of the greatest height obtainable by an oscillatory wave of permanent form, lead to the conclusion that in deep water the maximum s teepness of a wave is 0.11±2. In shallow water, however, the waves usually break before they reach their maximum steepness. For a solitary wave(l 3 ), it can be shown theoretically that the relationship between the wave height at the breaking point and the water depth is: H b = 0.78 d. (5) 14 0000 I x O' O O O 8 o 15 l.o 2 4 6 10.0 2 4 6 100.0 2 4 6 1000.0 2 4 10,000.0 2 4 100,000.0 gF/U* FIGURE 5a. WAVE HEIGHT AS A FUNCTION OF WIND VELOCITY AND FETCH In Lake Okeechobee measurements it was shown that in very- shallow water the envelope curves of the highest significant waves for varying wind speeds were limited by the maximum value: H l/3 * d * (6) Further, it was found(l^) at Lake Okeechobee that the maximum wave height was 1.3h f and the mean wave height 0.60, times the significant wave height. If in Equation (5) is assumed to be the maximum, then the significant wave height for Lake Okeechobee could be found by dividing the right side of Equation (5) by 1.3U. The result is very close to that in Equation (6). In the transitional region between that of deep water and shallow water, the wave height is affected by the wave length as well as by the depth of water. When the waves are exposed also to a strong wind action, this may cause the waves to break before they reach their maximum steepness in deep water, or the maximum height as indicated by Equation (5) for shallow water. In the present laboratory experiments H^/y/dg never exceeded 0.L8, or for the maximum wave height H max /dg never exceeded 0.6l. It is questionable if Equations (5) or (6) should be used to predict the maximum wave heights for shallow water. The question still remains open as to what should be considered shallow water, and the method may result in prohibitively high wave predictions for design purposes. The proper method should include the fetch and wind velocities as well as the depth of water. The wave heights as functions of water depth at the location of measurements were plotted in Figure 6a to d. H 0 in these graphs indicates the wave height for deep water and was found from the deep-water curve shown in Figure 5a; and dg is the water depth at the location .where the waves were measured (bottom to MWL). The graphs were based on: (a) the laboratory study with a smooth-bottom; (b) the laboratory study with a rough bottom; (c) the laboratory study with a rough bottom with strips of cheese cloth in the channel to simulate the roughness effect of vegetation in nature; and (d) field measurements as made on Lake Okeechobee for wind velocities up to 90 ft/sec. and fetches up to 25 miles (Saville)(l£). The smooth bottom condition was represented by the painted channel bottom and had an equivalent sand roughness# of 0.0135 foot (L.l mm.) ( Manning’s n - 0.0116). The wave data as obtained under this condition shows a scatter characteristic of all wave measurements, but it was re¬ latively easy to construct an average curve through the data. 80 percent *By equivalent sand roughness, K s ,is meant that grain size which has, according to the equation ^ 1 (2.0 log^o P + 1.74) 2 ^S for open channel flow, the same resistance, f , as the given roughness (where R is the hydraulic radius). 16 17 FIGURE 6 • HEIGHT OF WIND GENERATED WAVES AS A FUNCTION OF WATER DEPTH of the experimental points are inside the + 30 percent error limit from this curve, and 57 percent are inside the + 20 percent error limit. There still are some points considerably below the described curve and error limits. It is interesting to note, however, that all these points re¬ present the conditions of the lowest wind velocities and shortest fetch lengths (Element 3)« The rough bottom condition was obtained by using expanded metal lath on the smooth bottom (see Figure ?)• The equivalent sand roughness for this condition was found to be equal to 0.0635 foot (l9.it min.) (Manning's n = 0.0207). The wave data for this condition are plotted in Figure 6b. For comparison with the smooth bottom experiments, the average curve and the + 30 percent limits were transformed from Figure 6a. There appears to be no difference between the data as obtained with the smooth bottom and that with the rough bottom. Most of the data fit inside the + 30 percent limit as obtained for the smooth bottom. The points below this limit are again for the conditions with the lowest wind velocities and shortest fetches, and those points above the limits are for highest wind velocities. To make the identification of points easier, run numbers and wind velocities were given for all the experimental points in Figure 6b. The rough bottom and cheese cloth in the channel were introduced to simulate the roughness effect of vegetation in nature. The cheese cloth was fastened to the bottom across the entire width of the channel. The top of the cloth was made to float by the use of a thin piece of balsawood. The buoyancy of the cloth was kept to a minimum so that it could easily follow the current and the motion of water particles, as does the natural grass. The height of the cloth was approximately 0.30 foot and constant for all runs, hence, for the deepest depth of 0.37 foot as used in the experiments, the top of the cloth was slightly below SWL and for shallower depths it floated at SWL. One cloth was used for each foot of channel. The arrangement is shown in Figure 8. For this figure it is interesting to note that the cloth is inclined against the wave and wind direction (indicated by the arrow in the picture). This was always the case and was caused by the bottom return current which balanced the wind driven current on the water surface. Additional discussion on this phenomenon is given in Reference 9. The wave data with simulated vegetation are plotted in Figure 6c, and compared with that from the smooth-bottom experiments. The data show considerable scatter. A closer investigation of Figure 6c shows, however, a marked regularity in scatter. The + 30 percent error limit as found for the smooth-bottom tests includes most of the data where wind velocities were higher than 20 ft/sec. The data for U>20 ft/sec. are, however, slightly below the values with a smooth bottom, as one might expect. Lower wind velocities resulted in wave heights which were considerably smaller than the corresponding heights for smooth bottom, and the wind velocities below 12 ft/sec. did not generate waves in depths less than 0.20 foot. 18 FIGURE 7-EXPANDED METAL LATH AS USED FOR ROUGH BOTTOM IN CHANNEL Run No. 80 Station 42 Depth d=0.37 Wind Velocity U=25 FIGURE 8 • STRIPS OF CHEESE CLOTH IN CHANNEL TO SIMULATE ROUGHNESS EFFECT OF VEGETATION 19 The field data from Lake Okeechobee ) are plotted in Figure 6d and compared with the limiting curves from the smooth bottom experiments. The field data and computations are given in Table II. The scatter of the data is considerably larger than the scatter of the laboratory data, as could be expected. The trend, however, seems to be the same as indicated by the laboratory experiments. The wave heights are lower than expected for lower wind velocities, and higher than expected for higher wind velocities. This is especially pronounced for relatively shallow water. In deep water no trend with respect to the wind velocity could be established. Summarizing the data as given in Figures 6 a to d, it may be seen that the depth starts to affect wave heights when dg/H 0 < 5» Disregard¬ ing the differences as already discussed above, the general trend is the same for the laboratory and the field data. The experimental curve from Figure 6a is also shown in Figure 5b as a supplement to the deep water relationship. This curve was used to correct predicted deep water wave heights for Lake Okeechobee,and these corrected heights were compared with field measurements. The wave measurements for Lake Okeechobee were obtained from Reference 15 and are summarized in Table II in this report. The per¬ centage of error in the predictions is given in Figure 9 as a function of wind velocity, U. Most of the predictions agree with measurements within + 50 percent. The error seems to follow, however, a definite trend. For low wind velocities the wave height predictions were usually too high (approximately 1R) percent), while for high wind velocities the prediction was usually IR) or 50 percent too low. The best predictions were obtained for wind velocities between 50 and 60 ft/sec. The same trend was dis¬ covered for laboratory experiments with simulated vegetation, and was discussed above for Figure 6c. Some of the possible reasons for the large error and scatter in data may be listed as difficulties in obtaining accurate field measurements as well as in a correct selection of wind velocities and fetches. Furthermore, the corrections were based on the depth-wave height ratio, without con¬ sideration of the depth-length ratio which should also be taken into con¬ sideration. Application of different dimensionless parameters such as gd/u2 as recommended by Bretschneider could produce better methods of prediction. 1 Wave Periods in Shallow Water The significant wave periods, T-, as found from all the laboratory experiments, are plotted in Figure 10 7 and compared with the semi-empirical Sverdrup-Munk curve. Considering all the available laboratory and field data for deep-water, it was found desirable to shift the curve in Figure 10 slightly upward. The new curve is identical to the one determined by Bretschneider for gF/U^ > 100. For lower gF/U^ values the curve was shifted slightly upward to better fit the laboratory data approaching deep water characteristics. In the following discussions, this altered curve was used as the basis of the computation. 20 TABLE H WAVE MEASUREMENTS ON LAKE OKEECHOBEE DATE UJ 5 i— LAKE STA. WIND VELOCITY, U, ft./sec. I* O |_ Q> UJ -F Ll . E DEPTH AT GAGE, dg , ft. AVE. DEPTH across entire fetch, dp, ft. SIGNIF. WAVE HT., H 1/3 , ft. WAVE PERIOD, T, sec. CM ZD \ Lu cr> DEEP WATER WAVE HEIGHT, H 0 , ft. DEEP WATER WAVE PERIOD, T 0 ,sec. O X to X 0 cn -O A 5 \ 1- II lid Lk. l U. T3 0 -J CM O h- OJ id 1 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 1949 1900 14 60.5 23.9110.2 11.0 3.3 4.9 1240 8.30 6.67 0.40 1.23 0.73 0.045 0.048 6-26 2000 12 60.1 8.3 6.2 4.5 1.8 4.0 390 5.02 4.94 0.359 1.24 0.81 0.050 0.036 2100 12 70.4 6.4 5.0 4.0 1.8 3.5 286 5.86 5.20 0.307 0.853 0.67 0.036 0.028 2130 12 79.9 6.0 4.5 3*6 1.4 3.3 222 6.74 5.52 0.207 0.667 0.598 0.029 0.024 6-27 0200 12 91.0 25.5 12.5 10.8 4.0 5.6 576:13.26 8.09 0.301 0.942 0.692 0.037 0.032 0300 12 73.3 22.5 11.3 11.6 2.7 5.4 870 10.36 7.30 0.260 1.090 0.740 0.041 0.042 0400 12 60.5 20.0 10.7 12.7 ^ *4 5.0 1180 8.07 6.58 0.297 1.325 0.760 0.045 0.052 0500 12 52.9 18.3 10.7 12.5 2.3 4.4 1370 6.60 5.99 0.348 1.621 0.735 0.058 0.068 0600 12 49.1 20.0 10.7 12.4 2.3 4.2 1480 5.93 5.68 0.367 1.804 0.739 0.065 0.075 I960 1900 1C 31.5 2.4 3.3 3.4 0,5 2.0 410 1.39 2.55 0.359 2.374 0.784 0.099 0.102 10-17 14 33.0 6.3 7.7 11.4 1.2 3.0 980 2.22 3.38 0.540 3.468 0.888 0.132 0.194 2000 10 26.6 2.4 3.4 3.6 0.5 2.0 500 1.24 2.45 0.403 2.741 0.816 0.111 0.117 12 29.3 7.8 8.6 8.3 1.4 3.0 1540 2.14 3.44 0.654 4.018 0.872 0.142 0.136 14 29.6 9.0 7.6 10.8 1.2 3.0 1730 2.33 3.61 0.515 3.261 0.831 0.114 0.161 15 20.5 0.5 8.7 7.7 0.3 2.1 201 0.43 1.38 0.697 20.2 1.52 0.897 0.793 2100 10 33.3 2.5 3.4 3.9 0.8 2.0 38 4 1.49 2.66 0.536 •2.281 0.752 0.094 0.107 12 33.0 7.8 8.6 8.2 1,8 3.1 920 2.16 3.32 0.833 3.981 0.934 0.152 0.145 14 32.1 11.5 7.6 11.1 1.4 3.1 1890 2.81 3.95 0.498 2.704 0.785 0.095 0.138 15 25.3 0.8 8.7 7.7 0.4 2.0 248 0.62 1.66 0.645 14.0 1.205 0.617 0.546 2200 10 37.7 2.7 3.3 4.0 1.0 2.0 323 1.76 2.87 0.568 1.875 0.697 0.078 0.094 12 34.7 7.8 8.6 8.2 1.5 3.2 1100 2:59 3.68 0.579 3.320 0.870 0.124 0.118 14 38.0 12.8 7.6 11.0 1.7 3.4 1510 3.56 4.40 0.477 2.134 0.773 0.077 0.110 15 24.9 0.9 8.4 7.4 0.4 2.2 245 0.68 1.74 0.588 12.4 1.26 0.542 0.477 16 38.6 21.8 8.5 10.3 1.2 3.2 2480 4.54 5.10 0.264 1.872 0.627 O.O64 0.077 2300 10 39.6 2.7 3.5 4.2 0.9 2.1 294 1.88 2.95 0.478 1.861 0.712 0.079 0.094 12 39.1 7.8 8.5 8.1 1.8 3.4 863 2.93 3.87 0.614 2.901 0.879 0.111 0.105 14 39.9 13.4 7.8 11.0 2.0 3.7 1430 3.84 4.59 0.520 2.031 0.806 0.072 0.101 15 24.9 0.9 8.5 7.5 0.5 2.5 246 0.68 1.75 0.735 12.5 1.43 0.541 0.477 16 42.4 21.8 8.6 10.3 1.2 3.2 2060 5.04 5.28 0.238 1.706 O.606 0.060 0.072 2400 10 49.4 2.8 3.6 4.3 1.0 2.4 194 2 • 4^ 3.24 0.413 1.49 0.74 0.067 0.080 12 40.6 6.8 8.4 8.0 2.1 3.5 700 2.92 3.78 0.719 2.88 0.925 0.114 0.109 14 44.0 12.8 7.9 11.1 2.8 4.2 1120 4.22 4.73 0.663 1.87 0.887 0.068 0.096 15 38.1 1.0 8.3 7.3 1.1 3.3 116 1.17 2.19 0.940 7.09 1.506 0.337 0.296 16 44.4 21.8 8.7 10.2 1.3 3.2 1870 5.33 5.45 0.243 1.63 0.587 0.057 0.067 17 44.4 20.5 8.0 11.4 1.9 2.8 1760 5.21 5.38 0.364 1.54 0.520 0.053 0.076 -18 0100 10 57.9 2.9 3.8 4.4 1.5 3.2 153 3.O2 3.62 0.496 1.26 0.883 0.056 0.065 12 46.5 6.8 8.2 7.8 2.4 3.6 530 3.35 4.05 0.716 2.45 0.888 0.097 0.092 14 44.3 13.0 8.1 10.9 3.4 4.5 1130 4.28 4.76 0.794 1.89 0.945 0.069 0.093 15 38.1 0.9 8.1 7.1 1.0 3.3 105 1.12 2.12 0.892 7.23 1.556 0.352 0.308 16 49.3 21.7 8.9 9.4 1.9 3.5 1510 6.03 5.74 0.315 1.48 0.609 0.052 0.055 17 50.4 19.9 8.5 11.5 2.0 2.8 1320 5.93 5.67 0.337 1.43 0.493 0.051 0.069 0200 10 63.8 4.0 3.9 6.8 1.4 3.8 166 3.79 4.06 0.369 1.03 0.935 0.046 0.080 12 54.5 6.8 7.9 7.2 2.7 3.7 389 4.05 4.36 0.666 1.95 0.848 0.081 0.073 14 57.5 13.2 8.1 11.0 3.6 4.5 675 5.76 5.37 0.625 1.41 0.837 0.054 0.074 15 42.5 1.6 7.9 6.9 1.1 3.7 150 1.63 2.64 0.674 4.85 1.401 0.221 0.193 21 TABLE H (cont.) UJ 1— < Q UJ i- STATION * O Q) < V*— xT F , miles V*_ cn "O ^4— U- -O fO X O (/) CVJ X s u _ C7> **— O X Ci>i a> in O h- 0 X >, X 0 X CT> "O O I- N 1- 0 s O' X) 0 s u. x> 1 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 1950 0200 16 57.0 22.0 9.2 9.5 2.3 4.5 1150 7.16 6.14 0.321 1.28 0.732 0.047 0.049 10-18 17 53.7 20.0 8.9 11.1 2.0 2.6 1210 6.45 5.88 0.310 1.38 0.442 0.050 0.062 0300 10 60.7 9.0 4.1 8.9 1.9 3.2 414 5.16 4.91 0.368 0.79 0.651 0.033 0.072 12 55.4 6.8 7.6 7.1 2.9 4.0 375 4.10 4.37 0.707 1.85 0.915 0.077 0.072 14 62.3 15.1 8.7 10.9 3.6 4.8 660 6.65 5.78 0.541 1.31 0.830 0.050 0.063 15 42.5 1.9 8.1 7.0 1.1 3.5 179 1.74 2.77 0.632 4.66 1.263 0.206 0.178 16 62.6 22.1 9.3 9.2 2.5 4.7 965 7.89 6.40 0.316 1 . 18 - 0.734 0.044 0.043 17 59.5 20.0 9.5 10.6 3.3 2.7 ■959 7.16 6.10 0.460 1.33 0.442 0.049 0.055 0330 10 60.1 12.0 4.5 6.6 2.0 3.1 565 5.28 5.39 0.378 0.85 0.575 0.030 0.044 12 67.1 6.8 7.5 7.0 3.1 4.0 256 5.03 4.78 0.616 1.49 0.836 O . O64 0.059 14 64.2 16.8 8.9 11.1 3.6 5.1 694 8.09 6.00 0.444 1.10 0.850 0.048 0.060 15 44*0 1.9 7.5 6.5 1.1 3.5 167 1.81 2.81 0.607 4.14 1.245 0.185 0.160 16 66.8 22.0 9.6 9.4 2.6 4.6 837 9.58 6.61 0.271 1.00 0.695 0.042 0.042 17 63.6 20.0 9.9 10.7 3.8 2.9 840 7.68 6.04 0.494 1.29 0.480 0.052 0.057 0400 12 68.9 6.7 7.4 6.8 2.8 4.0 240 5.16 4.84 0.542 1.43 0.826 0.061 0.056 14 71.4 17.0 8.9 10.6 3.5 5.1 565 8.08 6.37 0.433 1.10 0.800 0.042 0.051 15 44.0 0.6 7.3 6.2 0.7 3.2 52.8 1.09 2.07 0.642 6.70 1.545 0.333 0.283 16 69.8 22.0 9.9 8.9 2.7 4.4 77.0 3.33 3.65 0.810 2.97 1.205 0.145 0.130 17 67.0 20.0 10.5 11.5 4.0 3.1 75.8 3.07 3.43 1.302 3.42 0.903 0.174 0.191 0430 10 88.0 2.8 3.5 3.8 1.4 2.7 61.0 4.82 4.27 0.290 0.73 0.632 0.037 0.040 12 67.6 6.8 7.0 6.7 2.4 3.9 252 5.11 4.83 0.469 1.37 0.807 0.058 0.056 14 71.8 11.5 8.6 11.5 3.1 5.0 378 6.88 5.69 0.450 1.25 0.878 0.051 0.069 15 44.0 0.5 6.8 5.8 0.6 2.7 44.0 1.03 1.99 0.582 6.60 1.356 0.334 0.285 16 74.3 22.2 9.8 9.0 2.7 4.2 690 9.61 6.93 0.280 1.02 0.606 0.039 0.036 17 72.7 20.0 10.9 11.5 3.0 3.2 6 « 8.87 6.67 0.338 1.23 0.479 0.047 0.050 0500 10 88.0 2.8 3.4 3.3 1.2 2.3 62.0 4.82 4.27 0.248 0.70 0.538 0.036 0.035 12 66.0 6.8 7.5 6.8 2.2 3.9 265 5.01 4.76 0.439 1.50 0.819 0.064 0.058 16 76.1 22.0 9.8 9.1 2.7 4.1 651 9.88 6.99 0.273 0.99 0.586 0.039 0.036 0900 10 46.3 6.0 2.5 1.0 0.5 2.3 475 3.20 3.90 0.156 0.78 0.589 0.032 C .012 14 51.2 7.4 6.8 5.2 0.8 2.8 480 3.91 4.31 0.204 ' 1.74 0.649 0.071 0.054 15 39.6 0.8 8.9 7.9 1.9 3.8 87.0 1.12 2.10 1.696 7.95 1.809 0.393 0.349 17 40.6 3.8 5.6 2.7 o.s 2.4 390 2.25 3.26 0.400 2.49 0.736 0.102 0.049 1000 10 64.8 6.0 2.2 1.0 0.7 2.5 243 4.69 4.54 0.149 0.47 0.550 0.020 0.009 14 51.3 7.9 6.7 5.0 0.9 2.9 510 4.00 4.42 0.225 1.68 0.656 0.067 0.050 15 31.5 1.7 8.7 7.7 1.8 3.8 293 1.17 2.34 1.538 7.44 1.623 0.309 0.274 17 45.0 3.8 5.4 2.2 1.2 2.5 320 2.52 3.43 0.476 2.40 0.728 0.089 O . O36 1100 14 66.0 6.3 7.0 5.1 0.9 2.8 246 4.87 4.65 0.184 1.44 0.602 0.063 0.046 15 38.1 0.9 9.4 8.4 1.4 3.8 105 1.12 2.12 1.250 8.39 1.792 0.408 0.365 17 45.4 3.8 5.4 1.9 0.8 2.7 304 2 . 5 C 3.40 0.320 0 0.794 0.091 0.032 1200 14 49.8 7.3 7.2 5.2 0.9 2.6 pQG 3.78 4.26 0.238 1.90 0.610 0.077 0.055 15 27.9 0.8 9.3 8.5 1.2 3.7 175 0.75 1.80 1.600 12.4 2.055 0.560 0.512 17 33.7 3.8 5.7 2.0 1.1 2.7 570 1.73 3.01 0.635 3.29 0.897 0.122 0.043 1300 14 34.5 7.7 7.3 5.5 0.8 2.7 1110 2.58 3.66 0.310 2.83 0.737 0.106 0.080 15 19.0 0.8 9.2 8.4 1.0 3.5 375 0.48 1.50 2.083 19.2 2.333 0.800 0.730 17 33.3 3.8 6.1 2.4 1.2 2.6 585 1.78 2.97 0.674 3.43 0.875 0.134 0.053 1400 14 33.0 7.6 7.5 5.7 0.6 2.6 1190 2.45 3.60 0.244 3.06 0.722 0.112 0.085 15 24.9 1.5 9.3 8.3 0.9 3.3 408 0.86 2.00 1.046 30.8 1.650 0.453 0.404 17 33.4 3.8 6.6 2.8 0.9 2.6 577 1.80 2.98 0.500 3.67 0.872 0.145 0.061 22 8 8 O CD O o CVJ O OJ I O o CD I O 00 o _ o o O < o o 0 o o 0 0 o < o ° > 5 O o < Ad ° o o D

9r~ o °0 8 0 C o oo )° o o o O o o o o o 0 < Oo o ° o » 9)00 oo° o G -o o ° o 0 o o o < G < 1 o o o G) O 00 o I s - ~o c o o a ; CO d > «-* > f - O o _l LU > Q O rO 8 O o OJ p3|Daji|S9jaAo saADM pa|Dwi|sajapun saAOM 0 , luaojad w t 00l 'H oi H - o H 23 FIGURE 9 PERCENTAGE ERROR IN PREDICTING SHALLOW WATER WAVES AS A FUNCTION OF WIND VELOCITY FOR LAKE OKEECHOBEE 2 4 FIGURE 10 • DEEP WATER WAVE PERIOD AS A FUNCTION OF WIND INTENSITY AND FETCH There is a definite trend for shorter periods in shallower water. The bottom effect on wave periods is not so pronounced as it was on wave heights. The changes in wave periods were plotted as a function of d g /L Q , where d was again the depth of water at the point of measurements, and L 0 the aeep-water wave length: L 0 - £.12T Q 2 , where T 0 is the deep-water wave period and could be predicted from the known fetch and wind velocity. All the laboratory experiments indicate the same trend for both the smooth and rough bottom and with the simulated vegetation. The smooth-bottom results were used again to obtain the empirical relationship between the wave periods and the depth of water. Figure 11a demonstrates that 90 percent of the results were within + 20 percent error limits from an average curve, and percent were within + 10 percent error limits. These curves from Figure 11a were transferred to Figure 11 b, c, d and e. The field measurements indicate the same trend for the region of d /L 0 between 0.2 and 0.07. The range dg/L 0 < 0.06 was not covered by the laboratory experiments. The laboratory experiments demonstrate further that with d g /L 0 > .2 the depth of water does not have any influence on wave period and the deep¬ water curves can be used. Wave Statistics For design purposes it is important to predict the maximum wave heights and periods when the mean or significant wave heights and periods are known. The relationships between the mean, significant, and maximum wave heights are shown in Figure 12 a to c. All the experimental points give a straight-line relationship.. The scatter is very small (+ 10 per¬ cent) when the mean and significant values were concerned. The maximum value represents only one measurement out of every 100 waves and so the scatter is expected to be larger. The + 20 percent scatter for these points may be considered as a very good result. The maximum wave height was found to be 1.3li times the significant wave height, which is exactly the same value as determined by the Jacksonville District, Corps of Engineers, for lake Okeechobee O-h) and slightly smaller than the 1.37 as given by Saville(l£) for the same lake. The ratio between the maximum and significant wave heights for the ocean was determined by Putz(l^) to be 1.8l. The measurements made by Wiegel(l7) for ocean waves along the Pacific Coast gave a value of 1.87 + 20 percent for this ratio. It should be noted that the Putz and Wiegel results concern only deep-water waves in the ocean. In shallow water the wave heights are also controlled by the water depth and so the shallower the water the more uniform probably would be the wave heights. Within the limits of this experiment, no different ratios for various depths could be obtained. The results were also the same for different lengths of fetch (except very short fetches which are not included in the data)• Statistical data for wave periods in shallow-water are shown in Figure 13a to c for individual wave periods; in Figure 1U for the periods of 25 26 FIGURE II • WAVE PERIOD AS A FUNCTION OF DEPTH BIO 2 7 FIGURE 12 • RELATIONSHIP BETWEEN MEAN, SIGNIFICANT AND MAXIMUM WAVE HEIGHTS 1 V 'N \ N t \ V \ o ' +s hoi +\+k v r \ x ▼ \ > \ X X xL\ < NS > ° & % * *<%> \ v ■—*3- 1 4 nx V* V V \ jc i 2“28 odd il ii il ■COT) T}- *i ■ — •MX c UJ \ \ ' ■ • ^ ; X N .. ■ ■ / l / *8j pv 4s Sf \ O 's * < - \i j\* c lV RX KjX lls^ ' |*N Xis_ a to 0 ' -X X 8 4» to c i CD 6 CO 6 N 6 to 6 m 6 6 ro 6 cvj o 28 FIGURE 13 • RELATIONSHIP BETWEEN MEAN, SIGNIFICANT AND MAXIMUM WAVE PERIODS 29 RELATIONSHIP BETWEEN INDIVIDUAL WAVE PERIODS AND WAVE PERIODS OF MEAN, SIGNIFICANT AND MAXIMUM WAVE HEIGHTS FIGURE 15 significant and maximum wave heights; while in Figure l5a to d the individual wave periods are compared with the periods 'of the mean, significant, and maximum wave heights. The data are unique for all cases, and no variation could be found for various water depths and lengths of fetch. The scatter, as expected, was large (+ 20 percent) for maximum values, and very small (+ 10 percent) where the significant and mean values were concerned. It is interesting to note that the maximum wave period never coincided with the maximum wave height, and that the period of the wave of maximum height-and the average period of the significant wave heights were of the same value and equal to 1.10 times the mean wave period, T mearr . Hence, the periods of the maximum and significant wave heights could be derived through the simple ob¬ servation of the mean wave periods. The complete results are given in Table III. Numbers indicate the ratio a/b The statistical distributions of wave heights are given in Figure 16. This figure demonstrates that i;5 percent of the waves are smaller than the mean wave height and approximately 90 percent are smaller than the significant wave height. The wave heights and periods were plotted for individual waves in Figure 17 a to c. The plots were made in three different groups: (a) for depths of water 0.30 to 0.37 foot; (b) for depths 0.100 to 0.150 foot; (c) for depths 0.055 to 0.085 foot. The wave steepnesses are also 30 X X 31 FIGURE 16 ■ STATISTICAL DISTRIBUTION OF WAVE HEIGHTS I s - X 32 FIGURE 17 • RELATIONSHIP BETWEEN WAVE HEIGHTS AND PERIODS FOR INDIVIDUAL WAVES indicated for each plot. The lines of equal wave steepness could be computed using the Stokes' first approximation: L » 5.12 T 2 tanh ( 7 ) L The wave steepness is given by definition as H/L, hence: H = (H/L) L. ( 8 ) Substituting Equation ( 8 ) into Equation (7) we have: H . 5.12 (HA) T 2 tanh 27rd/L. (9) Using H/L as parameter, the curves can be plotted for the given depth d. ■‘■he breaks in the computed curves in Figure 17 b and c resulted from the effect of depth variations in the last term of Equation (9). Corrections were also applied to the curves considering the increase in wave velocities when the wave steepness is increasing, or when the wave approaches the characteristics of a solitary wave in shallow water (Reference 18, Figure II 4 ) • Figure 17 a to c demonstrates the decrease in wave steepness as the depth decreases. For the depth 0.30 to 0.37 foot, the average wave steepness is approximately 1:13; for d = 0.100 to 0.150 foot, 1:15; and for very shallow water d 0.055 to 0.085 the average steepness is only 1:30. This demonstrates again that in deep-water the wave heights are controlled by the maximum wave steepness, while in shallow water the bottom contributes considerably in making the waves break before they reach the maximum steepness that is possible in deep water. For very shallow water, it is expected that the waves will approach the characteristics of the solitary wave. CONCLUSIONS The data indicate that Sverdrup-Munk-Bretschneider curves may be used to predict the wave heights and periods for relatively deep water. The experiments indicate that the depth starts to reduce the wave heights at approximately d/H 0 < 5. The wave periods are reduced when d/L 0 < 0.2. r The maximum wave height was found to be 1.3h times that of the significant wave height and 1.93 times that of mean wave height. The average periods of the significant waves and of the maximum waves were found to be of the same magnitude and equal to 1.10 times the mean wave period. 33 The maximum, wave period almost never coincided with the maximum wave height, and was found to be 1.25 times that of significant wave period and 1.42 times that of mean wave period, ACKNOWLEDGMENTS The author wishes to express his appreciation to J. W. Johnson, under whose direction the experiments were completed, for many helpful suggestions and for critical reading of the manuscript. He is also obliged to A. J. Cook, J. Kukk and W. F. Parker for their help in re¬ ducing the data, to M. M. Lincoln for the illustrations and E. Henderson for typing the manuscript. REFERENCES 1. Sverdrup, H. U., and Munk, W. H., Wind, sea and swellj theory of relations for forecasting. U. S. Hydrographic Office, Tech. Report No. 1, H. 0, Publication No. 601, March 1947 2. Flinsch, H.v.N., An experimental investigation of wind generated surface waves. Ph.D Thesis, Univ. of Minn. June 1946 (unpublished) 3. Johnson, J. W, and Rice, E.K., A laboratory investigation of wind¬ generated waves. Univ. of Calif. IER. Tech. Report HE-116-321, March 19^1. 4. Francis, J.R.D., The aerodynamic drag of a free water surface. Proc. Royal Soc. Ser. A, v. 106, pp. 387-406, 1951. 5. Johnson, J. W., The characteristics of wind waves on lakes and protected bays. Trans. Amer. Geophys. Union, v. 29, pp. 671- 681 , 1948. 6 . Johnson, J. W., Relationship between wind and waves, Abbotts Lagoon, California. Trans. Amer. Geophys. Union, V. 31* pp. 386-392, 1950. 7. Bretschneider, C. L., The generation and decay of wind waves in deep water. Trans. Amer. Geophys. Union, v. 33* No. 3* pp. 382-389, June 1952. 8 . Sibul, 0., Measurement of water surface roughness and wind shear stress by the use of a Pitot tube in a laboratory wave channel. Univ. of Calif. IER, Wave Research Lab., Series 71, Issue 2, Berkeley, 1954 (scheduled for publication as Beach Erosion Board Technical Memorandum). 34 9. Sibul, 0,, Laboratory studies of wind tides in shallow water. Univ. of Calif., IER. Wave Research Lab., Series 71, Issue 1*, Berkeley 195k, (scheduled for publication as Beach Erosion Board Technical Memorandum). 10. Michell, J. H., On the highest wave on water, Philos. Mag. Vol. XXXVI, pp. 1*30-1*37, 1893. 11. Stokes, C. G., On the theory of oscillatory waves. Trans. Cambridge Phil. Soc., Vol. VIII, p. 1*1*, 181*7. 12. Havelock, E. T., Periodic irrotational waves of finite height. Proc. of the Royal Soc., London, Ser. A, vol. 95, PP« 38-^1, 1918 . 13* Munk, W. H., The solitary wave theory and its application to surf problems. Annals of the N.Y. Acad, of Sci., v. 5l, art. 3, pp. 376-1*21*. 11*. Corps of Engineers, U. S. Army, Central and southern Florida Project, Part IV - Lake Okeechobee and Outlets, Jacksonville, Fla., April 27, 195k (unpublished). 15. Saville, T., Jr., Wind set-up and waves in shallow water. Beach Erosion Board, Tech. Memo. No. 27, Washington, D. C., June 19^2. 16 . Putz, R. R., Wave height variability; prediction of the distribution function. Univ. of Calif., IER, Wave Research Lab., Series 3, Issue 318, Berkeley 19^0. 17. Wiegel, R. L., An analysis of data from wave recorders on the Pacific Coast of the United States. Trans. Amer. Geophys. Union, v. 30, No. 5, October 191*9. 18. Sibul, 0., Laboratory study of depth determination; effect of off¬ shore bars. Univ. of Calif., IER, Wave Research Lab., Series 71*, Issue 8, Berkeley, Sept. 195'J. 35 A 56449 <• *