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On plume meandering under stable stratification
Atmospheric Environment Vol. 24A, No. 8, pp. 1979 1985, 1990. Printed in Great Britain.
0004~981/90 $3.00+0.00 ~, 1990 Pergamon Press pie
ON PLUME MEANDERING UNDER STABLE STRATIFICATION D. ETL1N~ Institut ffir Meteorologie und Klimatologie,Universit~itHannover, HerrenhfiuserStr. 2, 3000 Hannover 21, F.R.G. (First received 10 January 1989 and received for publication 29 September 1989)
Abstract--Under stable stratification and light winds large horizontal wind direction fluctuations have been observed quite often leading to meandering of pollutants plume downwind of elevated point sources. Due to this plume meandering long term concentration levelscan be reduced by a factor of 4 or more, compared to straight plume conditions. Some possible mechanisms causing plume meandering under stable conditions are discussed, including gravity waves and vortices with horizontal or vertical axis. Key word index: Plume meandering, stable stratification.
1. INTRODUCTION Air pollutants emitted from point sources are transported and dispersed by mean wind and wind fluctuations in the atmospheric boundary layer. In case of a continuous release the pollutants may form a coneshaped plume in the downwind side of the source. In this case, diffusion of material is due to small-scale turbulence (high frequency motions) with scales comparable to the plume width, sometimes called relative diffusion. On some occasions horizontal undulation (meandering) of the plume can be observed, due to eddies (low frequency motions) with length scales larger than the plume width. This is also referred as to single parti7le diffusion (Hanna, 1986; Skupniewicz, 1987). Although there are also vertical fluctuations of the plume, we will concentrate on the horizontal meander here. As is known from field experiments and theoretical considerations (Kristensen et al., 1981; Hanna, 1983), averaged concentrations of pollutants under meander conditions can be factor of 2-6 lower than for the situation with straight plumes downwind of point sources. Plume meandering may occur under different atmospheric conditions but is most effective for stable stratification and low wind speeds (Hanna, 1981; Leyi and Panofsky, 1983; Leahey et al., 1988). Observed meander periods range from say 5 min to 2 h and are assumed to be caused by gravity waves or vortices with horizontal or vertical axes. Some of the possible mechanisms causing plume meandering are discussed in this paper,
2. WINDDIRECTIONFLUCTUATIONS Lateral diffusion of air pollutants downwind of a point source is caused by wind velocity fluctuations v'
with standard deviation tro. In the widely used Gaussian plume model the standard deviation of the lateral concentration fluctuation %, for example, is related to cry,by (see, e.g. Pasquill and Smith, 1983) try, % = u x Fr(x)
(1)
where u is the mean wind speed and x is the downwind distance. F r is a dimensionless function to be determined from diffusion experiments. The standard deviation of the horizontal wind direction fluctuations a 0, on the other hand, is related to crL,by tan ao = trvu- 1
(2)
hence the lateral plume spread trr may be related to tro by t r r = t a n t r o x F r ( x ).
(3)
For practical applications of the Gaussian plume model wind direction fluctuations a o are attached to Pasquill-Gifford type stability classes as given in Table 1 (see, e.g. Hanna, 1983). As can be seen, wind direction fluctuations (and hence lateral plume spread) are larger under unstable than under stable stratification. This is true for those cases where diffusion is due to small scale turbulence eddies, not including the effect of plume meandering explicitly. On the other hand, observations under light wind and stable stratification show larger a0 due to low frequency motions (mesoscale eddies) than found in stability classes D-F. This has led to some proposals for a plume meandering correction factor for the Pasquill-Gifford classes (see, e.g. Kristensen et al., 1981;Hanna, 1983) which can lead, e.g. to an increase
1979
1980
D. ETLING Table 1. Standard deviation of wind direction fluctuations as related to Pasquill-Gifford stability classes Pasquill--Gifford stability class a 0 (deg)
A >22.5
Unstable B 17.5-22.5
of try by a factor of 4 for class F and wind speed <2ms-k Some typical horizontal wind direction fluctuations in the lower atmospheric boundary layer, presumably due to gravity waves, are shown in Fig. 1 (after Raynor and Hayes, 1984). In case (a), the period of fluctuations is about 4-5 min and the change in wind direction is about 15 ° during the meander period. Case (b) shows low frequency wind direction variations of about 450-70 ° with period of about 30 min. The mean wind speed was 8 m s - 1 in case (a) contrasted to 3 m s - 1 in case (b). More extensive field observations on wind direction fluctuations under stable stratification over slightly irregular terrain have been reported by H a n n a (1981) and Leahey et al. (1988). The resulting standard deviations ao are plotted in Fig. 2. The sampling time was 1 h in both cases. As can be seen, wind direction fluctuations can be quite large under low wind speed
120 ~
~
30- ~
~
._.--
"~. 0- . . , . . ( ~ . 0" 30" 60" 90" 120" wind direction
" ----~--
30- ~ .c e •~_
~ 0- ~_.
Stable E
D
12.5-17.5
7.5-12.5
90
8 oo o
8o
F
3.8-7.5
< 3.8
o
6, -- -~ ~
/
-~ ,o° ~®
70 60
o oo
50
o
O
o
~
o o
30
Z~oo o °
20 10
0,0
, 1.0
• • ~ %o | • l-"~ra....~ ' , , , 2,0 3.0 1,.0 5.0 6,0 u (ms")
>
Fig. 2. Variance of wind direction fluctuations a o for low wind speed conditions. ©, Observations by Hanna (1981). O, Observations by Leahey et al. (1988). Sampiing time 1-h.
L~
-~ ~ ,, 6 0 - ~ S . . . . _ _ _ •~ ~f " ~ "x'-x
C
-'-r~__ ~ ~ ~ ~ .... ~ _ ~
conditions, in contrast to tro related to Pasquill-Gifford stability classes. The regression curve a 0 = 4 5 u - l ( u in m s -1) fits the data quite well, supporting Hanna's (1983) proposal that av,.~ oou constant. We may remark at this point, that observed values oftr 0 or try depend on the sampling or averaging time T used in the evaluation of data. Using simultaneous Lidar and tracer observations Moore et al. (1988) found ay to be about 3 times larger for 1 h time averages than for 5 min sampling time. Using a Gaussian plume model, mean plume centreline surface concentrations C would be about 3 times lower for a 1 h sampling period than for 5 min averages in this case as C ~ a y -1 for this type of model. Some more detailed discussions on the problem of time averages in the application of Gaussian plume models can be found in Gifford (1975). With respect t o correction of ay values for different sampling time T, Kristensen et al. (1981), among others, have proposed the relation
~ry~ T 1/3. 0"
.30'
60" 90" wind direction Fig. 1. Examples of wind direction meander due to gravity waves (after Raynor and Hayes, 1984). Sampling time 1-h.
As can be seen from Table 1, Fig. 2 and Equations (1)-(3), simple concentration calculations using the Gaussian plume models may lead to strong overestimation of pollution concentrations under stable strati-
Plume meandering under stable stratification
fication and low wind speed. Hence it may be worthwhile to discuss some of the physical reasons for the observed plume meandering under these situations, as will be done in the following chapter,
With (4) or (5) we may define meander as motions, with typical horizontal dimensions 2 >>l (see also Fig. 4). As f is typically I0 m or less under stable stratification, plume meander is caused by motions (eddies) with say 2 ~ 100 m-10 km, depending on the distance from the source. In the following we will discuss some of these atmospheric motions in more detail.
3. CAUSESOF PLUME MEANDERING Although the exact reason for low frequency wind direction fluctuations could not be identified in the observations quoted above, these are believed to be due to gravity waves and boundary layer (BL)vortices with horizontal axis over flat terrain or coastal areas (see, e.g. Sethuraman, 1980; Raynor and Hayes, 1984) or due to terrain-induced mesoscale vortices (Hanna, 1983; Leahey et al., 1988). In any case, plume meandering is caused by motions with length- and time scales much larger than those of microturbulence. For the latter the mixing length ( in the stably stratified BL (SBL) may be regarded as typical length scale. In the surface layer the mixing length is usually described by
3.1. Gravity waves Gravity waves can be observed under stable stratification in the free atmosphere and also in the BL (Einaudi and Finnigan, 1981). Their period is governed by the Brunt-Vaisala frequency N (Equation (6)) and is typically between 3 and 30min. Observed wavelengths in the boundary layer range from say 200 m to 4 km, hence great variation in wind direction fluctuations might be observed (see Fig. 1 and also Raynor and Hayes (1984)). In order that gravity waves may cause plume meandering the waves have to propagate in a direction not parallel to the mean wind, i.e. the phase velocity has to have a direction different from the mean wind u. This is illustrated in Fig. 3 and can be accomplished if gravity waves have their origin (e.g. orographic forcing) outside the area of plume meandering or if the wind is turning with height, as is often observed in the stably stratified nocturnal boundary layer (de Baas and Driedonks, 1985).
xz
= 1+ ~
(4)
where K is von Karman's constant, L the Monin-Obukhov length and ~ a constant about 5.0 (see, e.g. Dyer, 1974). In the upper part of the BL the mixing length might be limited by the so-called buoyancy-scale (Brost and Wyngaard, 1978) defined by
3.2. Vortices with horizontal axis A similar effect on plume meandering may be caused by longitudinal eddies with a horizontal axis (see also Fig. 3). As observations on wind direction fluctuations are often obtained only at one location and one height above ground, it is difficult to distinguish meandering due to gravity waves and from that due to vortices. Some cases of meandering due to roll eddies in coastal areas are described by Raynor and Hayes (1984). Although it is well known, that roll
O"w
f = c(5) N where aw is the standard deviation of the vertical velocity fluctuation and c is a constant about 1.7. N is the Brunt-Vaisala frequency defined by: (,q ~0 ']21 N= \O~z /
(6)
"
/
/
,
1981
/
/
y
)
/
Y
Fig. 3, Flow pattern for plume meandering due to gravity waves and vortices with horizontal axis. (a): Top view. (b): front view.
D. ETLING
1982
vortices with horizontal wavelength about 1-4 km exist in the atmospheric BL (see Brown (1980) for a review), they occur predominantly under unstable and near neutral conditions. Whether they also exist in the SBL over land is not clear to date, because observations of vortex motions are difficult to obtain under these conditions. But as Brown (1980) pointed out, vortex rolls induced by inflection point instability should also exist under stable stratification if the Richardson number Ri does not exceed a critical value about Ri=0.25. Another possible mechanism creating vortices with horizontal axis in the SBL in the wake of quasi twodimensional ridges was proposed by Scorer (1955). As a combined effect of lee waves and leeside rotor flow periodic separation of horizontal eddies from the downwind slope of a hill may occur. The vertical extent of shed eddies is less than the hill height, a few hundred m say, the horizontal wavelength is in the order of the slope length, l-km or so. 3.3. Vortices with vertical axis As vertical motions will be suppressed by buoyancy forces in stably stratified flows, vortices with a horizontal axis are much affected in their growth and intensification under stable conditions. This is not the case for eddies with a vertical axis where the main motion is confined to horizontal planes perpendicular to gravity forces. Hence it seems likely that in many cases observed plume meandering is due to those vortices (see Fig. 4), although their origin is not always clear. Especially over complex terrain observations like those displayed in Fig. 2. have been interpreted as caused by "two-dimensional mesoscale horizontal eddies produced by terrain interactions with the flow or surface inhomogeneities" (Hanna, 1983). One specific mechanism producing quasi-two-dimensional eddies is due to vortex shedding in the wake of obstacles (hills), sometimes called (Karman-) vortex streets. Regarding mesoscale vortex streets, i.e. with scales of several km, most atmospheric observations have been documented in the wake of large islands over the oceans (see, e.g. Thomson et al., 1977; Etling, 1989). From these observations it is clear now, that atmospheric vortex streets can be formed only if there is a stably stratified inversion layer below the summit of a hill or mountain (Etling and Wamser, 1987). This
y
_
JN~L --
l
~ ×
Fig. 4. Flow pattern for plume meandering due to horizontal vortices with vertical axis (top view),
is due to the fact, that in order to produce a twodimensional horizontal flow around obstacles of conical shape a dividing streamline has to exist which can be found only under stable stratification (Spangler, 1987). The relevant parameter is the Froude number Fr defined by u Fr= N H (7) where H is the height of the obstacle (hill, mountain), u the mean wind speed and N the Brunt-Vaisala frequency. Although Fr < 1 is a sufficient condition for a two-dimensional flow around the obstacle to exist, laboratory experiments (Brighton, 1978), which seem to be more relevant for the problem of vortex shedding over land, have shown that vortex streets are formed only for Fr<0.3. Hence these kind of vortices form only under stable stratification and low wind speeds, which are also favorite conditions for observed large wind direction fluctuations. In laboratory experiments and in the atmosphere it has been found (see, e.g. Thomson et al., 1977) that the shedding frequency is governed by the Strouhal number St defined by nD St = - u(8) where n is the shedding frequency (the number of vortices shed on one side of the obstacle per time interval) and D the obstacle diameter (in case of conical shaped hills or mountains the average diameter). Except for some scatter all data indicate that St ~ 0.2 for observed vortex shedding independent of environmental flow condition and obstacle size. Hence for vortex shedding to be observed in the stably stratified boundary layer one has two limiting conditions, i.e. S t y 0 . 2 and Fr~<0.3 Taking these conditions one can give some estimates on hill height, wind speed and stratification for which vortex streets may be found. We may take St =0.2 and F r = 0 . 3 as an example. If we choose low wind speed conditions (u = 1 m s - 1, 5 m s - 1) as were found for the large amplitude meandering cases (see Fig. 2) with a moderately stable stratification (~0/~z -- 1 K/100 m) and a strongly stratified case (O0/Oz = 4 K/100 m), the minimum height of hills or mountains producing vortex shedding is given in Table 2. As the shedding frequency is dependent also on the diameter of the obstacle (Equation (8)), one has to specify the slope of the hills, defined by H/B, in addition to the hill height, where B is the baseline radius of a cone-shaped obstacle (in this special geometry also the average diameter, i.e. D = B). Instead of the shedding frequency n we will calculate the shedding period T = 1/n which would be also equivalent to the plume meandering period. Using Equations (7) and (8) with conditions St=0.2, Fr=0.3 we obtain shedding periods as given in Table 3 and 4 for H / B = 1 : 10 (fiat hill) and H / B = 1:2 (steep hill), respectively.
Plume meandering under stable stratification Table 2. Minimum height (in m) of threedimensional obstacles (hills) producing vortex shedding for F r =0.3 and St =0.2 fY0 -1 K/100 m 4 K/IOO m cz
I ms 1 U 5ms 1
180 900
90 450
1983
called vortical modes (Lilly, 1983; Ruscher and Mahrt, 1989). They are believed to be produced by collapse of three-dimensional turbulent regions in strongly stratifled flows with subsequent transformation of energy into horizontal motions (Fig. 5). From laboratory experiments it has become evident (see Hopfinger (1987) for a review) that turbulence collapse can occur if the turbulent Froude number F r t defined by b/'
Table 3. Shedding periods (in min) for hill slope H / ' B = I : I O for conditions from Table 2 ~0 ~z U Ires 1 5 ms '
1 K/100m
4 K/100 m
150 150
75 75
Table 4. Shedding periods (in min) for hill slope H / B = I : 2 for conditions from Table 2 r,o -~z I ms ~ u 5ms '
1 K/100m
4 K/IOO m
30 30
15 15
It may be seen that the shedding period decreases with increasing stability and increasing slope (decreasing hill diameter). The non-dependence of period on wind velocity u is due to the fact that Tables 1-3 are calculated with Fr=0.3, hence H (Table 1) and consequently D increases with u for those obstacles which possibly produce vortex shedding. Shedding periods in those examples ran from about 150min to 15 min covering the range of time periods observed for low frequency wind direction fluctuations. Hanna (1983) observed periods of lateral meander between 50 min and 4 h over complex terrain. Shedding periods for vortex streets caused by large islands over the oceans are about 2 h (Thomson e t al., 1977). Over land direct evidence of vortex shedding has not been documented often so far, but recent doppler-radar observations in Colorado (Peterson, 1985) indicate vortices with diameters of about 3 km shed with periods about 20 min. Hence although orographically shed vortices may be not easily related to observed plume meandering in a specific case, those kind of eddies with vertical axis could be responsible for parts of observed wind direction fluctuations like those displayed in Fig. 2. 3.4.
Fr t =
(9)
N{
is below a critical value of F r , < 1. In (8) u' is the characteristic horizontal turbulent velocity and ( the vertical extent of the active turbulence region (e.g. turbulent spot). It has been found from these experiments that in cases also relevant for atmospheric applications, e.g. in free shear layers and turbulent wakes produced by obstacles, turbulence collapse with subsequent transformation to quasi-two-dimensional vortices can take place if F r t < 0.3. Although theoretical reasoning (Lilly, 1983) suggests that vortical modes should also exist in the stably stratified atmosphere, observational evidence only recently has been provided by Ruscher and Mahrt (1989). In a nocturnal wind shear layer with low wind speed (1-2 m s - t ) at about 50 m above ground they found vortex-like structures with an average diameter of about 500 m which they attributed to quasihorizontal vortical modes. The origin of the observed vortical modes is not clear to date but one possible mechanism could be wave breaking due to Kelvin-Helmholtz instability in shear layers. If the criteria Frt<0.3 as found in laboratory flows is also adopted for the atmosphere, one may give the following estimate: Let us assume the typical extent of the shear layer to be f ~ 50 m in a strongly stratified environment with O 0 / ~ z =4K/100m. As we are looking for low wind speed conditions we may estimate horizontal wind fluctuation as u'~0.5 m s-1. With these typical values we get from (9) F r t ~ 0 . 2 5 m s - 1 which is in the order of the critical Froude number turbulence collapse. Although observational research on vortical modes in the stably stratified boundary layer is only in its beginning, observations of long-period wind fluctuations obtained in the past might be interpreted in
l
g
z ~
y
~
z ~ .
y
Fq "1 1×
Vortical modes
Even without vortex shedding by obstacles quasihorizontal vortices may exist in the SBL. These pancake-like vortices with horizontal extension much larger than their vertical thickness are sometimes
---
==::I>
, ._ -- ~ : . i -
3-D
/X
~ I
Quasi 2-O
Fig. 5. Vortex formation due to turbulence collapse in stably stratified flow.
1984
D. ETLING
xo E N . ~ Wt~ • 5
. . ' ~ '
-100 oE 80 60
.
.
40 $ 2o 0
, 0
,
t , 30
.
~A
,
. ~"
. ' ~ '
Ad~rl
I , 60
:
' 90
k
:
:
, 120
time(minutes)
Fig. 6. Observations of wind fluctuations under stable stratification due to gravity waves(period ~ 8 min) and possibly vortical modes (period ~ 30min), after Maitani et al. (1984).
terms of these vortical modes. One possible example due to Maitani et al. (1984) is shown in Fig. 6. Displayed are observations of wind speed and wind direction in the nocturnal stably stratified surface layer obtained at 1.5 m height. Besides a period of about 8 min, which is ascribed to gravity waves, a longer period of about 30 min can also be found, especially in the wind direction time series. Maitani et al. analyzed these motions as anticlockwise rotating horizontal vortices, but could not identify the source of these motions. Similar observations at greater height over land are reported by Leyi and Panofsky (1983) and in situations of internal wave breaking near coastal areas by Sethuraman (1980) and Raynor and Hayes (1984). In all these cases long-term fluctuations of about 30 min accompanied with large wind direction variations were superimposed on short fluctuations of a few minutes due to gravity waves. 4. CONCLUSIONS Low frequency large amplitude wind direction fluctuations have been observed quite often under low wind speed and stable stratification. These are clearly distinguishable from high-frequency small scale turbulent motions which usually are responsible for diffusion of air pollutants in the BL. Low frequency wind direction fluctuation may cause so-called plume meandering downwind of point sources leading to reduction in mean concentration levels compared to straight plume situations, affected only by small scale turbulent diffusion. Hence under low wind speed and stable stratification dispersion estimates by standard methods like the Gaussian plume model may not be applicable without modification, especially for Pasquill~Gifford stability classes E-G. As most observations of low frequency wind fluctuations have been performed only at one location at a
oi, t,twas , cu,tfor i rentaut ors,o
identify the type of motions leading to these fluctuations. In some cases wind direction meander was clearly due to gravity waves with periods of 5-30 min. Long term fluctuations of 30 min to 4 h have been most often attributed loosely to "quasi-horizontal mesoscale eddies", especially for observations performed over slightly complex terrain. As horizontal motions are much less affected by buoyancy forces than vertical motions under stable stratification, these type of vortices with vertical axis may persist in those situations for a long time, also due to reduced microscale turbulent friction in stably stratified flows. As was argued, these vortices could be created by vortex shedding from three-dimensional obstacles (hills, mountains) or by collapse of three-dimensional turbulence in strongly stratified flows with subsequent transformation to quasi two-dimensional horizontal motions. Although direct observational support for either of these vortex types over land surfaces is rather scarce to date, future experiments on plume meandering under stable stratification could be arranged with special focus on observations of accompanying vortex structures. More knowledge on plume meandering would not only be helpful in estimating mean concentration levels under stable conditions but also for recently increasing interest in the problem of concentration fluctuations (Wilson et al., 1985; Hanna, 1986). Acknowledgement--Thanks to R. Lorenz for typing the
manuscript and drafting the figures.
REFERENCES de Baas A. F. and Driedonks A. G. M. (1985) Internal gravity waves in a stably stratified boundary layer. BoundaryLayer Met. 32, 303-323. Brighton P. M. (1978) Strongly stratified flow over threedimensional obstacles. Q. Jl R. met. Soc. 104, 289-307. Brost R. and Wyngaard J. C. (1978) A model study of the stably stratified planetary boundary layer. J. atmos. Sci. 35, 1427-1440. BrownR. A. (1980) Longitudinal instabilities and secondary flows in the planetary boundary layer. Rev. Geoph. Space Phys. 18, 683-697. Dyer A. J. (1974) A review of the flux-profile relationships. Boundary-Layer Met. 7,363-372.
Einaudi F. and FinniganJ. J. (1981) The interaction between an internal gravity wave and the planetary boundary layer. (2. JI R. met. Soc. 107, 793-806. Etling D. and Wamser M. (1987) Some aspects of atmosphericvortex streets formed in the wake of large islands.Proc. 4th AMS Conf. on Mountain Meteorology, Am. Met. Soc. Boston, 108-109. Etling D. (1989) Atmospheric vortex streets in the wake of large islands. Met. Atmos. Phys. 41, 157-164. Gifford F. D. (1975) Atmospheric dispersion models for environmental pollution applications. In Lectures on Air Pollution and Environmental Impact Analyses (edited by D. A. Haugen), pp. 35-58. Am. Met. Soc., Boston. Hanna S. R. (1981) Diurnal variation of horizontal wind direction fluctuations tre in complex terrain at Geysers. Boundary-Layer Met. 58, 207-213.
161ume meandering under stable stratification Hanna S. R. (1983) Lateral turbulence intensity and plume meandering during stable conditions. J. clim. appl. Met. 22, 1424-1431. Hanna S. R. (1986) Spectra of concentration fluctuations: the two time scales of meandering plume. Atmospheric Environment 20, 1131-1137. Hopfinger E. J. (1987) Turbulence in stratified fluids: a review. J. geophys. Res. 92, 5287-5303. Kristensen L., Jensen N. O. and Peterson E. L. (1981) Lateral dispersion of pollutants in a very stable atmosphere. Atmospheric Environment 15, 837-844. Leahey D. F., Hansen M. C. and Schroeder M. B. (1988) An analysis of wind fluctuation statistics collected under stable atmospheric conditions at three sites in Alberta, Canada. J. appl. Met. 27, 774-777. Leyi Z. and Panofsky H. A. (1983) Wind fluctuations in stable air at the Boulder tower. Boundary-Layer Met. 25, 353-362. Lilly D. K. (1983) Stratified turbulence and mesoscale variability of the atmosphere. J. atmos. Sci. 40, 749-761. Maitani T., Hiramatsu Y. and Seo T. (1984) Wave-like wind fluctuations observed in the stable surface layer over a plant canopy. Boundary-Layer Met. 29, 273-283. Moore G. E., Milich L. B. and Liu M. K. (1988) Plume behaviour observed using LIDAR and SF6 tracer at a flat and hilly site. Atmospheric Environment 22, 1673-1688. Pasquill F. and Smith F. B. (1983) Atmospheric Diffusion. Ellis Horwood, Chichester.
1985
Peterson E. C. (1985) JAWS microbursts occuring from orographic vortex streets. Proc. 14th Conf. Severe Local Storms, pp. 156-159. Am. Met. Soc. Boston. Raynor G. S. and Hayes J. V. (1984) Wind direction meander at a coastal site during onshore flows. J. clim. appl. Met. 23, 967-978. Ruscher P. and Mahrt L. (1989) Coherent structures in the very stable atmospheric boundary layer. Boundary-Layer Met. 47, 41-54. Scorer R. S. (1955) Theory of airflow over mountains IV. Separation of flow from the surface. Q. Jl R. met. Soc. 81, 340-350. Sethuraman S.(1980) A case of persistent breaking of internal waves in the atmospheric surface layer over the ocean. Boundary-Layer Met. 19, 67-80. Skupniewicz C. E. (1987) Measurements of overwater diffusion: the separation of relative diffusion and meander. J. clim. appl. Met. 26, 949-958. Spangler T. C. (1987) Comparison of actual dividing streamline heights to height predictions using the Froude numbet. J. appl. Met. 26, 204-207. Thomson R. E., Gower J. R. R. and Bowker N. W. (1977) Vortex streets in the wake of the Aleutian islands. Mon. Wea. Rev. 105, 873-884. Wilson D. J., Robins A. G. and Fackrell J. E. (1985) Intermittency and conditionally averaged concentration fluctuation statistics in plumes. Atmospheric Environment 19, 1053-1064.
0004~981/90 $3.00+0.00 ~, 1990 Pergamon Press pie
ON PLUME MEANDERING UNDER STABLE STRATIFICATION D. ETL1N~ Institut ffir Meteorologie und Klimatologie,Universit~itHannover, HerrenhfiuserStr. 2, 3000 Hannover 21, F.R.G. (First received 10 January 1989 and received for publication 29 September 1989)
Abstract--Under stable stratification and light winds large horizontal wind direction fluctuations have been observed quite often leading to meandering of pollutants plume downwind of elevated point sources. Due to this plume meandering long term concentration levelscan be reduced by a factor of 4 or more, compared to straight plume conditions. Some possible mechanisms causing plume meandering under stable conditions are discussed, including gravity waves and vortices with horizontal or vertical axis. Key word index: Plume meandering, stable stratification.
1. INTRODUCTION Air pollutants emitted from point sources are transported and dispersed by mean wind and wind fluctuations in the atmospheric boundary layer. In case of a continuous release the pollutants may form a coneshaped plume in the downwind side of the source. In this case, diffusion of material is due to small-scale turbulence (high frequency motions) with scales comparable to the plume width, sometimes called relative diffusion. On some occasions horizontal undulation (meandering) of the plume can be observed, due to eddies (low frequency motions) with length scales larger than the plume width. This is also referred as to single parti7le diffusion (Hanna, 1986; Skupniewicz, 1987). Although there are also vertical fluctuations of the plume, we will concentrate on the horizontal meander here. As is known from field experiments and theoretical considerations (Kristensen et al., 1981; Hanna, 1983), averaged concentrations of pollutants under meander conditions can be factor of 2-6 lower than for the situation with straight plumes downwind of point sources. Plume meandering may occur under different atmospheric conditions but is most effective for stable stratification and low wind speeds (Hanna, 1981; Leyi and Panofsky, 1983; Leahey et al., 1988). Observed meander periods range from say 5 min to 2 h and are assumed to be caused by gravity waves or vortices with horizontal or vertical axes. Some of the possible mechanisms causing plume meandering are discussed in this paper,
2. WINDDIRECTIONFLUCTUATIONS Lateral diffusion of air pollutants downwind of a point source is caused by wind velocity fluctuations v'
with standard deviation tro. In the widely used Gaussian plume model the standard deviation of the lateral concentration fluctuation %, for example, is related to cry,by (see, e.g. Pasquill and Smith, 1983) try, % = u x Fr(x)
(1)
where u is the mean wind speed and x is the downwind distance. F r is a dimensionless function to be determined from diffusion experiments. The standard deviation of the horizontal wind direction fluctuations a 0, on the other hand, is related to crL,by tan ao = trvu- 1
(2)
hence the lateral plume spread trr may be related to tro by t r r = t a n t r o x F r ( x ).
(3)
For practical applications of the Gaussian plume model wind direction fluctuations a o are attached to Pasquill-Gifford type stability classes as given in Table 1 (see, e.g. Hanna, 1983). As can be seen, wind direction fluctuations (and hence lateral plume spread) are larger under unstable than under stable stratification. This is true for those cases where diffusion is due to small scale turbulence eddies, not including the effect of plume meandering explicitly. On the other hand, observations under light wind and stable stratification show larger a0 due to low frequency motions (mesoscale eddies) than found in stability classes D-F. This has led to some proposals for a plume meandering correction factor for the Pasquill-Gifford classes (see, e.g. Kristensen et al., 1981;Hanna, 1983) which can lead, e.g. to an increase
1979
1980
D. ETLING Table 1. Standard deviation of wind direction fluctuations as related to Pasquill-Gifford stability classes Pasquill--Gifford stability class a 0 (deg)
A >22.5
Unstable B 17.5-22.5
of try by a factor of 4 for class F and wind speed <2ms-k Some typical horizontal wind direction fluctuations in the lower atmospheric boundary layer, presumably due to gravity waves, are shown in Fig. 1 (after Raynor and Hayes, 1984). In case (a), the period of fluctuations is about 4-5 min and the change in wind direction is about 15 ° during the meander period. Case (b) shows low frequency wind direction variations of about 450-70 ° with period of about 30 min. The mean wind speed was 8 m s - 1 in case (a) contrasted to 3 m s - 1 in case (b). More extensive field observations on wind direction fluctuations under stable stratification over slightly irregular terrain have been reported by H a n n a (1981) and Leahey et al. (1988). The resulting standard deviations ao are plotted in Fig. 2. The sampling time was 1 h in both cases. As can be seen, wind direction fluctuations can be quite large under low wind speed
120 ~
~
30- ~
~
._.--
"~. 0- . . , . . ( ~ . 0" 30" 60" 90" 120" wind direction
" ----~--
30- ~ .c e •~_
~ 0- ~_.
Stable E
D
12.5-17.5
7.5-12.5
90
8 oo o
8o
F
3.8-7.5
< 3.8
o
6, -- -~ ~
/
-~ ,o° ~®
70 60
o oo
50
o
O
o
~
o o
30
Z~oo o °
20 10
0,0
, 1.0
• • ~ %o | • l-"~ra....~ ' , , , 2,0 3.0 1,.0 5.0 6,0 u (ms")
>
Fig. 2. Variance of wind direction fluctuations a o for low wind speed conditions. ©, Observations by Hanna (1981). O, Observations by Leahey et al. (1988). Sampiing time 1-h.
L~
-~ ~ ,, 6 0 - ~ S . . . . _ _ _ •~ ~f " ~ "x'-x
C
-'-r~__ ~ ~ ~ ~ .... ~ _ ~
conditions, in contrast to tro related to Pasquill-Gifford stability classes. The regression curve a 0 = 4 5 u - l ( u in m s -1) fits the data quite well, supporting Hanna's (1983) proposal that av,.~ oou constant. We may remark at this point, that observed values oftr 0 or try depend on the sampling or averaging time T used in the evaluation of data. Using simultaneous Lidar and tracer observations Moore et al. (1988) found ay to be about 3 times larger for 1 h time averages than for 5 min sampling time. Using a Gaussian plume model, mean plume centreline surface concentrations C would be about 3 times lower for a 1 h sampling period than for 5 min averages in this case as C ~ a y -1 for this type of model. Some more detailed discussions on the problem of time averages in the application of Gaussian plume models can be found in Gifford (1975). With respect t o correction of ay values for different sampling time T, Kristensen et al. (1981), among others, have proposed the relation
~ry~ T 1/3. 0"
.30'
60" 90" wind direction Fig. 1. Examples of wind direction meander due to gravity waves (after Raynor and Hayes, 1984). Sampling time 1-h.
As can be seen from Table 1, Fig. 2 and Equations (1)-(3), simple concentration calculations using the Gaussian plume models may lead to strong overestimation of pollution concentrations under stable strati-
Plume meandering under stable stratification
fication and low wind speed. Hence it may be worthwhile to discuss some of the physical reasons for the observed plume meandering under these situations, as will be done in the following chapter,
With (4) or (5) we may define meander as motions, with typical horizontal dimensions 2 >>l (see also Fig. 4). As f is typically I0 m or less under stable stratification, plume meander is caused by motions (eddies) with say 2 ~ 100 m-10 km, depending on the distance from the source. In the following we will discuss some of these atmospheric motions in more detail.
3. CAUSESOF PLUME MEANDERING Although the exact reason for low frequency wind direction fluctuations could not be identified in the observations quoted above, these are believed to be due to gravity waves and boundary layer (BL)vortices with horizontal axis over flat terrain or coastal areas (see, e.g. Sethuraman, 1980; Raynor and Hayes, 1984) or due to terrain-induced mesoscale vortices (Hanna, 1983; Leahey et al., 1988). In any case, plume meandering is caused by motions with length- and time scales much larger than those of microturbulence. For the latter the mixing length ( in the stably stratified BL (SBL) may be regarded as typical length scale. In the surface layer the mixing length is usually described by
3.1. Gravity waves Gravity waves can be observed under stable stratification in the free atmosphere and also in the BL (Einaudi and Finnigan, 1981). Their period is governed by the Brunt-Vaisala frequency N (Equation (6)) and is typically between 3 and 30min. Observed wavelengths in the boundary layer range from say 200 m to 4 km, hence great variation in wind direction fluctuations might be observed (see Fig. 1 and also Raynor and Hayes (1984)). In order that gravity waves may cause plume meandering the waves have to propagate in a direction not parallel to the mean wind, i.e. the phase velocity has to have a direction different from the mean wind u. This is illustrated in Fig. 3 and can be accomplished if gravity waves have their origin (e.g. orographic forcing) outside the area of plume meandering or if the wind is turning with height, as is often observed in the stably stratified nocturnal boundary layer (de Baas and Driedonks, 1985).
xz
= 1+ ~
(4)
where K is von Karman's constant, L the Monin-Obukhov length and ~ a constant about 5.0 (see, e.g. Dyer, 1974). In the upper part of the BL the mixing length might be limited by the so-called buoyancy-scale (Brost and Wyngaard, 1978) defined by
3.2. Vortices with horizontal axis A similar effect on plume meandering may be caused by longitudinal eddies with a horizontal axis (see also Fig. 3). As observations on wind direction fluctuations are often obtained only at one location and one height above ground, it is difficult to distinguish meandering due to gravity waves and from that due to vortices. Some cases of meandering due to roll eddies in coastal areas are described by Raynor and Hayes (1984). Although it is well known, that roll
O"w
f = c(5) N where aw is the standard deviation of the vertical velocity fluctuation and c is a constant about 1.7. N is the Brunt-Vaisala frequency defined by: (,q ~0 ']21 N= \O~z /
(6)
"
/
/
,
1981
/
/
y
)
/
Y
Fig. 3, Flow pattern for plume meandering due to gravity waves and vortices with horizontal axis. (a): Top view. (b): front view.
D. ETLING
1982
vortices with horizontal wavelength about 1-4 km exist in the atmospheric BL (see Brown (1980) for a review), they occur predominantly under unstable and near neutral conditions. Whether they also exist in the SBL over land is not clear to date, because observations of vortex motions are difficult to obtain under these conditions. But as Brown (1980) pointed out, vortex rolls induced by inflection point instability should also exist under stable stratification if the Richardson number Ri does not exceed a critical value about Ri=0.25. Another possible mechanism creating vortices with horizontal axis in the SBL in the wake of quasi twodimensional ridges was proposed by Scorer (1955). As a combined effect of lee waves and leeside rotor flow periodic separation of horizontal eddies from the downwind slope of a hill may occur. The vertical extent of shed eddies is less than the hill height, a few hundred m say, the horizontal wavelength is in the order of the slope length, l-km or so. 3.3. Vortices with vertical axis As vertical motions will be suppressed by buoyancy forces in stably stratified flows, vortices with a horizontal axis are much affected in their growth and intensification under stable conditions. This is not the case for eddies with a vertical axis where the main motion is confined to horizontal planes perpendicular to gravity forces. Hence it seems likely that in many cases observed plume meandering is due to those vortices (see Fig. 4), although their origin is not always clear. Especially over complex terrain observations like those displayed in Fig. 2. have been interpreted as caused by "two-dimensional mesoscale horizontal eddies produced by terrain interactions with the flow or surface inhomogeneities" (Hanna, 1983). One specific mechanism producing quasi-two-dimensional eddies is due to vortex shedding in the wake of obstacles (hills), sometimes called (Karman-) vortex streets. Regarding mesoscale vortex streets, i.e. with scales of several km, most atmospheric observations have been documented in the wake of large islands over the oceans (see, e.g. Thomson et al., 1977; Etling, 1989). From these observations it is clear now, that atmospheric vortex streets can be formed only if there is a stably stratified inversion layer below the summit of a hill or mountain (Etling and Wamser, 1987). This
y
_
JN~L --
l
~ ×
Fig. 4. Flow pattern for plume meandering due to horizontal vortices with vertical axis (top view),
is due to the fact, that in order to produce a twodimensional horizontal flow around obstacles of conical shape a dividing streamline has to exist which can be found only under stable stratification (Spangler, 1987). The relevant parameter is the Froude number Fr defined by u Fr= N H (7) where H is the height of the obstacle (hill, mountain), u the mean wind speed and N the Brunt-Vaisala frequency. Although Fr < 1 is a sufficient condition for a two-dimensional flow around the obstacle to exist, laboratory experiments (Brighton, 1978), which seem to be more relevant for the problem of vortex shedding over land, have shown that vortex streets are formed only for Fr<0.3. Hence these kind of vortices form only under stable stratification and low wind speeds, which are also favorite conditions for observed large wind direction fluctuations. In laboratory experiments and in the atmosphere it has been found (see, e.g. Thomson et al., 1977) that the shedding frequency is governed by the Strouhal number St defined by nD St = - u(8) where n is the shedding frequency (the number of vortices shed on one side of the obstacle per time interval) and D the obstacle diameter (in case of conical shaped hills or mountains the average diameter). Except for some scatter all data indicate that St ~ 0.2 for observed vortex shedding independent of environmental flow condition and obstacle size. Hence for vortex shedding to be observed in the stably stratified boundary layer one has two limiting conditions, i.e. S t y 0 . 2 and Fr~<0.3 Taking these conditions one can give some estimates on hill height, wind speed and stratification for which vortex streets may be found. We may take St =0.2 and F r = 0 . 3 as an example. If we choose low wind speed conditions (u = 1 m s - 1, 5 m s - 1) as were found for the large amplitude meandering cases (see Fig. 2) with a moderately stable stratification (~0/~z -- 1 K/100 m) and a strongly stratified case (O0/Oz = 4 K/100 m), the minimum height of hills or mountains producing vortex shedding is given in Table 2. As the shedding frequency is dependent also on the diameter of the obstacle (Equation (8)), one has to specify the slope of the hills, defined by H/B, in addition to the hill height, where B is the baseline radius of a cone-shaped obstacle (in this special geometry also the average diameter, i.e. D = B). Instead of the shedding frequency n we will calculate the shedding period T = 1/n which would be also equivalent to the plume meandering period. Using Equations (7) and (8) with conditions St=0.2, Fr=0.3 we obtain shedding periods as given in Table 3 and 4 for H / B = 1 : 10 (fiat hill) and H / B = 1:2 (steep hill), respectively.
Plume meandering under stable stratification Table 2. Minimum height (in m) of threedimensional obstacles (hills) producing vortex shedding for F r =0.3 and St =0.2 fY0 -1 K/100 m 4 K/IOO m cz
I ms 1 U 5ms 1
180 900
90 450
1983
called vortical modes (Lilly, 1983; Ruscher and Mahrt, 1989). They are believed to be produced by collapse of three-dimensional turbulent regions in strongly stratifled flows with subsequent transformation of energy into horizontal motions (Fig. 5). From laboratory experiments it has become evident (see Hopfinger (1987) for a review) that turbulence collapse can occur if the turbulent Froude number F r t defined by b/'
Table 3. Shedding periods (in min) for hill slope H / ' B = I : I O for conditions from Table 2 ~0 ~z U Ires 1 5 ms '
1 K/100m
4 K/100 m
150 150
75 75
Table 4. Shedding periods (in min) for hill slope H / B = I : 2 for conditions from Table 2 r,o -~z I ms ~ u 5ms '
1 K/100m
4 K/IOO m
30 30
15 15
It may be seen that the shedding period decreases with increasing stability and increasing slope (decreasing hill diameter). The non-dependence of period on wind velocity u is due to the fact that Tables 1-3 are calculated with Fr=0.3, hence H (Table 1) and consequently D increases with u for those obstacles which possibly produce vortex shedding. Shedding periods in those examples ran from about 150min to 15 min covering the range of time periods observed for low frequency wind direction fluctuations. Hanna (1983) observed periods of lateral meander between 50 min and 4 h over complex terrain. Shedding periods for vortex streets caused by large islands over the oceans are about 2 h (Thomson e t al., 1977). Over land direct evidence of vortex shedding has not been documented often so far, but recent doppler-radar observations in Colorado (Peterson, 1985) indicate vortices with diameters of about 3 km shed with periods about 20 min. Hence although orographically shed vortices may be not easily related to observed plume meandering in a specific case, those kind of eddies with vertical axis could be responsible for parts of observed wind direction fluctuations like those displayed in Fig. 2. 3.4.
Fr t =
(9)
N{
is below a critical value of F r , < 1. In (8) u' is the characteristic horizontal turbulent velocity and ( the vertical extent of the active turbulence region (e.g. turbulent spot). It has been found from these experiments that in cases also relevant for atmospheric applications, e.g. in free shear layers and turbulent wakes produced by obstacles, turbulence collapse with subsequent transformation to quasi-two-dimensional vortices can take place if F r t < 0.3. Although theoretical reasoning (Lilly, 1983) suggests that vortical modes should also exist in the stably stratified atmosphere, observational evidence only recently has been provided by Ruscher and Mahrt (1989). In a nocturnal wind shear layer with low wind speed (1-2 m s - t ) at about 50 m above ground they found vortex-like structures with an average diameter of about 500 m which they attributed to quasihorizontal vortical modes. The origin of the observed vortical modes is not clear to date but one possible mechanism could be wave breaking due to Kelvin-Helmholtz instability in shear layers. If the criteria Frt<0.3 as found in laboratory flows is also adopted for the atmosphere, one may give the following estimate: Let us assume the typical extent of the shear layer to be f ~ 50 m in a strongly stratified environment with O 0 / ~ z =4K/100m. As we are looking for low wind speed conditions we may estimate horizontal wind fluctuation as u'~0.5 m s-1. With these typical values we get from (9) F r t ~ 0 . 2 5 m s - 1 which is in the order of the critical Froude number turbulence collapse. Although observational research on vortical modes in the stably stratified boundary layer is only in its beginning, observations of long-period wind fluctuations obtained in the past might be interpreted in
l
g
z ~
y
~
z ~ .
y
Fq "1 1×
Vortical modes
Even without vortex shedding by obstacles quasihorizontal vortices may exist in the SBL. These pancake-like vortices with horizontal extension much larger than their vertical thickness are sometimes
---
==::I>
, ._ -- ~ : . i -
3-D
/X
~ I
Quasi 2-O
Fig. 5. Vortex formation due to turbulence collapse in stably stratified flow.
1984
D. ETLING
xo E N . ~ Wt~ • 5
. . ' ~ '
-100 oE 80 60
.
.
40 $ 2o 0
, 0
,
t , 30
.
~A
,
. ~"
. ' ~ '
Ad~rl
I , 60
:
' 90
k
:
:
, 120
time(minutes)
Fig. 6. Observations of wind fluctuations under stable stratification due to gravity waves(period ~ 8 min) and possibly vortical modes (period ~ 30min), after Maitani et al. (1984).
terms of these vortical modes. One possible example due to Maitani et al. (1984) is shown in Fig. 6. Displayed are observations of wind speed and wind direction in the nocturnal stably stratified surface layer obtained at 1.5 m height. Besides a period of about 8 min, which is ascribed to gravity waves, a longer period of about 30 min can also be found, especially in the wind direction time series. Maitani et al. analyzed these motions as anticlockwise rotating horizontal vortices, but could not identify the source of these motions. Similar observations at greater height over land are reported by Leyi and Panofsky (1983) and in situations of internal wave breaking near coastal areas by Sethuraman (1980) and Raynor and Hayes (1984). In all these cases long-term fluctuations of about 30 min accompanied with large wind direction variations were superimposed on short fluctuations of a few minutes due to gravity waves. 4. CONCLUSIONS Low frequency large amplitude wind direction fluctuations have been observed quite often under low wind speed and stable stratification. These are clearly distinguishable from high-frequency small scale turbulent motions which usually are responsible for diffusion of air pollutants in the BL. Low frequency wind direction fluctuation may cause so-called plume meandering downwind of point sources leading to reduction in mean concentration levels compared to straight plume situations, affected only by small scale turbulent diffusion. Hence under low wind speed and stable stratification dispersion estimates by standard methods like the Gaussian plume model may not be applicable without modification, especially for Pasquill~Gifford stability classes E-G. As most observations of low frequency wind fluctuations have been performed only at one location at a
oi, t,twas , cu,tfor i rentaut ors,o
identify the type of motions leading to these fluctuations. In some cases wind direction meander was clearly due to gravity waves with periods of 5-30 min. Long term fluctuations of 30 min to 4 h have been most often attributed loosely to "quasi-horizontal mesoscale eddies", especially for observations performed over slightly complex terrain. As horizontal motions are much less affected by buoyancy forces than vertical motions under stable stratification, these type of vortices with vertical axis may persist in those situations for a long time, also due to reduced microscale turbulent friction in stably stratified flows. As was argued, these vortices could be created by vortex shedding from three-dimensional obstacles (hills, mountains) or by collapse of three-dimensional turbulence in strongly stratified flows with subsequent transformation to quasi two-dimensional horizontal motions. Although direct observational support for either of these vortex types over land surfaces is rather scarce to date, future experiments on plume meandering under stable stratification could be arranged with special focus on observations of accompanying vortex structures. More knowledge on plume meandering would not only be helpful in estimating mean concentration levels under stable conditions but also for recently increasing interest in the problem of concentration fluctuations (Wilson et al., 1985; Hanna, 1986). Acknowledgement--Thanks to R. Lorenz for typing the
manuscript and drafting the figures.
REFERENCES de Baas A. F. and Driedonks A. G. M. (1985) Internal gravity waves in a stably stratified boundary layer. BoundaryLayer Met. 32, 303-323. Brighton P. M. (1978) Strongly stratified flow over threedimensional obstacles. Q. Jl R. met. Soc. 104, 289-307. Brost R. and Wyngaard J. C. (1978) A model study of the stably stratified planetary boundary layer. J. atmos. Sci. 35, 1427-1440. BrownR. A. (1980) Longitudinal instabilities and secondary flows in the planetary boundary layer. Rev. Geoph. Space Phys. 18, 683-697. Dyer A. J. (1974) A review of the flux-profile relationships. Boundary-Layer Met. 7,363-372.
Einaudi F. and FinniganJ. J. (1981) The interaction between an internal gravity wave and the planetary boundary layer. (2. JI R. met. Soc. 107, 793-806. Etling D. and Wamser M. (1987) Some aspects of atmosphericvortex streets formed in the wake of large islands.Proc. 4th AMS Conf. on Mountain Meteorology, Am. Met. Soc. Boston, 108-109. Etling D. (1989) Atmospheric vortex streets in the wake of large islands. Met. Atmos. Phys. 41, 157-164. Gifford F. D. (1975) Atmospheric dispersion models for environmental pollution applications. In Lectures on Air Pollution and Environmental Impact Analyses (edited by D. A. Haugen), pp. 35-58. Am. Met. Soc., Boston. Hanna S. R. (1981) Diurnal variation of horizontal wind direction fluctuations tre in complex terrain at Geysers. Boundary-Layer Met. 58, 207-213.
161ume meandering under stable stratification Hanna S. R. (1983) Lateral turbulence intensity and plume meandering during stable conditions. J. clim. appl. Met. 22, 1424-1431. Hanna S. R. (1986) Spectra of concentration fluctuations: the two time scales of meandering plume. Atmospheric Environment 20, 1131-1137. Hopfinger E. J. (1987) Turbulence in stratified fluids: a review. J. geophys. Res. 92, 5287-5303. Kristensen L., Jensen N. O. and Peterson E. L. (1981) Lateral dispersion of pollutants in a very stable atmosphere. Atmospheric Environment 15, 837-844. Leahey D. F., Hansen M. C. and Schroeder M. B. (1988) An analysis of wind fluctuation statistics collected under stable atmospheric conditions at three sites in Alberta, Canada. J. appl. Met. 27, 774-777. Leyi Z. and Panofsky H. A. (1983) Wind fluctuations in stable air at the Boulder tower. Boundary-Layer Met. 25, 353-362. Lilly D. K. (1983) Stratified turbulence and mesoscale variability of the atmosphere. J. atmos. Sci. 40, 749-761. Maitani T., Hiramatsu Y. and Seo T. (1984) Wave-like wind fluctuations observed in the stable surface layer over a plant canopy. Boundary-Layer Met. 29, 273-283. Moore G. E., Milich L. B. and Liu M. K. (1988) Plume behaviour observed using LIDAR and SF6 tracer at a flat and hilly site. Atmospheric Environment 22, 1673-1688. Pasquill F. and Smith F. B. (1983) Atmospheric Diffusion. Ellis Horwood, Chichester.
1985
Peterson E. C. (1985) JAWS microbursts occuring from orographic vortex streets. Proc. 14th Conf. Severe Local Storms, pp. 156-159. Am. Met. Soc. Boston. Raynor G. S. and Hayes J. V. (1984) Wind direction meander at a coastal site during onshore flows. J. clim. appl. Met. 23, 967-978. Ruscher P. and Mahrt L. (1989) Coherent structures in the very stable atmospheric boundary layer. Boundary-Layer Met. 47, 41-54. Scorer R. S. (1955) Theory of airflow over mountains IV. Separation of flow from the surface. Q. Jl R. met. Soc. 81, 340-350. Sethuraman S.(1980) A case of persistent breaking of internal waves in the atmospheric surface layer over the ocean. Boundary-Layer Met. 19, 67-80. Skupniewicz C. E. (1987) Measurements of overwater diffusion: the separation of relative diffusion and meander. J. clim. appl. Met. 26, 949-958. Spangler T. C. (1987) Comparison of actual dividing streamline heights to height predictions using the Froude numbet. J. appl. Met. 26, 204-207. Thomson R. E., Gower J. R. R. and Bowker N. W. (1977) Vortex streets in the wake of the Aleutian islands. Mon. Wea. Rev. 105, 873-884. Wilson D. J., Robins A. G. and Fackrell J. E. (1985) Intermittency and conditionally averaged concentration fluctuation statistics in plumes. Atmospheric Environment 19, 1053-1064.