1. Introduction
One of the consequences of density stratification in the atmosphere or ocean is the formation of disk-shaped density inhomogeneities due to the collapse of internal waves arising in stratified fluids [
1]. In a stably stratified atmosphere, this leads to the appearance of anisotropic discoid turbulent temperature inhomogeneities. Radio occultation methods are widely used to study anisotropic turbulence in free atmosphere [
2,
3,
4]. In accordance with previously published results [
2,
3], the spatial spectrum of the temperature turbulence in a stable atmosphere can be represented as the sum of an isotropic and anisotropic component, which are statistically independent. The results presented in [
4] show that anisotropic turbulence begins to play the predominant role at heights above four to five kilometers, where the anisotropy coefficient (ratio of the horizontal scale to the vertical scale of the correlation of air temperature fluctuations) can exceed 30.
The anisotropy of turbulent fluctuations of temperature and wind velocity manifests in the atmospheric boundary layer (ABL) as well. To date, a number of questions regarding the anisotropy of wind turbulence remain unexplored. In particular, in the scientific literature, no data have been published on the anisotropy of wind turbulence in a stable ABL in the presence of low-level jets (LLJs). Typically, LLJs with maximum wind speed of 15–25 m/s occur at night, when stratification of the air temperature is stable, at a height of 200–700 m above ground level. The mechanism of formation of the nocturnal LLJ was described in detail by Blackadar [
5]. Accounting for wind turbulence anisotropy is important in the development of ABL mathematical models used for various practical applications, such as weather forecast, wind energy, air transport safety, diffusion of atmospheric impurities, etc.
In the ABL, air flow is always turbulent. Therefore, components of the wind vector V = {Vz,Vx,Vy} (where Vz is the vertical component, and Vx and Vy are horizontal components) are random functions at time t and radius vector r = {z, x, y} in a Cartesian coordinate system centered at a point on the Earth’s surface (z is the vertical coordinate, x and y are the horizontal coordinates). Let the direction of the average horizontal wind be parallel to the axis x, and the average value of the vertical component be zero. In this case, Vx is the longitudinal component and Vy is the transverse (on the horizontal plane) component of the wind velocity vector. Average values < Vz > and < Vy > are equal to zero. Hereinafter, the angular brackets denote ensemble averaging. Denote the fluctuations of the vertical, longitudinal, and transversal components of the wind as w = Vz, u = Vx - < Vx >, and v = Vy, respectively.
Pulsed coherent Doppler lidars (PCDLs) are widely applied to investigate wind turbulence in the ABL [
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25]. Strategies to conduct measurements with a scanning PCDL to study wind turbulence have been proposed [
6,
15], along with methods to estimate turbulence parameters, such as momentum fluxes <
wu >, <
wv >, and <
uv >; and variances of the vertical
= <
w2 >, longitudinal
= <
u2 >, and transversal
= <
v2 > components of wind velocity vector, respectively. These methods provide an estimation of the differences in magnitude of
,
, and
due to wind turbulence anisotropy, but do not allow estimation with respect to the spatial scales of the correlation of turbulent fluctuations of the wind velocity components, such as the integral spatial scales of longitudinal correlation
,
, and
. Here,
Bw(
r, 0, 0) = <
w(
z+
r,
x0,
y0)
w(
z,
x,
y) >,
Bu(0,
r, 0) = <
u(
z,
x+
r,
y)
u(
z,
x,
y) >, and
Bv(0, 0,
r) = <
v(
z,
x,
y+y)
v(
z,
x,
y) > are spatial correlation functions of the vertical, longitudinal, and transversal components of the wind velocity vector, respectively.
A method was proposed for estimation of the turbulent energy dissipation rate ε and the radial velocity variance
with measurements by a conically scanning PCDL at elevation angle
ϕ [
19,
20]. The estimate for
found by the method described [
19,
20], is a result of averaging the variances of the radial velocities measured with the lidar at all azimuth angles
θ, which are set during the scan. With the assumption that the turbulence structure is described by the von Kàrmàn model [
26,
27], the integral scale of longitudinal correlation of the radial velocity fluctuations
LV can be calculated from the lidar estimates
ε and
by the following equation [
19,
20]:
The integral scale
LV is, just as
, the result of averaging over all the azimuth angles
θ. Similar to
, the scale
LV at a fixed height depends on the elevation angle
ϕ employed in the conical scanning due to the turbulence anisotropy, even at horizontally statistically homogeneous wind velocity fluctuations. If the scanning is conducted at the angle
ϕ = tan
−1(1/
) ≈ 35.3°, then the kinetic energy of turbulence
E = (1/2)(
+
+
) can be calculated from the lidar estimates
as
E = (3/2)
[
6,
19,
20].
In this paper, a method is proposed to estimate wind turbulence parameters, including the integral spatial scales of turbulence based on Equation (1), from lidar measurements employing conical scanning at different elevation angles. This method also allows us to determine the anisotropy of the spatial correlation of wind velocity fluctuations. The method was tested in an experiment with a Stream Line lidar (Halo Photonics, Brockamin, Worcester, United Kingdom) under stable temperature stratification conditions in the atmospheric boundary layer.
2. Lidar Method to Determine Parameters of Anisotropic Turbulence
The instantaneous radial velocity
Vr, which is the projection of the wind velocity vector onto the optical axis of the probing beam, at point
r =
RS(
θ,
ϕ), can be represented in the form [
14]:
where
R is the distance from the lidar to the point
r and
S(
θ,
ϕ)
= {sin
ϕ, cos
ϕ cos
θ, cos
ϕ sin
θ} is the unit vector along the optical axis. Difference
Vr’ =
Vr - <
Vr > represents turbulent fluctuations in the radial velocity. Due to statistical inhomogeneity and anisotropy, the radial velocity variance
is a function of both the parameters, characterizing wind turbulence, and of the distance
R and the angles
θ and
ϕ. We assume that the wind field is statistically homogeneous in the horizontal plane. Then, the radial velocity variance
averaged over all azimuth angles
θ (in the range from 0 to 2
π) can be represented in the form [
6,
20]:
where
h =
Rsin
ϕ =
z is the height and
is the wind velocity variance defined as an average of variances of the longitudinal and transversal components of the wind velocity vector in the horizontal plane. Experiments [
28] showed that the variance
differs much more from the variances
and
than variances
and
differ from each other. Often, the variances
and
coincide. Therefore, for an experimental study of the anisotropy of wind turbulence, measuring only two variances:
and
may suffice.
According to Equation (3), the variance
, besides the height
h, depends on the elevation angle
ϕ due to the anisotropy of turbulence (
). To obtain estimates of the variances
and
, simultaneous lidar measurements at two different elevation angles are necessary. Given two different angles
ϕ = ϕ1 and
ϕ = ϕ2 (
ϕ1 ≠
ϕ2) in Equation (3), we obtain a system of equations for the height profiles of the variances
and
:
To retrieve the vertical profile of the turbulent kinetic energy
E(
h) from lidar data, we take
ϕ1 = 35.3° in Equation (4) [
6]. The angle
ϕ2 is taken as 60°. Then, the solution of the system of Equation (4) has the following form:
where
ϕ1 = 35.3° and
ϕ2 = 60°.
The turbulent energy dissipation rate
ε is a characteristic of locally isotropic wind turbulence within the inertial subrange. In the case of statistical homogeneity of the wind field in the horizontal plane, the dissipation rate is a function of height
h and does not depend on horizontal coordinates
x and
y. After substitution of the values of the variance
and the dissipation rate
ε(
h) obtained from lidar measurements at different elevation angles
ϕi (
i = 1, 2) into Equation (1), the integral scales
LV(
h,
ϕi) at the angles
ϕi are calculated. The estimation method of
and
ε from the data measured by the conically scanning PCDL is described in [
20]. Employing the von Kàrmàn model in Equation (1) yields the vertical profiles of longitudinal correlation scales of fluctuations of the vertical
Lw(
h) and horizontal
LH(
h) wind velocity, if the variance
in Equation (1) is replaced with
and
, respectively. Because
, we assume that the value of
LH is between values of
Lu and
Lv.
On obtaining scales
LV1 =
LV(
h,
ϕ1) and
LV2 =
LV(
h,
ϕ2) from lidar measurements at the scanning elevation angles
ϕ1 = 35.3° and
ϕ2 = 60°, and employing Equations (1), (5), and (6), the scales
Lw and
LH can be respectively calculated as:
To apply the described method to estimate the variances and correlation scales of fluctuations of vertical and horizontal wind velocity, measurements should be recorded simultaneously by two lidars scanning at different elevation angles. However, considering that the lidar data has to be averaged over a long period of time to obtain a statistically significant estimate of the variance of radial velocity, this method can be applied using a single lidar.
Therefore, as shown in
Figure 1, the lidar probing beam conducts conical scanning about the vertical axis alternatively at the elevation angles of 35.3° (odd scan numbers) and 60° (even scan numbers).
Before the measurements were taken, elevation angle was set to ϕ = 35.3°. Then, the scanning starts with constant angular velocity ωs = dθ/dt. During the scanning, the azimuth angle θ of the probing direction varies from 0° to 360°. After a full turn, the scanning stops and the elevation angle of 35.3° changes to 60°, which takes approximately 1 s. Then, the scanning starts in the opposite direction. The azimuth angle θ changes from 360° to 0°. At θ = 0°, the elevation angle of 60° again changes to 35.3° and the procedure repeats.
3. Experiment
The experiment was conducted on 6–24 June 2018 at the Basic Experimental Observatory (BEO) of the Institute of Atmospheric Optics SB RAS (IAO) in Tomsk, Russia (56.475448° N, 85.048115° E), employing a Stream Line PCDL (Halo Photonics, Brockamin, Worcester, United Kingdom). The experimental geometry is shown in
Figure 1, which shows conical scanning with alternating elevation angle (35.3° and 60°). The duration of every scan was
Tscan = 60 s. Adding the time
δt ≈ 1 s needed to change the elevation angle from 35.3° to 60° and vice versa, the duration of one measurement cycle
Tcircl = 2(
Tscan +
δt) was a little bit longer than 2 min. For accumulation of raw lidar data,
Na = 7500 laser shots were used. The pulse repetition frequency was
fp = 15 kHz. Thus, the duration of measurements for every azimuth angle ∆
t =
Na/
fp = 0.5 s. The azimuth resolution was ∆
θ = 360°/
M = 3°, where
M =
Tscan/∆
t = 120 was the number of rays for one conical scan.
As a result of the measurements, we obtained arrays of estimates of the signal-to-noise ratio SNR (Rk, θm; n) and the radial velocity VL (Rk, θm; n). Here, the SNR is the ratio of average heterodyne signal power to the average detector noise power in a 50 MHz bandwidth. Estimates of SNR and VL are functions of the parameters Rk, θm, and n, where Rk = R0 + k∆R is the distance from the lidar to the center of the sensing volume, k = 0,1,2,…,K−1; ∆R = 18 m is the range gate length; θm = m∆θ is the dependence of the azimuth angle on the ray number m = 0,1,2,…,M−1 at the elevation angle ϕ = 35.3°; θm = 360°−m∆θ is the azimuth angle at ϕ = 60°; n = 1,3,5,7,… is the conical scan number at the elevation angle ϕ = 35.3°; and n = 2,4,6,8,… is the conical scan number at the elevation angle ϕ = 60°. Each of the arrays SNR (Rk, θm; n) and VL (Rk, θm; n) is divided into two sub-arrays: SNRi (Rk, θm; n) and VLi (Rk, θm; n) with odd (i = 1) and even (i = 2) numbers n. The subscript i = 1 corresponds to the elevation angle ϕ = 35.3°, whereas i = 2 denotes ϕ = 60°.
To increase the accuracy of SNR measurement, SNR estimates were averaged over all azimuth angles for every distance
Rk and scan number
n,
. Estimates of the wind velocity vector
Vi(
Rk,
n) = {
Vzi(
Rk,
n),
Vxi(
Rk,
n),
Vyi(
Rk,
n)}, where
Vzi is the vertical component and
Vxi and
Vyi are the horizontal components, were determined from the arrays of lidar estimates of the radial velocity
VLi (
Rk,
θm;
n) using the direct sine-wave fitting method [
14,
29]. The wind speed
Ui and the wind direction angle
θVi were calculated from the horizontal components of the velocity vector as
Ui = |
Vxi +
jVyi| and
θVi = arg{
Vxi +
jVyi }, respectively, where
j is an imaginary unit.
4. Results of the Measurements
To retrieve information about turbulence from lidar data, the probability of bad (false) estimates of radial velocity has to be nearly zero [
30]. That is, the SNR during the measurements should be high. For accumulation number
Na = 7500, the SNR should exceed –16 dB. Therefore, to study the anisotropy of wind turbulence in a stable ABL, we had to select data corresponding to the stable temperature stratification and SNR > –16 dB. Lidar data obtained in the 12-hour period from 20:00 on 23 July to 08:00 on 24 July met this requirement. Using the data for the average temperature of air
T(
h,
t) measured by sonic anemometers during this time interval at heights
h1 = 3 m and
h1 = 42 m, we calculated the potential temperature derivative
dTp/
dh by the equation:
dTp/
dh = [
T(
h2,
t) −
T(
h1,
t) ]/(
h2 − h1) +
ya, where
ya = 0.0098 °K/m is the adiabatic gradient of dry air temperature. Under the condition
dTp/
dh > 0, the temperature stratification is stable; if
dTp/
dh = 0, the stratification is neutral; and when
dTp/
dh < 0, the stratification is unstable. Calculations show that beginning with 20:00 on 23 July to 08:00 on 24 July, the value of
dTp/
dh varied in the range of 0.005 to 0.02 °K/m. Therefore, the temperature stratification of the surface atmospheric layer was stable in this period.
The estimates of the radial velocity with subscript
k obtained from lidar measurements at different values of the elevation angles,
ϕ1 = 35.3° and
ϕ2 = 60°, correspond to different heights,
hki =
h0i +
k∆
hi, where
h0i =
R0 sin
ϕi is the initial height and ∆
hi = ∆
R sin
ϕi is the vertical step. By sorting the obtained data in heights, two two-dimensional (2D) composite plots corresponding to the elevation angles of 35.3° and 60° were sampled for each of the following parameters: the signal-to-noise ratio
, wind speed
Ui(
hki, tn), wind direction angle
θVi(
hki, tn), and the vertical wind speed
Vzi(
hki, tn). Here,
tn =
t0 +
nTcircl/2 is the current time and
t0 is the measurement starting time. The obtained distributions are shown in
Figure 2, which shows that the
for the elevation angle of 35.3° becomes much smaller than
for the elevation angle of 60° starting from heights at 400–500 m. This is caused by the longer distance to the probed volume at
ϕ = 35.3° than at
ϕ = 60° and, possibly, by the horizontal inhomogeneity of the aerosol backscatter coefficient. In the zones where
–16 dB, differences in the height-time distributions of the wind speeds U
1(
h, tn) and
U2(
h, tn) and the wind direction angles
θV1(
h, tn) and
θV2(h, tn) are not as significant. (Compare
Figure 2c with
Figure 2d and
Figure 2e with
Figure 2f.) These differences are mainly caused by turbulent variations in the wind field. The low-level jet (LLJ) at heights of 350–700 m is easily observed. At the LLJ center, the wind speed sometimes achieved 25 m/s. The estimates of the vertical component of the wind velocity vector at
do not go beyond, with one exception—the range from –1 to 1 m/s (
Figure 2g–h). This agrees with the results reported by Lolli et al. [
31]. Due to large-scale turbulent inhomogeneities of the wind flow and fast mesoscale processes, a significant difference was observed in estimates of vertical wind velocity
Vz1(
h, tn) and
Vz2(
h, tn).
To obtain estimates for the wind turbulence parameters, we used the measured data obtained at
, when the probability of bad estimates of the radial velocity [
32] was close to zero. According to the data in
Figure 2a–b, this requirement was fulfilled for heights up to 600 m. The turbulent energy dissipation rates
ε1(
hk1, tn) and
ε2(
hk2, tn), radial velocity variances
and
, and integral scales of turbulence
LV1(
h k1, tn) and
LV2(
h k2, tn) were estimated from the arrays of fluctuations of lidar estimates of the radial velocity
VLi’ using the method described thoroughly by Smalikho and Banakh [
20]. Here,
VLi’(
Rk,
θm;
n) =
VLi(
Rk,
θm;
n) -
Si(
θm)⋅
V(
Rk,
n);
Si(
θm) = {sin
ϕi, cos
ϕicos
θm, cos
ϕi sin
θm},
i = 1,2; and
i = 1 and
i = 2 correspond to measurements at the elevation angles of 35.3° (odd scan numbers
n) and 60° (even
n), respectively. For the averaging, we used estimates of
VLi’(
Rk,
θm;
n) obtained from lidar measurements for 20 scans for each elevation angle. This corresponds to 40-min time averaging.
Figure 3 depicts the obtained spatiotemporal distributions of turbulence parameters
,
εi(
hki, tn), and
LVi(
hki, tn). In every distribution, the black curve shows the temporal profile of the height of maximal wind speed assessed from the data in
Figure 2c. This curve is a boundary between the top and bottom parts of the LLJ and can be considered as its center. The wind turbulence is very weak in the top part of the LLJ; in particular, the turbulent energy dissipation rate does not exceed 10
–4 m
2/s
3, and the variance of radial velocity
at the elevation angle of 60° is below 0.08 m
2/s
2.
Assuming horizontal statistical homogeneity of the wind, the kinetic energy of turbulence was calculated as
from the data for the variance of radial velocity
obtained from measurements at the elevation angle of 35.3°. Combining calculated
E(
hk1, tn) and data of
Figure 2c,e, and
Figure 3a,c, we drew vertical profiles of the wind speed and direction, kinetic energy of turbulence, and its dissipation rate in
Figure 4. The turbulence was strong on 23 July in the bottom part of the LLJ at heights 200–400 m at wind speeds exceeding 15 m/s. The kinetic energy
E ranged from 1.0 to 0.5 m
2/s
2, and the dissipation rate varied within 7 10
–3–10
–3 m
2/s
3. We calculated the errors of estimation of the kinetic energy
E and the dissipation rate
ε using the technique described in [
30]. According to our calculations, the relative error of the kinetic energy estimates was 7%–10% in the bottom part of the LLJ, whereas the accuracy of the dissipation rate estimates was 6%–8%.
In this experiment, the minimum height for retrieving vertical profiles of velocity from lidar measurements with acceptable accuracy was 100 m. The maximum height at which measurements were recorded with sonic anemometers was 42 m (a sonic anemometer was installed on top of the mast, located 150 m from the lidar). In
Figure 4, in addition to lidar data, we depict the results of measurements with the sonic anemometer at a height of 42 m. Sonic anemometer measurement data show that, despite the conditions of stable temperature stratification, in the surface layer of the atmosphere (layer thickness of about 100 m in height above the ground), wind turbulence was quite strong.
The turbulent energy dissipation rate is a characteristic of the locally isotropic field of wind velocities. Assuming that the wind velocity field is statistically homogeneous in the horizontal plane, the lidar estimates of the dissipation rates
ε1(
h, tn) and
ε2(
h, tn) obtained for the same height
h, but for different elevation angles (35.5° and 60°), should fully coincide on average. To verify this, we used the data in
Figure 3c–d and their vertical interpolation with a step of 10 m, starting from 100 m and ending at a height of 500 m.
Figure 5 depicts the results of the comparison of the lidar estimates of the dissipation rate
ε1(
h, tn) and
ε2(
h, tn) in four vertical layers: (1) 100–200, (2) 200–300, (3) 300–400, and (4) 400–500 m. The analysis of these results showed that, on average,
ε1 is 20% less than
ε2 in the first layer,
ε1 and
ε2 practically coincide in the second layer, and
ε1 exceeds
ε2 1.5 and 2 times in the third and fourth layers, respectively. The reason for the small discrepancy in dissipation rate estimates in the lowest layers is unclear. On average, at heights from 170 m to 320 m, the absolute value of the discrepancy between of the dissipation rate estimates [2(
ε1 –
ε2)/(
ε1 +
ε2)]×100% does not exceed 10%. This indicates the horizontal statistical homogeneity of the wind velocity field at these heights. The significant discrepancy of the dissipation rate estimates from lidar measurements at the elevation angles of 35.3° and 60° in the upper layers may originate from horizontal mesoscale inhomogeneities in the wind field caused, for example, by internal atmospheric waves being stronger against the weakly turbulent background.
Accessible experimental data (see, for example, [
28]) indicate that in the atmospheric boundary layer, the variance of horizontal wind velocity
exceeds the variance of the vertical component
, and the correlation scale of the fluctuations of the horizontal velocity
Lu(
h) is larger than the correlation scale of fluctuations of the vertical velocity
LW(
h) due to anisotropy of wind turbulence. Since
, according to Equation (4), we expect that the variance
exceeds
in our experiment at the elevation angles
ϕ1 = 35.3° <
ϕ2 = 60°.
Figure 6 shows the vertical profiles of the variances
and
, and integral correlation scales
LV1(
hk1) =
LV(
Rk,
ϕ1) and
LV2(
hk2) =
LV(
Rk,
ϕ2) of the radial velocity fluctuations, as retrieved from the lidar measurements at elevation angles
ϕ =
ϕ1 = 35.3° and
ϕ =
ϕ2 = 60°, respectively. At the same height
h, the variance satisfies
(
Figure 6a,c,e). The integral scales
LVi were calculated, according to Equation (1), as:
From the analysis of the results of estimation of the turbulent energy dissipation rate
εi shown in
Figure 5,
ε1 ≈
ε2 at heights of 100–320 m and
ε1 >
ε2 at heights of 320–500 m. This means that
LV1 obtained by Equation (9) in the 320–500 m layer is underestimated, whereas the
LV2 in this layer is overestimated. In spite of that, the inequality
LV1(
h) >
LV2(
h) holds at all heights, due to the anisotropy of turbulence (
Figure 6b,d,f).
The data in
Figure 3a–b show that the ratio of the radial velocity variances
averaged employing all estimates in the 100–300 m layer is equal to 1.4. Thus, on average, the ratio of the integral scales is
LV1/
LV2 =
μ3/2 = 1.7. Approximately the same result
LV1/
LV2 ≈ 1.8 was obtained from direct averaging of the ratios of the integral scales in this layer based on the data in
Figure 3e–f. Thus, due to the anisotropy of turbulence, the variance of the radial velocity at the elevation angle of 35.3° is 1.4 times larger than that at 60°, whereas the integral scale of turbulence at the elevation angle of 35.3° exceeds the integral scale at the elevation angle of 60° by 1.7 times.
Assuming that the wind field is horizontally statistically homogeneous in the 100–300 m layer, applying
(Equation (3) [
20]), where
ϕ1 = 35.3° and
ϕ2 = 60°, we find:
for the ratio of the average between the variances of the longitudinal and transversal components of the wind vector
to the variance of vertical component
. Substituting
μ = 1.4 into Equation (10) yields that the variance
is 2.26 times larger than the variance
. On the assumption that the spatial structure of the wind turbulence is described by the von Kàrmàn model (Equation (1)), we obtain
for the ratio of integral longitudinal correlation scales of fluctuations in the horizontal
LH and vertical
Lw components of the wind velocity vector. Substituting
= 2.26 into this formula yields that the correlation scale of fluctuations of the horizontal wind component
LH is 3.4 times larger than that of fluctuations of the vertical component
Lw. The obtained estimates of the anisotropy coefficient of wind turbulence parameters do not contradict the known experimental data [
28].
Using the data (three components of the wind vector) measured with a sonic anemometer at a height of 42 m (
Figure 4), we obtained the variances
and
versus time
t for the period under consideration from 20:00 on 23 July to 08:00 on 24 July 2018. Each variance estimate was derived from 30-minute measurement data. The anisotropy coefficient
averaged over all the measurement period was approximately 2, which is only 13% less than the lidar estimate (
vσ = 2.26) for heights of 100–300 m.
As follows from
Figure 3e–f and
Figure 6b,d,f, the lidar estimate of the integral scale
increases with height and takes overstated values at heights above 450 m at the central and upper parts of the LLJ. In
Figure 3e–f, the zones where the estimates of the integral scale of turbulence
LVi(
hki,
tn) exceed 200 m are shown in white. To find the reason for this error, by analogy with Banakh and Smalikho. [
25], we studied fluctuations in the lidar estimates of the radial velocity
. As a result, we found that inhomogeneities in the wind flow with scales comparable to the base radius of the scan cone occur above 300 m. This effect is mostly pronounced at the central part of the LLJ and especially in the zones where the wind direction changes strongly with height (
Figure 2e–f and
Figure 4b). It is possible that mesoscale processes occur here, like internal atmospheric waves arising under stable temperature stratification conditions and a strong change in the wind velocity with height.
For a more accurate estimation of the scales
LH and
Lw in the upper part of the LLJ, we used the following approach. Consider the 100–300 m layer, where the contribution of mesoscale processes to wind variations is negligibly small in comparison with wind turbulence, and the conditions of horizontally statistically homogeneous turbulence are fulfilled (
ε1 ≈
ε2,
Figure 5). In this layer, as depicted in
Figure 6b,d,f, on average, the integral scales
LV1 and
LV2 increase linearly with height and have realistic values. Thus, at a height 100 m, on average,
LV1 = 45 m and
LV2 = 26 m, whereas at 300 m
LV1 = 93 m and
LV2 = 51 m. Assuming that in the 300–500 m layer, the characteristic of the change in the integral scale
LVi with height does not considerably differ from that observed in the lower layer, we linearly extrapolated the scales in the 100–300 m layer to higher layers. As a result, we found that at
h = 500 m, the integral scales are
LV1 = 136 m and
LV2 = 80 m. These values of the turbulent scales
LVi for the central part of the LLJ do not contradict the published experimental data [
25]. According to Equations (7) and (8), at the central part of the LLJ at a height of 500 m with
LV1= 136 m and
LV2 = 80 m, the horizontal
LH and vertical
Lw scales of longitudinal correlation of wind velocity are approximately 183 m and 54 m, respectively.