- /r.^* 
 
 ESSA TR ERL 175- ITS 112 
 
 A UNITED STATES 
 DEPARTMENT OF 
 COMMERCE 
 PUBLICATION 
 
 / v\ 
 
 
 ESSA Technical Report ERL 175-ITS 112 
 
 U.S. DEPARTMENT OF COMMERCE 
 Environmental Science Services Administration 
 Research Laboratories 
 
 On the Role of Vertical Neutral-Gas 
 in Producing Ion Convergence 
 at E-Region Heights 
 
 WILLIAM H. HOOKE 
 
 BOULDER, COLO. 
 JULY 1970 
 
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 Robert M. White, Administrator 
 RESEARCH LABORATORIES 
 Wilmot N. Hess, Director 
 
 ESSA TECHNICAL REPORT ERL 175-ITS 112 
 
 On the Role of Vertical Neutral-Gas Motions 
 in Producing Ion Convergence 
 at E-Region Heights 
 
 WILLIAM H. HOOKE 
 
 INSTITUTE FOR TELECOMMUNICATION SCIENCES 
 BOULDER, COLORADO 
 July 1970 
 
 For sale by the Superintendent of Documents, U. S. Government Printing Office, Washington, D. C. 20402 
 
 Price 30 cents 
 
TABLE OF CONTENTS 
 
 Page 
 
 ABSTRACT 1 
 
 1. INTRODUCTION 1 
 
 2. VERTICAL MOTIONS OF THE NEUTRAL 
 
 GAS AT E -REGION HEIGHTS 3 
 
 3. VERTICAL NEUTRAL-GAS MOTIONS IN 
 
 THE MAGNETOSHEAR THEORY 8 
 
 4. VERTICAL NEUTRAL -GAS MOTIONS 
 AUGMENTING AND OPPOSING CORRESPONDING 
 HORIZONTAL MOTIONS 1 5 
 
 5. VERTICAL NEUTRAL -GAS MOTIONS AND 
 
 THE CORKSCREW EFFECT 17 
 
 6. E3 LAYERS PRODUCED BY TRANSVERSE 
 
 WAVES 21 
 
 7. CONCLUDING REMARKS 23 
 
 8. REFERENCES 25 
 
 111 
 
ON THE ROLE OF VERTICAL NEUTRAL-GAS MOTIONS 
 IN PRODUCING ION CONVERGENCE AT E -REGION HEIGHTS 
 
 William H. Hooke 
 
 Theoretical and observational results are used 
 to suggest that vertical neutral-gas motions are generally- 
 important in applications of the magnetoshear theory of 
 sporadic E, as has been recently demonstrated in a parti- 
 cular instance by M, A. MacLeod. It is argued that much 
 of the vertical neutral-gas motion present at these heights 
 must be of gravity -wave origin and shown that gravity- 
 wave -associated vertical motions of the neutral gas should 
 support (oppose) the action of wave-associated horizontal 
 motions in producing ion convergence when the wave is 
 propagating toward the east (toward the west). It is also 
 argued that the full vector ion velocity, rather than only 
 its vertical component, must be used in applications of 
 the magnetoshear theory. 
 
 1. INTRODUCTION 
 
 Recent experimental work, for example that by MacLeod (1966) 
 and Wright et al. (1967), shows that the magnetoshear theory of spor- 
 adic E, as developed by a number of researchers (Dxingey, 1959; 
 Whitehead, I960, 1961, 1966; Axford, 1961, 1963; Axf ord and Cunnold, 
 1966; MacLeod, 1966; Chimonas and Axford, 1968), can make use of 
 rocket -trail measurements of the neutral-gas motion at E -region heights 
 to predict the altitudes of the relatively thin layers of enhanced electron 
 density commonly known as sporadic -E layers or E layers. There 
 are exceptions to this rule, however. In 5 of the 28 cases he studied, 
 MacLeod (1968) found E layers where theory predicted a region of 
 depleted free electron number density. Since it is assumed in the usual 
 application of the theory that the neutral-gas motions are perfectly 
 
horizontal, he reasoned that vertical neutral-gas motions, if present, 
 
 might account for the occasional discrepancies. By programming a 
 
 rocket to release puffs rather than a continuous trail of TMA (trim- 
 
 ethylaluminum) , he was able to determine vertical as well as horizontal 
 
 neutral-gas velocities. In the single case he reported, these vertical 
 
 motions (as great as 24 m/ s) were found to be the dominant contribution 
 
 to ion convergence. 
 
 The present paper deals, in a general way, with the role of 
 
 vertical neutral-gas motions in producing ion convergence at E -region 
 
 heights. Section 2 briefly reviews the observations of such motions and 
 
 the theory of their origin, both of which suggest that the motions are of 
 
 turbulent or internal -gravity -wave origin. The next three sections 
 
 assume, corresponding to the usToal practice in applications of the 
 
 magnetoshear theory, that only the vertical ion velocity u. is rele- 
 
 iz 
 
 vant, and explore the implications of including non-zero vertical neutral - 
 
 gas motions in the standard equations for u. . Section 3 shows that 
 
 ° iz 
 
 because the ratio of ion -neutral collision frequency to ion gyrofrequency 
 is large in the lower E region, vertical neutral-gas motions, even if 
 small compared with the horizontal neutral -gas motions, contribute 
 significantly to u. . Section 4 shows that vertical neutral-gas motions 
 of internal gravity-wave origin affect u. in such a way as to favor E 
 production by waves propagating in certain azimuthal directions. Such 
 vertical motions similarly affect the wave transport of ionization (the 
 so-called corkscrew mechanism discussed by Axford (1961, 1963) and 
 Chimonas and Axford (1968). In particular, they change the height at 
 which a layer is dumped by a wave (sec. 5). 
 
 Section 6 suggests, however, that in applications where the 
 vertical neutral-gas velocities are significant, their effects on u. and 
 hence on ion convergence may be cancelled by accompanying effects of 
 the wave on the horizontal ion motion. As a resiilt, the theory developed 
 
 -2- 
 
in sections 3 through 5 may be of merely academic interest. By the 
 same token, however, section 6 suggests that sporadic -E experiments 
 in which only the vertical wind variation is measured and wind variations 
 in the horizontal are ignored, do not provide a definitive test of the 
 theory. Section 7 contains concluding remarks. 
 
 2. VERTICAL MOTIONS OF THE NEUTRAL GAS AT E -REGION HEIGHTS 
 
 Few observations of neutral-gas vertical motions at E -region 
 heights have been reported. Manning et al. (1950) found the mean winds 
 to be horizontal to within a few degrees. They later found that while 
 the vertical component of these mean motions was very nearly zero, it 
 could possibly be as large as 3 m/ s (Manning et al. , 1954). On the 
 other hand, they found the rms irregular vertical winds to lie between 
 and 20 m/ s for the various times they attempted the relevant data 
 reduction. They attributed these vertical motions to turbulence, but it 
 is now believed (Hines, I960, 1963) that a significant component of the 
 motions considered turbulent at that time is, in fact, properly a portion 
 of the internal -gravity -wave spectrum. 
 
 Elford and Robertson (1953) found vertical motions of relatively 
 great horizontal extent ( > 50 km) and persistence ( > 1 hr) that varied 
 between + 6 m/ s. The average angle of tilt of the wind vector from 
 the horizontal was less than 5* . They pointed out, however, that more 
 irregular motions of the neutral gas, even if present, would not be 
 detected by their observational method. 
 
 Because early observations revealed the dominance of the hori- 
 zontal motions of the neutral gas at E -region heights, many of the data 
 obtained on neutral gas motions since then have been reduced routinely 
 on the assumption that the observed motions are strictly horizontal. 
 There are, fortunately, several exceptions: 
 
 -3- 
 
(a) By studying the motion of filaments of rocket releases that 
 had been blown nearly horizontal by a large wind shear, Manring et al. 
 (1961) measured vertical neutral-gas velocities in two separate cases, 
 finding in the first case a mean downward motion of 3. 67 m/ s and in 
 the second an average upward velocity of 10 m/ s. 
 
 (b) By photographic observations of chemical releases, Moseley 
 and Justus (1967) found an rms turbulent vertical velocity at E -region 
 heights the order of 1 5 m/ s. The turbulence appeared to be isotropic, 
 
 (c) Murphy et al, (1967) found that the motion of a cesium cloud 
 at 100 km, observed optically, had a 35 m/ s upward component for a 
 period of several minutes. Later motion of the cloud was deduced in- 
 directly from iono sonde data; it apparently moved upward at 3 m/ s for 
 at least 10 min. The authors also reported optical observations of the 
 apax of a TMA rocket trail that indicated a mean upward velocity of some 
 30 m/ s throughout a 4-min observing period. 
 
 (d) MacLeod (1968) measured the vertical motion height profile 
 at Arecibo in the manner described briefly in section 1. He found a 
 rather oscillatory vertical velocity profile with an amplitude of the 
 order of 10 to 20 m/ s. He gave no information about the persistence 
 of this profile. 
 
 (e) Wright and Fedor (1969) describe an extension of the radio 
 drift measurement technique that permits measurements of the vertical 
 drift of small-scale ionospheric irregularities. They tentatively equate 
 the vertical drifts they observe with the vertical neutral -gas velocity 
 at the irregularity height, and find E -region vertical velocities up to 
 
 15 ral s by this means. 
 
 Accoi-ding to theory, vertical neutral-gas motions of the order 
 of a few centimeters per second if constant for periods of several days 
 and if of wide spatial extent, should have profound, easily detectable 
 atmospheric effects on temperatures (Kellogg, 1961), on airglow 
 
 ■4- 
 
(Tohmatsu and Nagata, 1963; Gadsden and Marovich, 1969), and on 
 noctilucent cloud forniation (Chapman and Kendall, 1965). The prevail- 
 ing vertical motions indeed appear to be limited to this small magnitude. 
 
 Liindzen (1967) has calculated the vertical motions resulting 
 from the thermally driven diurnal tide in an equinoctial, isothermal 
 model atmosphere. His results show that at the equator, where the 
 amplitude of the vertical velocity fluctuations is largest, both in absolute 
 terms and relative to the horizontal motions, it is of the order of 1 m/ s 
 at E -region heights. 
 
 Internal atmospheric gravity w3.ves are similar in many respects 
 to atmospheric tides. They are characterized by smaller temporal 
 and spatial scales, however, so that the earth' s rotation and spheri- 
 city can be ignored in their description, 
 
 Hines (i960) finds that for a single plane internal gravity wave of 
 
 angular frequency uo, horizontal wave number k^ , and vertical wave 
 
 number k satisfying 4k^ >> 1/H^ , where H is the neutral-gas 
 z z 
 
 scale height, 
 
 ^ • ^ . (2.1) 
 
 The gravity-wave dispersion equation in this case reduces to Hines, 
 1960) 
 
 k^ X? T^-T^ 
 
 ^ 
 
 ^=-T^^ . (2.2) 
 
 X2 t2 
 
 z g 
 
 where thZtt/oj is the wave period and t - 2n C/ [(y -l)^g] is the 
 Brunt period. At E -region heights, t^^| nain and H ~ 6 km. 
 Figure 1 shows the dependence of the ratio iu^/uj on the ratio t/t 
 
 g 
 
 -5- 
 
Hines (I960) foiond that waves of 12 -km vertical wavelength and 
 a period of the order of 1 to 2 hours were dominant in the meteor trail 
 observations. Kochanski (1964) found from analysis of rocket release 
 trails an average amplitude for the wave -associated horizontal velo- 
 cities of '^ 50 m/ s. From the above equations one finds an average 
 amplitude for the vertical motions associated with these dominant 
 waves of ^ 2. 5 to 5 m/ s. Hines (1963) noted that smaller-scale waves 
 (with vertical wavelengths of the order of 1 km) seemed to contribute 
 the same amount to the total wind shear as did the larger -scale, domi- 
 nant waves. Thus the horizontal motions associated with the smaller - 
 scale wave components must be ~ 5 m/ s. He also pointed out that 
 such small-scale waves must have very short periods or else they 
 would be subject to severe viscous dissipation at these heights. He con- 
 cluded that their horizontal and vertical wavelengths must be compar- 
 able. The equations above tell us that in this event the smaller -scale 
 wave components must also cause vertical motions of '-^ 5 m/ s. Thus 
 the smaller-scale wave components may well be the important contri- 
 butors to the vertical neutral-gas motions at E -region heights. 
 
 The above numbers represent average values. Some fraction of 
 the broad spectrum of waves present at any one time may well be creat- 
 ing vertical motions > 10 m/ s. For example, Rosenberg (1966) states 
 that while the mean maximum wind shear at E -region heights is 0. 02 s" , 
 the maximum wind shear at these heights is on occasion as great as 
 0. 1 s"^ . A wave of 1 -km horizontal and 1 -km vertical wavelength, the 
 smallest -scale wave that can survive viscous dissipation at these 
 heights, would generate 8 m/ s vertical motions in creatiag this shear. 
 A wave of 10 -km vertical wavelength and 100 -km horizontal wavelength 
 would generate 20 m/ s vertical motions in creating this shear. 
 
 -6- 
 
T/Tr 
 
 Fig. 1. The ratio of internal-gravity-wave -produced horizontal to 
 vertical velocities as a function of the ratio of the wave 
 period T to the Brunt period T . The solid curve is 
 calc\ilated from (2. 1) and (2. 2). The dashed curve shows 
 
 the approximate result ju, /u \ = t/t 
 
 g 
 
 Neutral -gas turbulence at low E -region heights is maintained by- 
 processes not yet fully \inder stood, but it seems likely that the energy 
 for its maintenance is supplied by dissipation of internal atmospheric 
 gravity waves and the atmospheric tides (Hines, 1963, 1965). Hines 
 (1965) estimates the rate of wave energy loss per unit mass e to be of 
 the order of 10 ^ watt/ kg. This estimate is a factor of 10 larger than 
 the estimate he had used previously (Hines, 1963) to determine the order 
 of magnitude of the turbulent velocity v associated with the large-scale 
 eddies, and gives v < 10 m/ s, which agrees in order of magnitude 
 with the findings by Moseley and Justus (1967). 
 
 -7- 
 
In conclusion, then, the largest vertical neutral -gas motions at 
 E -region heights are probably produced by motions of small temporal 
 and spatial scales, caused by internal gravity waves and turbulence. 
 The gravity-wave -associated vertical neutral-gas motions should 
 typically be '-^ 5 to 10 m/ s, some 10 percent of the dominajit horizontal 
 motions, though they may be larger on occasion. Turbulence -associated 
 vertical motions of the neutral gas may be typically '--IS m/ s. The 
 vertical motions of the neutral gas are probably only rarely comparable 
 to the horizontal. If the two types of motion are to be of roughly eqaal 
 importance in producing ion convergence, the reason must lie in other 
 factors, discussed in the next section, 
 
 3. VERTICAL NEUTRAL-GAS MOTIONS IN THE MAGNETOSHEAR THEORY 
 
 According to the raagnetoshear theory, the mean ion velocity 
 u. at any point is related to the mean neutral-gas velocity u at that 
 point by (MacLeod, 19 66) 
 
 u 
 
 i 1+ p' 
 
 1 
 
 p^ u+ p. (u X r) + (u . r)r 1 , o.i) 
 
 where p. = v./uo. is the ratio of the ion -neutral momentum transfer 
 
 1 11 
 
 collision frequency V. to the ion gyrofrequency uo. , and T is a unit 
 
 1 1 '^ 
 
 vector directed parallel to the earth' s magnetic field. Here inertial 
 effects, electric field effects, and diffusion effects are ignored. 
 I This equation has rarely been applied in its general form. In 
 
 the usual applications it is assumed first tbat only the vertical ion 
 velocity is of interest: 
 
 -8- 
 
u. = T^-2 r{p^ + r^) u + p.r u +r r u 1 , (32) 
 
 iz 1 + pi L 1 z z 1 y X y z y J w» '^Z 
 
 where x, y, and z are the axes of a Cartesian coordinate system -with 
 X-axis directed toward geomagnetic east, y-axis directed toward geo- 
 magnetic north, and z-axis directed vertically upward. It is then 
 
 assumed that u = 0, so that 
 z 
 
 u. = Y^TS- [P-^ u + r r u ] . (3.3) 
 
 izl + plLiyxyzyJ 
 
 A number of authors have pointed out that at E -region heights at low 
 magnetic latitudes (where tenaperate -latitude E occurs most fre- 
 quently) , p. > > F , so that if u and u are comparable, or if u 
 
 greatly exceeds u , 
 
 P. r u 
 
 1 y X 
 
 -i.-^r^ ■ (3.4) 
 
 1 
 
 In part this sinnplification results from the fact that p. > 1 throughout 
 the E region and that p. > > 1 in the lower part of the E region. 
 
 Note, however, that if p >>1, then u , when unequal to 
 
 i ^ 
 
 zero, may be relatively the more important contributor to u^^ , even 
 
 if u < < u , u , since the u coefficient in (3.2) is of the order of 
 
 z X y z 
 
 p^ . Thus, for example, if u - 0. 1 u , as suggested in section 2, 
 
 the contributions for u. from the two velocities should be roughly 
 
 iz 
 
 equal when p.'- 10, and the contribution to u. from u maybe 
 
 1 
 
 dominant when p. > 10. 
 
 1 
 
 -9- 
 
At the moment, p. is not well known as a function of height. 
 Figure 2 shows several estimates of this quantity. MacLeod' s (1966) 
 estimate is taken from Axford (1963, fig. 2) which is in turn based on 
 Ratcliffe (1959, fig. 6). These estimates were apparently obtained by 
 dividing by 50 the theoretical estimates for the electon -neutral colli- 
 sion frequency as a f\inction of height calculated by Nicolet (1953). Be- 
 cause theoretical and observational estimates of the electron -neutral 
 collision frequency at E -region heights still disagree (Thrane and 
 Piggott, 1966), the validity of this profile may be somewhat question- 
 able. Wand and Perkins (1968) calculated a v. height profile usiag the 
 CIRA (1965) model atmosphere and formulas for the ion -neutral 
 momentum transfer cross section obtained by Banks (1966). In this 
 paper this V. height profile has been converted into a p. height pro- 
 file by dividing by uo. = 1. 62 X ICP sec"""" (the value of uo. appropriate 
 to the E region at Boulder) and multiplying by 0. 5 to convert the coUi- 
 sional frequency into a "frictional" frequency (see, for example, Stubbe, 
 1968). Wand and Perkins also measured v. height profiles (similarly 
 converted into p. profiles in this paper) using the incoherent scatter 
 technique. Their results suggest significant temporal variations in this 
 quantity (see also Wand, 1969). The Wright and Fe dor (1970) p. pro- 
 file shown is based on Banks' (1966) results and a model atmosphere 
 developed by Shimazaki (1967). Variations of p. with ionic species, 
 latitude, and time complicate the picture further. 
 
 Figure 2 shows that the various estimates for p. differ by as 
 much as a factor of four. Thus, according to MacLeod (1966), p. > 10 
 only at heights below 100 km, while according to Wright and Fedor 
 (1970), p. > 10 at all heights below 104 km. The profile computed 
 from the CIRA (1965) model atmosphere suggests that p. > 10 at all 
 heights below 107 km. 
 
 -10- 
 
10- 
 
 102 
 
 p. 10 
 
 MacLeod 
 
 Axford 
 Ratcliffe 
 
 (1966) 
 (1963) 
 (1959) 
 
 Wand and Perkins (1968) 
 calculaled 
 
 Wright and Fedor (1970) = 
 
 10- 
 
 Wand and Perkins (1968) 
 measured Sept.5, 1967 
 
 0818-0951 AST 
 
 0951-1122 AST 
 
 _L 
 
 90 100 
 
 110 120 130 
 Height (km) 
 
 140 150 
 
 Fig. 2. Various estimates of tibe dimensionless parameter p.=V./iu. 
 as a function of height. 
 
 Which p. profile one uses, then, may determine the impor- 
 tance to be attached to vertical motions of the neutral gas in producing 
 ion convergence. In -what follows the Wright and Fedor (1970) profile 
 is taken to be representative. 
 
 Vertical neutral-gas velocities, if typically some 10 percent of 
 the horizontal velocities, as suggested in section 2, should then be 
 important contributors to the vertical ion velocity at heights below 
 about 110 km, where they may affect the latter velocity by as much as 
 30 percent, while they should be dominant contributors to the ion 
 vertical velocity at heights below 104 km. In a few instances, when 
 
 -11- 
 
the vertical velocities may be an even larger fraction of the total 
 neutral-gas velocities, they may contribute significantly to the ion 
 velocities even at the greater heights. 
 
 Note that p. '--50 in the height range of 90 to 100 km. Values 
 of p. of this magnitude imply that even small vertical neutral-gas 
 motions of tidal origin might be as important as horizontal neutral- 
 gas motions in producing ion convergence at these heights. 
 
 Ion convergence depends, of course, not only upon the ion 
 velocity but also upon the variation of that velocity. The physical 
 quantity of interest in the magnetoshear theory is the divergence of 
 the ion fltix, 
 
 Z' (N. ^i)=u. . VN.+N. V. u. , ^ (3.5) 
 
 where N. is the ion number density (equal to N , the free electron 
 nuniber density). It is known from observations that vertical gradients 
 of ionization density in E layers are much greater than the corre- 
 spending horizontal gradients. Observations of neutral-gas motions 
 also show that the dominant motions exhibit vertical variations much 
 greater than the corresponding horizontal variations. Asa result, 
 (3. 5) is usually written as (although see sec. 6) 
 
 SN. du. 
 
 V • (N u. ) i u. — - + N. -^ . (3.6) 
 
 ^ 1 '^1 IZOZ lOZ 
 
 Ionization may accumulate near levels where the negative of this 
 
 expression (the convergence) achieves maximum values, to an extent 
 
 limited by ion diffusion and chemical loss. The ion velocity u thus 
 
 iz 
 
 contributes to ion convergence in two we It- known ways. First, it may 
 act on a large gradient of N. to produce convergence. Vertical and 
 
 -12- 
 
horizontal neutral-gas velocities contribute to ion convergence through 
 this term in the same proportion as they contribute to the ion velocity 
 itself. Thus, when vertical neutral-gas motions are an important con- 
 tributor to u. itself, they are an important contributor to this term 
 
 iz 
 
 of the ion convergence. 
 
 The ion velocity may also exhibit large, rapid spatial varia- 
 tions, thus contributing significantly to the ion convergence through the 
 rightmost term of (3. 6). The relative contribution of vertical and 
 horizontal neutral-gas velocities to this term depends not only on their 
 relative magnitudes, but also on their spatial variation. If the spatial 
 
 variations of u and u are related, as when for example both 
 z X 
 
 motions are associated with the passage of a single atmospheric wave, 
 then their relative contribution to the rightmost term of (3. 6) is again 
 
 the same as their relative contribution to u. itself. 
 
 iz 
 
 The situation is more complicated when all the neutral-gas 
 motion present is of wave origin and several waves are present. 
 Models could obviously be chosen that would lead to almost any con- 
 clusion concerning the relative importance of wave -associated vertical 
 and horizontal neutral-gas motions in producing sporadic-E layers, and 
 in the light of our present poor knowledge concerning details of the 
 upper atmospheric motions, any such discussion must be speculative. 
 
 Nevertheless, one simple case is instructive. Suppose there 
 
 are two internal gravity waves present, both satisfying (2,1). Suppose, 
 
 further, that the first of these waves has a 10 -km vertical wavelength 
 
 and a 60-min period, while the second has a 1 -km vertical wavelength 
 
 and a 10-min period. It follows from (2. 2) (remembering that 
 
 T ~ 5 min) that the vertical neutral-gas motions associated with the 
 
 g 
 first wave are --^ 0, 1 of the corresponding horizontal motions, while 
 
 the vertical neutral -gas motions associated with the second wave are 
 
 -13- 
 
comparable to the corresponding horizontal motions. Suppose in addi- 
 tion that the neutral -gas wind shear resulting from each of the two 
 waves is comparable, as Hines (1963) has suggested would typically be 
 the case (see sec. 2). Then 
 
 K^ ^T,i ^^.9 ^1,9 ' (3.7) 
 
 z 
 
 1 hi z2 h2 
 
 where the subscripts 1 and 2 refer to the first and second waves 
 respectively. Since k .'-'0.1k , u^ must be ^ 10 u- . The hori- 
 zontal motions of the larger -scale wave are the dominant motions 
 present. The wave -associated vertical motions in this case are some 
 10 percent of the horizontal motions, and they would probably not be 
 noticed in the usual type of wind measurement now made. 
 
 It follows from (2. 1) that 
 
 V^^^^zl ^^^ ^2^^z2 ' ^^-^^ 
 
 so that while k , u , , the variation of u . in the vertical direction, 
 zl zl zi 
 
 is only ~ 0. 1 k ^ u . , just as u -^ 0. 1 u.^^, it turns out that 
 
 k ^ u ^ -^ k , XI, , , even though u ^ -- 0. 1 u, , . This suggests that in 
 z2 z2 zl hi z2 nl 
 
 the typical case, the contribution of the small-scale vertical motions of 
 
 the neutral gas to the ion convergence may be much more important 
 than the relative magnitudes of the horizontal and vertical neutral-gas 
 
 motions might suggest. 
 
 •14- 
 
4. VERTICAL NEUTRAL -GAS MOTIONS AUGMENTING AND OPPOSING 
 CORRESPONDING HORIZONTAL MOTIONS 
 
 Obviously, if the amplitude and phase of the vertical and hori- 
 zontal motions of the neutral gas are not physically related, these 
 motions may in general act either in concert or in opposition in pro- 
 ducing ion convergence, to the resulting benefit or detriment of the 
 ionospheric irregularity so produced. Even when the two components 
 of motion are related in amplitude and phase, however, as they are 
 when associated with the passage of a single atmospheric wave, they 
 
 may still act either in concert or in opposition. Consider, for example, 
 a single, plane internal gravity wave propagating either due east or 
 west in an otherwise stationary atmosphere. Then (3,2) reduces to 
 
 ^- = TT~nS r (p^ + r^ ) u + p. r u 1 . (4. 1) 
 
 iz 1+pLi zz lyxJ ^ 
 
 Using (2.1), one fmds that 
 
 Thus, whether the effects of u and u add to produce a relatively 
 
 X 
 
 large u. , and hence a larger convergence or divergence of ionization, 
 
 or partially or completely cancel to produce a small u. , and hence a 
 
 small convergence or divergence of ionization, depends only upon the 
 
 sign of k /k , since p. > and T (which is directed northward) is 
 X z 1 y 
 
 of the same sign in both hemispheres. Most internal gravity waves are 
 
 thought to be energized below the region of observation and thus to have 
 
 vertically upward energy propagation and vertically downward phase 
 
 propagation, i.e., a negative k (Hines, i960). Therefore, when 
 
 z 
 
 -15- 
 
k > (when the wave is propagating eastward), the effects of vertical 
 and horizontal wave -associated motions of the neutral gas add con- 
 structively, while when k < (when the wave is propagating westward), 
 the effects cancel partly or completely. It follows that two waves, alike 
 in all respects other than the sense of their east-west propagation, may 
 have ionospheric effects of different magnitude (see also Hooke, 1968, 
 1969b). 
 
 It also follows that, when k /k is negative, u. has the same 
 
 X z iz 
 
 sign it would have if only the horizontal component of the neutral-gas 
 motions were present; only the magnitude of u. relative to u is 
 changed. In this case, regions considered to be regions of ion conver- 
 gence based only upon measurements of the horizontal motions will then 
 still be regions of convergence when the measurements of the vertical 
 motions present are included. Comparisons between theory and experi- 
 ment on the positions of the E -layer height should then agree, even 
 though it may be the vertical neutral gas motions, traditionally ignored, 
 that are the raajor contributors to the ion convergence. 
 
 When k /k is positive, however, u. may have either the 
 X z iz 
 
 same sign it would have had if only the horizontal component of the 
 neutral-gas motions had been present, or, if the vertical neutral-gas 
 motions are the dominant contributor to the ion convergence, the 
 opposite sign. In the fornaer case, the magnitude of u. will be greatly 
 reduced; in the latter, we may expect to find discrepancies between 
 observed E -layer heights and E -layer heights calculated on the 
 basis of assumed purely horizontal motions of the neutral gas. 
 
 -16- 
 
5. VERTICAL NEUTRAL-GAS MOTIONS AND THE CORKSCREW EFFECT 
 
 Axford (1961, 1963) and Chimonas and Axf ord (1968) have deve- 
 loped the subject of downward vertical ion transport by atmospheric 
 waves. This effect, known as the corkscrew effect, may be simply 
 described as follows: 
 
 It is well known that the wind patterns observed at E -region 
 
 heights are not stationary. Instead, they progress vertically downward 
 
 with time, because much of the atmospheric motion at these heights is 
 
 of wave origin, and because the waves, energized from below, exhibit 
 
 a vertically downward phase propagation. E layers tend to form in 
 
 convergent regions of the wind profile at heights where the downward 
 
 velocity of the individual ions of the layer matches the vertical phase 
 
 velocity v of the waves, i. e. , where u. = v , and follow the v/ave 
 z iz z 
 
 downward. In predicting E -layer heights, therefore, it is not enough 
 to know the wind profile at a given instant; one must also know the phase 
 velocity of this pattern. According to the usual picture (modified below) 
 in which u = 0, the amplitude of the fluctuations in the velocity u. 
 decreases with decreasing height, primarily because the coefficients 
 of u and u in (3,2) decrease with decreasing height roughly as pT^ 
 and pT , respectively. Below some height, the amplitude of the fluctu- 
 ations in u. falls below the value of v , and the E layer can no 
 iz z s "^ 
 
 longer follow the downward phase progression of the wave; the ionization 
 
 is "dumped", (It does continue to exercise an oscillatory motion with a 
 
 mean downward drift much less than the wave phase velocity, however; 
 
 see Chimonas and Axford, 1968), 
 
 The contribution of vertical neutral -gas motions to u. obviously 
 
 plays an important role in determining the height at which an E layer 
 
 s 
 
 is dumped by the atmospheric wave responsible for its transport, 
 especially since the relative importance of the vertical neutral-gas 
 
 -17- 
 
motions is greatest at the lowest E -region heights, where the dumping 
 
 occurs. While the contributions to u. (see (3.2)) from u and u 
 
 '-1Z X y 
 
 decrease roughly as p. and p~ with decreasing height, the contribu- 
 tion to u. from u remains roughly constant throughout the lower 
 iz z 
 
 E region. Again, whether the vertical motions present tend to increase 
 
 or decrease the amplitude of the u. variations - and hence to decrease 
 
 iz 
 
 or increase the dumping height - depends upon whether they act in con- 
 cert with or opposition to the action of the horizontal neutral-gas motions 
 in creating ion convergence. This in turn depends upon the direction of 
 propagation of the waves responsible for the motion (see sec. 4). 
 
 These features are illustrated in figures 3, 4, and 5. Figure 3 
 
 shows a plot of the maximum downward velocity u. within the shear 
 
 iz 
 
 layer as a function of height computed from (3. 2) under the assumption 
 
 u = u =0, and u = -50 m/ s, and based on values for the u coef- 
 z y X X 
 
 ficient tabulated by Wright and Fedor (1970). Also shown are the dump- 
 ing heights corresponding to v = -2. 5 m/ s and 0. 25 m/ s. The value 
 
 z 
 
 V = -2. 5 m/ s is the vertical phase velocity of a gravity wave of 9 -km 
 vertical wavelength and 1 -hour period, while the value v = -0. 25 na/ s 
 is taken to correspond roughly to the vertical phase velocity of the di- 
 urnal tide; u = 50 m/ s is chosen as a moderate amplitude for the 
 wave -associated winds. Figure 3 shows that this maximum downward 
 velocity falls below v , that is, the wave dumps its associated E 
 layers at a l05-km height in the gravity -wave case, and at 93 -km height 
 in the tidal. 
 
 It is assumed in the construction of figure 3, in disregard of 
 
 fact, that u =0. We now examine the changes in figure 3 and the 
 z 
 
 conclusions drawn from it when u 7^ 0. In the construction of figure 4, 
 
 z 
 
 the ratio u. /u is calculated from (4.2); the remaining assumptions 
 iz X 
 
 remain unchanged. The value of |k /k | is taken to be 0. 01, that of 
 
 -18- 
 
(uj>i) mbpH 
 
 •H 
 
 E 
 
 o 
 
 ^4 
 
 O 
 
 
 m 
 
 .5P 
 
 to f^ 
 
 <U CO 
 
 (U 
 +-> 
 
 B-8 
 
 CO 
 
 ^ 
 
 o o 
 
 • H 
 
 In 
 
 CO t: 
 CO jj 
 rt „ 
 
 I 
 
 o 
 
 CO 4j^ 
 
 2 CO „-. <1 
 
 bO 53 >^ ""^ 
 
 •"-I rCj ^"^ CO 
 
 50 > jU *^ 
 
 g j5 « in 
 
 3 S t^ f^ O 
 
 ^ +J .. .. 
 
 
 (Lu>|) iq5!9H 
 
 -19 
 
120 
 
 £ 
 
 X 
 
 100 
 
 80 
 
 J L 
 
 J L 
 
 J L 
 
 -12 
 
 -4 
 Uj2 (m/s) 
 
 Fig. 5. 
 
 The maximum downward ion velocity u. within the shear 
 layer computed from (4, 2) on the assumption u = -50 m/ s, 
 |k /k \ = 0. 1, and v = -2. 5 m/ s. Also shown is the 
 dumping height (x) for the westward propagating wave. 
 
 V is taken to be -0. 25 m/ s, and that of u is taken to be 50 m/ s. 
 z X 
 
 Note that for k /k =0.01 (westward -propagating wave) the dumping 
 height increases to 100 km, while there exists no dumping height for 
 k /k = -0. 01 (eastward-propagating wave). In fact, of course, con- 
 servation of energy requires that at heights below 100 km \n \ de- 
 creases with decreasing height (see Hines, I960) contrary to the assump- 
 tion made here, so that ultimately even an eastward -propagating wave 
 should dump its trapped ionization. Similar comments apply to the 
 
 internal -gravity -wave example depicted in figure 5. Here jk /k | is 
 
 ^ z 
 
 taken to be 0. 1, v is taken to be -2. 5 m/ s, and u is again taken 
 
 z ^ 
 
 to be -50 m/s. The westward -propagating wave dumps its trapped 
 ionization at a height of 113 km, while the eastward -propagating wave 
 would carry its ionization downward through all altitudes, were it not 
 for the decrease in wave amplitude with decreasing height not taken into 
 accoiint here. 
 
 -20- 
 
Thus it seems that the westward -propagating waves dump their 
 trapped ionization because the efficiency of the magnetoshear process 
 decreases with decreasing altitude and because wave -associated verti- 
 cal motions oppose the action of the wave -associated horizontal motions 
 in the convergence process. The wave -associated vertical motions 
 can increase the dumping height by as much as a scale height. The 
 eastward-propagating waves, on the other hand, dump their trapped 
 ionization not for this reason but rather because of the decrease of 
 wave amplitude with decreasing height. 
 
 It should be mentioned, however, that when wave -associated 
 
 vertical ion velocities are important to ion transport, wave -associated 
 
 horizontal phase velocities are also important. It is not enough that 
 
 the vertical ion velocity u. = v ; instead the ion motion must satisfy 
 
 ±z z 
 
 the condition k • u. = o) for effective transport to occur. This requires 
 a three-dimensional treatment of the problem. 
 
 6. E LAYERS PRODUCED BY TRANSVERSE WAVES 
 
 The preceding sections contained the implicit assumption, 
 us\aally made in applications of the magnetoshear theory, that the rele- 
 vant ion velocity is the vertical component, u. , and that the other 
 components of u. may be ignored. It is easy to show this assumption 
 
 is a poor one. Consider the formation of an E layer in an originally 
 
 s 
 
 homogeneous ionosphere. Then 
 
 7 • (N u.) = N V • u. . (6.1) 
 
 If u varies rapidly (on spatial scales ~ one scale height or less), 
 then variations in u. resulting from variations in p. (see MacLeod, 
 (1966) are negligible compared with variations in u. caused by variations 
 
 ■21- 
 
in u . If the neutral -gas motions are themselves of wave origin, then 
 V • u =-ik • u , where k is the wave vector, and (3,1) can be used to 
 give 
 
 ^ • ^- - 1 1^3 r p^ k • u+ p. r . (kx u) + (u • r)(k • r)l . 
 
 (6.2) 
 
 Note that this expression contains all the components of u. , including 
 
 u and u , the components that are usually neglected in calcula- 
 
 ix ly 
 
 tions of ion convergence. 
 
 For internal gravity waves and the atmospheric tides, however, 
 k • u = (see, e. g. , Hines, i960), so that 
 
 /•sj r-^ 
 
 V • u. = riWrp. r- (kxu) + (u- r)(k. r)l . 
 
 (6.3) 
 
 P' 
 
 1 
 
 The term p^ u of (3.2), the term usually neglected but emphasized 
 by MacLeod (1968) as important has been cancelled b y other terms 
 appearing in the other component equations of (3. 1) that are also 
 usually ignored. 
 
 This raeans that vertical neutral -gas motions of wave origin 
 should in fact play only a minor role in creating E layers, although 
 once the layer is created, they may play an important role in 
 intensifying , maintaining , or destroying it. Even in this case, 
 however, considering u. and neglecting u. and u. implies 
 
 keeping terms of the order of [p^ / (1 + p^)]u dN./dz and neglecting 
 
 1 1 Z 1 o e> 
 
 terms of the order of [p^/(l + p!)] u dN./3x. It is not obvious, a 
 
 11X1 
 
 priori, that this procedure is at all legitimate. In fact, it woxild appear 
 
 -22- 
 
that the opposite is so, and that any assumption such as the above should 
 be justified empirically on a case by case basis. J. D. Whitehead (pri- 
 vate communication) has raised similar questions. 
 
 Asa result, the development of sections 3 through 5 may be of 
 only academic interest. Unfortunately, however, this Cctncellation also 
 implies that to specify the neutral-gas wind field at E -region heights 
 for comparison of magnetoshear theory with observed E -layer heights 
 and intensities, puffs giving the height variations of all three wind 
 components are insufficient. The horizontal variations of all three 
 wind components are also required, 
 
 7. CONCLUDING REMARKS 
 The work presented above prompts the following conclusions: 
 
 (a) The limited observations and theory available suggest 
 strongly that vertical neutral-gas motions at E -region heights are of 
 amplitude sufficient to be important in the study of sporadic E. 
 
 (b) These vertical motions may act either in concert with, or in 
 opposition to, the action of horizontal motions of the neutral gas in pro- 
 ducing ion convergence, not only when the state of E -region motion is 
 chaotic but even in cases when the components of motion are associated 
 with a single -wave system. They may therefore affect not only the 
 magnitude but also the sense, or sign, of the ion convergence, changing 
 the E -layer intensity, E -layer height, and the dumping height. It 
 appears that eastward -propagating waves should be more successful 
 than westward -propagating waves in producing E layers, 
 
 (c) There is theoretical reason to expect that the full magneto - 
 shear equation (3. 1) and not just the vertical component (3. 2) of that 
 eq\iation, together with full knowledge of the state of E -region neutral- 
 gas motion, are required to obtam a consistent agreement between the 
 
 ■23- 
 
magnetoshear theory and observation. Such discrepancies as now 
 exist appear to resiilt from an incomplete specification of neutral-gas 
 motion rather than from any basic shortcomings of the miagnetoshear 
 theory itself. 
 
 Since eastward-propagating waves appear to be more successful 
 than westward -propagating waves in creating E layers, one might 
 conclude that most E layers should be observed traveling eastward. 
 There is some evidence that the o pposite is the case (Egan and Peterson, 
 1962). This may pose a serious problem for E theory. 
 
 The observations, however, reflect the outcome of an interplay 
 among several competing factors. For instance, Hines (1963) and 
 Hines and Reddy (1967) show that wind -shear filtering may cause con- 
 siderable a-nisotropy in the directions of wave propagation at ionosphe- 
 ric heights. Perhaps in some cases, only westward propagating waves, 
 or only eastward -propagating waves, are permitted at these altitudes. 
 Then any E "patches", or "clouds" observed must be propagating in 
 that direction. The rates of photochemical processes in E layers are 
 affected by atmospheric waves in a way dependent upon the direction of 
 wave propagation (Hooke, 1969a; 1969b); this may also influence the 
 preferred direction of E "patch" or "cloud" travel. 
 
 Moreover, T, M, Georges (private communication) has noted 
 that the HF ground backscatter observations of Egan and Peterson 
 suggest that E patches move circumferentially, indicating an obser- 
 vational bias of some kind. 
 
 Finally, the dominant atmospheric tides (which are also likely 
 to be the principal contributors to E ) propagate only westv^^rd. 
 
 -24- 
 
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 -25- 
 
Hines, C. O, , (I960), Internal atmospheric gravity waves at iono- 
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 -26- 
 
Manning, L. A., O, G. Villard, Jr., and A. M. Peterson, (1950), 
 
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 -27- 
 
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 -28- 
 
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 -29- 
 
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