Mean turbulent properties of the stable boundary layer observed during the “coast” experiment

Atmospheric Research, 20 (1986) 151--164 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

151

MEAN TURBULENT PROPERTIES OF THE STABLE BOUNDARY LAYER OBSERVED DURING THE "COAST" EXPERIMENT

GEORGES DESBRAUX and ALAIN WEILL CNET/CRPE/CNRS, 38/40 re du Gdnedral Leclerc, 92131 Issy-les-Moulineaux (France) (Accepted for publication May 1, 1986)

ABSTRACT

Desbraux, G. and Weill, A., 1986. Mean turbulent properties of the stable boundary layer observed during the "Coast" experiment. Atmos. Res., 20: 151--164. A n acoustic Doppler sounder has been used to document the behaviour of the stable atmospheric boundary layer during the "Coast" experiment, in April--May, 1983, on a homogeneous terrain near the Dutch coast. It has been shown that Kaimal's model of the spectrum of velocity in the stable surface layer can be applied and that surfacelayer parameterization can be used in the whole stable surface layer. Velocity spectra have been computed between .0005 c.p.s, and .1 c.p.s, and for the stability range for z/L between 0 and 10. It is to be noted that the information has been obtained using only sodar data.

P SUM Un sondeur acoustique Doppler monostatique avec trois antennes a ~t4 utilis~ pendant l'exp4rience Coast pour documenter le comportement turbulent de la couche d'inversion de sol. I1 a ~t4 montr~ que les param~trisations de la couche de surface stable pouvalent ~tre ~tendues ~ toute la couche stablement stratifi~e. Des spectres de vitesse dans la couche stable ont ~t~ obtenus et compares aux modules de Kaimal. La bande de fr~quence utilis~e a 4t~ entre .0005 Hz et .1 Hz et le domaine de stabilitY, pour z/L compris entre 0 et 10. L'ensemble des informations provient uniquement du sodar.

INTRODUCTION T h e t e r m "stable b o u n d a r y l a y e r " is i m p r o p e r l y a t t r i b u t e d t o the d y n a mically unstable b o u n d a r y layer with statically stable stratification. O n land, in t e m p e r a t e latitudes, such a stable stratification is f r e q u e n t l y observed d u r i n g the night and also during w i n t e r days. T h e stable b o u n d a r y layer ( S T B L ) is n o t as well u n d e r s t o o d as the convective b o u n d a r y layer and this is certainly due to the variability associated with the smallness o f its flux: each t e r m in the t e m p e r a t u r e variance b u d g e t or t u r b u l e n t kinetic e n e r g y b u d g e t can have an equal i m p o r t a n c e . Additionally, the S T B L can s u p p o r t wave m o t i o n , and the role o f gravity waves, particularly in the p r o d u c t i o n o f t u r b u l e n c e , is q u a n t i t a t i v e l y unclear. 0169-8095/86/$03.50

© 1986 Elsevier Science Publishers B.V.

152 Nevertheless, some studies have been made of the stable surface layer and sometimes the models have been generalized over the whole STBL. This paper presents some results mainly concerning velocity spectra, turbulent dissipation rate, and characteristic length of the turbulent dissipation rate in the STBL. Studies have been made on the modeling of velocity spectra in the STBL. Using data from the "Kansas" experiment (1968), Kaimal (1973) proposed normalized forms for the velocity spectra in the stable surface layer. Caughey (1977) attempted to generalize Kaimal's model for the entire STBL. A contribution to the generalization of the behaviour of the STBL spectrum, with acoustic-sounder data, is one of the purposes of this paper. Several studies have been undertaken (Wyngaard and Cote, 1971; Caughey et al., 1979; Weill et al., 1978) on the turbulent dissipation rate in the STBL. Some numerical models have been established (Wyngaard, 1975; Brost and Wyngaard, 1978), but systematic sodar estimates have not yet really been undertaken. Hence, from our measurements made during the "Coast 8 3 " experiment we have tried to compute systematically the turbulent dissipation rate, and also to estimate the behaviour of "universal" functions (normalized wind shear and dissipation) in a large fraction of the STBL. These estimation enable us to compute the dissipation lengths, which are fundamental for high-order closure models (Andr~ et al., 1978). Indeed, modelers generally have to use empirical adjustments of this parameter. Mellor (1973) takes the dissipation length (simply denoted by l) as directly proportional to height, whereas Delage (1974) relates it to the mixing length. The most powerful models are those of Mellor and Yamada (1974) and Deardoff (1976) who relate l to the Brunt-Vai~ala frequency. More recently, Andr5 et al. (1978) have parameterized the tubulent dissipation rate by means of the two previous models, and Louis et al. (1983) tested this parameterization. We shall try here to describe the behaviour of l with stability experimentally. The data used in this study were collected during the "Coast 8 3 " experiment, which took place in April/May, 1983 in Woubrugge (Netherlands). This experiment was conducted by the KNMI (Royal Netherlands Meteorological Institute) with the collaboration of the CRPE (Centre de Recherches en Physique de l'Environnement), the LA (Laboratoire d'A6rologie), the EERM (Etablissement d'Etudes et de Recherches M~t6orologiques) and the MPI (Max Planck Institute). The site of the experiment was very flat and homogeneous. Measurements were essentially carried out with a three-antenna monostatic Doppler sodar. These data, as described in Weill et al. (1978), correspond in the first place to "primary data", which are, respectively, backscattering intensity, mean horizontal wind velocity and vertical velocity. Sodar parameters are indicated in Table I. The data concern the four nights of April 23--24, 24--25 and May 5--6, 15--16. These nights were chosen because they presented a strong groundbased stable echo layer.

153 TABLE I Main parameters of the acoustic Doppler sounder Acoustic emission frequency (Hz) Width of the aerialbeam (deg.) Pulse duration ffiduration of a gate analysis (ms) Pulse length - gate length (m) Repetition rate (s) N u m b e r of points used in a gate for the Doppler shift computation using the last Fourier transform

2000 10 100 17 4 32

DATA

Mainly turbulent parameters discussed in this study. Turbulence statistics (variances, spectra, dissipation parameters, ...) were c o m p u t e d for a time interval of 33 min. In the variance estimates, the linear trend of the mean wind speed was eliminated. Spectra were computed using Fourier transforms of the time series and a Papoulis window (Papoulis, 1973). With an integration period of 33 min and a sampling rate of 4 s, we obtained spectra in a frequency band of 0.0005--0.125 Hz (but we have to take into account the sodar response: a cut-off frequency near 0.1 Hz). This frequency band is well representative of the large and mean scales of the turbulent flow (Kaimal, 1973; Caughey, 1977). The dissipation rate was c o m p u t e d by using the "inertial method": following Kolmogorov's law for the inertial vertical velocity spectrum, we have: have: S(k) -- a e 2/3 k -s/3

(1)

where k is the wave number, e the dissipation rate, a is a universal constant (assumed to be equal to 0.5), and S ( k ) the spectral density of turbulent energy (see also the Notation). Using Taylor's hypothesis, eq. 1 becomes: n S ( n ) = a e 2i3 ( 2 ~ I U ) -213 n 2i3

(2)

where n is the cyclic frequency, U the mean wind speed, and n S ( n ) the spectral energy. Eq. 2 allows us to c o m p u t e e if the spectra follow the - 5 / 3 law. Hence, the dissipation length scale l was computed using the formula: l = E3nle

This "special m e t h o d " does not as described by Gaynor (1977), estimated by E = ~ Z. ai 2, where of space. Measured turbulent dissipation

(3) differ from the structure function method where E is the turbulent kinetic energy, a i is the variance of the ith c o m p o n e n t rates generally present large incertitudes

154

due to i n t e r m i t t e n c y o f t u r b u l e n c e . Hence, to take this intermittency and the i n c e r t i t u d e s on each profile into a c c o u n t , statistical errors were computed: assuming Gaussian distributions, a confidence interval in measuring o f 95% is chosen. RESULTS

Velocity spectra Fig. 1 presents our results for horizontal and vertical velocity spectra. Each curve was obtained by averaging over approximatively 35 h and for 3-gate spectra computed for a time period of 33 min. Thus, in the horizontal case, the two curves are characteristic of the heights of 48 m and 93 m and in the vertical case 56 m and 107 m (height resolution 15 m and 17 m for the horizontal and vertical components, respectively) the spectrum corresponding to one horizontal component is presented since it is similar to the other component.

~9

'-5

a,

,

:9

|1

I

I~T £ ttlttti~!

+l] . ~..LL!+.U~ ~+d :::: #::+;+-t+;+'~:P :4 1~:7

+:

Fig.

!

T

+ +r ~+

[

+

k+i

::::::}::~: I +

r,

[

+

+,

+

i

i

~'

E i ':i:+:]!]__+t+2

1.a.

Mean horizontal velocity spectra obtained during the "Co+utt 83" experiment,

in a case of strong stability. Each curve was o b ~ n e d by a v e r ~ n g approximately 200 spectra computed for a time period o f 33 min and for heights o f 4 8 m and 93 m. b. Mean vertical velocity spectra obtained during the "Coast 83" experiment for heights o f 56 m and 107 m.

155 The spectra exhibit the usual features observed in stable conditions: we can observe a beginning of high-frequency n decay. The strong fall-off for frequencies larger than 0.1 Hz is associated with the filter effect of the sodar. Our spectra also present a roll-off at low frequencies with a slope of power one. However, for horizontal spectra, the level of energy is greater than for the vertical ones for frequencies below 0.005 Hz, and the slope does not exhibit the n behaviour. This result is associated with an anisotropy of the turbulence at the largest scales (Louis et al., 1983). It must be emphasized that some spectra were excluded for the mean, because they showed significant peaks in the low-frequency band, characteristic of gravity waves. To some extent, spectra could also be observed which seemed to represent a spectral gap in the production range, as observed by Caughey (1977). According to this author, this gap is located in the vicinity of the Brunt-V~iis~il~i frequency, and delimits the "wave subrange" and the "turbulent subrange". In our case, it seems that the "turbulent subrange" is restricted to small scales, so we have excluded these spectra before averaging. Kaimal (1973) proposed a model for velocity spectra in the stable surface layer. It is known that the turbulent range depends on the wind speed, height and stability; so n was expressed in the non-dimensional form f = n z / U (reduced frequency). Finally, the collapse of the spectra into a universal curve was achieved by introducing a new scaling parameter f0, which is the frequency for which the extrapolated inertial subrange line (with slope - 2 / 3 ) takes the value nS(n)/o~= 1. Then the model taken the form:

nS(n)/al 2 = A fifo~1 + (f/fo)Sl3;

(4)

using the Kansas data (1968), Kalmal et al. (1972) found A = 0.16. A peculiarity of the spectra obtained with the "Coast" experiment data is that the maxima of these spectra remained approximately constant with height and time, which differs from Kaimal's and Caughey's results. Thus, in our case, spectra expressed in cyclic n frequency are already convergent. M o r e o v e r mean wind profiles being (for the most part) rather similar and quasi-linear with height, the normalisation by z / U implies only a displacement of the average spectra on the frequency axis. Horizontal and vertical spectra are well fitted by Kaimal's model, which gives a constant value of A --- 0.26. This value is in good agreement with Kaimal's and Caughey's results (see Fig. 2). Following Caughey (1977), the differences between the A values are probably associated with the different frequency bands over which the variances have been computed. Table II presents the different A values and frequency bands used. Fig. 3 presents the mean values of the characteristic wavelength km corresponding to the spectrum maximum normalized by the STBL depth, H, and plotted versus z/H. Typically, k m = U/n is of the order of 100 or 200 m. We have already noted that the maximum of the spectrum is nearly

156 TABLE II A-values and frequency bands in which the spectrum variance is estimated

Kaimal (1973) Caughey (1976) Coast experiment

Freq. band

A

0.005--10 Hz 0.008-- 0.5 Hz 0.0005--0.1 Hz

0.164 0.3 (hot.) 0.16 (vert.) 0.26

%.

"o.

/ 'c

-.

-5;tb~"ib~

........

I'~'

a )

........

,~o

f/fo

°~

n~vnt % ,_o

c,

s.lo~" 'i'0-2

........

bl

l'~

......

I'00

fifo

Fig. 2.a. Adjustment of our mean horizontal velocity spectra (full line) with the Kaimal et al's model 1973 (dotted line) obtained with the K a m m data: nSu(n)/o ~ = 1 + A fifo~ 1 ( f i f o ) 5~. The dashed lines represent the Caughey's adjustment (1977) with the Cardington experiment data: ...... A = 0.164; - - - - --A = 0.3; A = 0.26. b. Adjustment of our mean vertical veloeity spectra (full line) with the ~ model (Kaimal et al., 1972) (dotted line) obtained with the Irumm~ data: n S w ( n ) / a ~ v = 1 + A ( f i f o ) / 1 + (f/fo)s~3; .... -A = 0.16; A = 0.26.

157

O ÷

O

4o

4-

4-

•

4o o

4.

o

+

N

4-

+

4•

+o +

++ 4-

O'0

0.5

1,0

1.5

~M / H

Fig. 3. M e a n value o f t h e n o r m a l i z e d c h a r a c t e r i s t i c w a v e l e n g t h p l o t t e d versus h e i g h t . H is t h e S T B L d e p t h (Coast 83: o ffi 22 April, o = 24 April, • ffi 5 May, + = 15 May). Large crosses are results o b t a i n e d b y C a u g h e y e t al. ( 1 9 7 9 ) w i t h t h e M i n n e s o t a d a t a

/

150 E ~'100 Z WI

=

5O

a)

1~}

WIND SPEED(rn-~)

200

150

/

~-- 1 0 0 Z E tU 5O

b)

WIND

SP~ED(m~

Fig. 4.a. S o m e o f t h e m e a n w i n d s p e e d profiles o b s e r v e d in t h e " C o a s t 8 3 " in t h e n o c t u r n a l s t a b l e b o u n d a r y layer. E a c h profile was o b t a i n e d w i t h a p e r i o d . C o a s t 83, 5 May: 1 ffi 1 h 1 6 - - 1 h 36; 2 = 1 h 3 6 - - 1 h 56; 3 = 2 h b. Coast 83, 15 May: 1 = 23 h 3 3 - - 2 3 h 53; 2 ffi 1 h 5 3 - - 2 h 13; 3 = 3 h

experiment, 20-ram time 3 6 - - 2 h 56. 1 3 - - 3 h 33.

158 constant with height, when expressed in cyclic frequency, so Xm varies only approximately with the mean wind speed. Fig. 3 effectively shows a quasi-linear height behaviour which can be related to the tendency of the mean wind speed to be quasi-linear during the "Coast" experiment (Fig. 4). Large crosses in the figure represent Caughey's measurements obtained with the "Minnesota" experiment data, for z / H >0.1. For z / H < 0 . 5 these points are in good agreement with our measurements, but spread out at higher levels. Universal functions

In order to observe whether parameterization in the surface layer (Businger et al., 1971) can be applied to the whole ground-based stable layer, "universal functions" for wind velocity and turbulent dissipation rate have been computed and compared with the surface layer parameterization. In the stable surface boundary layer, the wind shear, non-dimensionalised by the basic Monin-Obukhov similarity, takes the form:

where Cu is the universal function of wind shear. Under strongly stable conditions the mean wind profiles are known to be logarthmic in the surface layer and linear at upper heights; hence, Cu takes the form: Cu(z/L) = 1 + ~z/L

(6)

where /3 is an experimental constant. Several values, ranging from 4.5 to 7, have been suggested for /3, For instance, Webb (1970) and Sethuraman and Brown (1976) proposed a value of 5.2. The more c o m m o n l y accepted value is that of Businger et al. (1971), /3 = 4.7, deduced from data from the "Kansas" experiment. In the case of strong stability (corresponding to z / L >>1), turbulence is locally intermittent and it is assumed that most turbulent profiles are independent of height (Wyngaard, 1973). The relevant length scale is the Monin-Obukhov length, L, and similarity theory leads to" L dU U. dz

-~

(7)

If we consider sodar data from strong temperature inversions associated with "sporadic stable layers", one observes that mean wind profiles are often quasi-linear with height (see Fig. 4); hence it seems reasonable to apply eq. 7, and in particular to test ~ e constant proposed by Businger et al. (1971). To do this o n e has to consider the turbulence behaviour

159

in the whole STBL, and not only for L < z < H . Nevertheless, estimation is not easy: for sufficiently large values of z/L, we have:

The wind shear and U can be measured accurately: U is estimated from the covariance function between radial and vertical velocities. The negative heat flux is obtained by means of the turbulent kinetic energy budget in which divergence terms are neglected (Wyngaard and Cote, 1971): g _ U 2d~ ~Q0 = e "dz

(9)

In any event, Q0 is very small, and the uncertainty on e consequently involves large errors of L and/~. Thus some scattering of the results can be observed (see Fig. 5). However, the mean value of ~ is 4.2, which is in good agreement with Businger's value (assuming a Gaussian distribution and a confidence interval of 95%, the uncertainty is of the order of 5%. It must be noted that the "Kansas" experiment gave values of z/L for the range O
a O A*O D /

O

ZCH 8

/

o

D

D

~

O

A

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ID

.4.

g

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,~

Z/L

g

g

~o.

o

2'o.

4b.

6'0-

8'0.

TURBULENT DISSIPATION(cm2s-'3/

Fig. 5. E s t i m a t i o n o f the universal f u n c t i o n o f w i n d shear ~u(Z/L) = 1 + ~z/L. The dashed line represents the m o d e l o f Businger et al. w i t h ~ ffi 4.7 A . The full line (ffi 4 . 2 ) f, its our results. Fig. 6. Mean dissipation rate profiles o b t a i n e d during the "Coast 8 3 " e x p e r i m e n t . It can be s e e n that e remains nearly c o n s t a n t w i t h height at heigher levels, according t o the similarity t h e o r y . (Coast 83: o = 2 2 April; o = 2 4 April; ~ = 5 M a y , + ffi 15 May).

160 On the other hand, if all the terms in eq. 8 are normalized by kz/u,, the equation becomes: kze

z -

u?

L

z

z

~ Cu(~-) = 1 + ( ~ -

z

1) L =

¢(~- )

(10)

where k is the Von K a r m a n constant, assumed to be equal to 0.4, and ~e is the well-known universal function of the dissipation rate. For the asymptotic case of large values of z/L, eq. 9 becomes:

kL

u.-7 = ~ - 1

(11)

Hence, it can be expected that e remains constant with height. Mean dissipation rates obtained during the " C o a s t " experiment corroborate this result, for z/H>0.3 (see Fig. 6). The greatest values of e observed in the lowest levels are certainly associated with a larger wind shear, and consequently with a more intensive production of turbulence. Fig. 7 shows the results obtained for the estimation of Ce(z/L). Eq. 9 does not mean that Cu(z/L) - (~e(z/L) = 1 in all cases, because of the uncertainties in u , and essentially in e. The mean value obtained is 5.6, with a statistical error of about 5%.

// :

°a / f *~/f

o

A

/ / O ~' °o

~//a / /

.y:ro 6

o.

Z/I.

Fig. 7. Estimation o f the univa~ml function of dimfipation rate ¢ e ( z / L ) = i + ( ~ - 1 ) z / L . The full line represents the model with Btminger et al's eor, stant, 0 ffi 4.7. A better adjustment o f our results gives 0 = 5.6 (Coast 83: u ffi 22 April; o = 24 April; ~ ffi 5 May, + = 15 May).

Dissipation length scale Our measurements of the dissipation length scale l show a large scatter. However, the mean profile~ ~ n t a correct ~ a v i o u r : in pa~,cu.hr, l approaches a c o n s t a n t v a l u e a s h e i g h t i n c r e a ~ s :

161

Night of:

April 22/23 1=150m

April 24/25 I=250m

May 5/6 1=150m

M a y 15/16 l=90m

l is k n o w n to be p r o p o r t i o n a l to height in t h e surface layer and nearly c o n s t a n t a b o u t it. Mellor and Yamada's (1974) m o d e l leads to 1 = 15l B, where l B is the mixing length m o d e l e d by Blackadar (1962) in the f o r m :

lB-k/(l z-

+ kz lo /

(12)

l B is defined b e t w e e n t w o limits, l B = kz as z-*0 and l B = lo as z-* oo. l0 is representative of the e x t e n t o f the t u r b u l e n t field and usually takes the form: lo = So

f°°E1/2zdz

(13)

f~o El/~dz

where E is the mean t u r b u l e n t kinetic energy, and s0 is an empirical constant. Mellor and Y a m a d a have set s0 = 0.1. If E is supposed to be c o n s t a n t with height, l simply takes the f o r m lo = 0.05 H. Then the Mellor and Y a m a d a m o d e l becomes:

l/z = A/1 + B z / H

(14)

w i t h A -~ 6 and B -~ 8. A d j u s t m e n t of o u r m e a n profiles w i t h eq. 14 gives A = B ~- 11 (see Fig. 8), leading to the relation:

l/z = 27.5k/(1 + kz/lo) °~I ~

(15)

0

• I q A

o

°

\~oo ~\a

o

....

o

I/z"

8.

Fig. 8. Mean prof"fles o f the dissipation length scale o b t a i n e d during t h e " C o a s t 8 3 " e x p e r i m e n t , in n o c t u r n a l stable c o n d i t i o n s ([] ffi 15 May, v ffi 24 April; ~ = 22 April; + ffi 5 May). The full line represents t h e Mellor and Y a m a d a ' s m o d e l (1974), with the a d j u s t m e n t constants 15 and % ffi 0,1. The dashed line represent t h e a d j u s t m e n t o f our m e a n results with this m o d e l (except for the 24 April data), which gives the new adjustm e n t constants 27.5 and ~0 = 0.072.

162 with l0 = 0.036 H. This implies that the constants taken by Mellor and Yamada (15 and a0 = 0.1) in our case are 27.5 and a0 = 0.072. This leads us to try to model the variations of 1/z with the stability of the STBL. For the asymptotic stable case (z/L>> 1) similarity theory involves: l/L

=

(16)

C

where C is a constant; or l/z = C ( z / L ) -1 for large values of z / L . Fig. 9 presents our measurement of l/z versus ( z / L ) -~. In spite of a rather large scatter, the data points could be adjusted by a straight line. We preferred to use the following formula: l - - ~ A ( z / L ) - ~ / [ 1 + B ( z / L ) -~] z

(17)

implying a quasi-linear variation of l/z for large values of z / L and leading to l = Cz as z-~0. A least-squares fitting gives A = 4 and B = 0.33, or the equivalent form: I/z = 12/[1 + 3 z / L ]

(lS)

-oo ~&

o o" 2 . 0

1'°

L/Z

Fig. 9. Modeling o f l / z w i t h stability (Coast 83: o = 22 April; o = 24 April; ~ = 5 May; + = 15 May). We have fitted these results w i t h a m o d e l o f the form: t / Z = A ( Z / L ) - I / 1 + f l ( Z / L ) -l w i t h A = 4 and fl = 0 . 3 3 .

CONCLUDING REMARKS We have used sodar data to study the behaviour of the STBL. Some concluding results have been obtained: Kaimal's model of the spectrum of velocity has been shown to be valid in the whole STBL; in particularly, universal f u n c t i o n s of wind shear and dissipation can be extended to a range of stability larger than in the "Kansas" experiment. Therefore, it seems that M ~ i n ~ b ~ o v ~e,layer parmneten~tion can be applied without difficulty in numerical m o d e l s w h e n b e first levels

163 o f these m o d e l s are higher t h a n the surface layer. It has to be n o t e d t h a t , using a t h r e e - a n t e n n a m o n o s t a t i c D o p p l e r sodar, it has b e e n possible to u n d e r t a k e a q u a n t i t a t i v e b o u n d a r y layer s t u d y using o n l y p a r a m e t e r s as given b y the sodar: h o r i z o n t a l w i n d profile, s p e c t r u m o f h o r i z o n t a l and vertical v e l o c i t y f l u c t u a t i o n s , f r i c t i o n v e l o c i t y and sensible h e a t flux and t u r b u l e n t dissipation rate: this is a d e m o n s t r a t i o n t h a t s o m e relevant results c o n c e r n i n g the b o u n d a r y layer can be o b t a i n e d with acoustic D o p p l e r s o u n d e r s w h i c h c o m p l e m e n t i n f o r m a t i o n given b y n u m e r i c a l facsimile records. O f course, t h e main l i m i t a t i o n in t u r b u l e n c e studies is generally d u e to t h e low sodar c u t - o f f f r e q u e n c y . ACKNOWLEDGEMENTS T h e a u t h o r s wish t o t h a n k t h e technical staff o f C.R.P.E. f o r t h e i r assistance and p a r t i c i p a t i o n in t h e Coast e x p e r i m e n t . Special t h a n k s are d u e t o F. Baudin, J. Fevre, J. Bilbille, A. Sauvaget and B. Piton. This s t u d y has been u n d e r t a k e n w i t h the s u p p o r t o f INSU (CNRS) and C N E T . T h e Coast e x p e r i m e n t was organized b y t h e K.N.M.I.: it is a pleasure f o r us to t h a n k A.G.M. D r i e d o n k s and his colleagues.

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NOTATION

a f f0 g k 1

: Kolmogorov's constant (0.5) : normalized frequency (= nz/U) : adjustment frequency of Kaimal et al. : acceleration of gravity : Von Karman constant (0.4) : dissipation length scale 1b : mixing length of Blackadar 10 : mixing length limit (= lim IB) n : cyclic frequency u, : friction velocity z : height E : mean turbulent kinetic energy H : STBL depth L : Monin-Obukhov length [=-u3,/k(g/T)Qo] Q0 : surface heat flux S(n) : spectral density T : thermodynamic temperature U : mean wind speed : constant which appears in the universal functions X : wavelength (= n/U) e : dissipation rate ~u : universal function of wind shear Ce : universal function of dissipation a~ : variance of velocity [i = u, v, w ]