# The Impact of Internal Gravity Waves on the Spectra of Turbulent Fluctuations of Vertical Wind Velocity in the Stable Atmospheric Boundary Layer

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Measurement Technique

## 3. Results of the Measurements

#### 3.1. The IGW on 6 July 2021

#### 3.2. The IGW on 28 May 2022

^{2}/s

^{3}to $5\cdot {10}^{-4}$ m

^{2}/s

^{3}, and it does not exceed 10

^{−5}m

^{2}/s

^{3}in 75% of cases and 10

^{−6}m

^{2}/s

^{3}in 50% of cases.

#### 3.3. The IGW on 30 May 2022

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Vertical profiles of the horizontal wind velocity component ${U}_{1}$(

**a**) and the wind direction angle ${\theta}_{V}$ (

**b**) calculated from lidar measurements at 03:06 (curves 1), 03:16 (curves 2), 03:26 (curves 3), 03:36 (curves 4), 03:46 (curves 5), and 03:56 (curves 6) of local time on July 6 of 2021. Each profile is drawn from measurement data obtained in one conical scan for 1 min.

**Figure 2.**Height–time distribution of the vertical component of the wind velocity vector (

**a**) and time series of the vertical component of the wind velocity vector at heights of 207, 297, 405, and 513 m (

**b**). The red circles in (

**b**) are for the estimates of the vertical velocity ${\overline{V}}_{z}$ determined from conical scanning data. Measurements within an hour starting from 03:00 LT on 6 July 2021.

**Figure 3.**Time series (

**a**) and power spectra of the vertical component of wind velocity at time intervals of 03:06–03:26 LT (blue arrow, blue curve) and 03:26–03:46 LT (red arrow, red curve) (

**b**) at a height of 405 m. Black arrows in (

**a**) show time intervals for which the spectra in Figure 4 calculated. Measurements were taken on6 July 2021.

**Figure 4.**Spectra of the vertical component of the wind velocity vector at a height of 297 m calculated for the measurement intervals shown by the black arrows in Figure 3a (black curves). Green dashed lines show the noise component of the spectrum. Red arrows show the interval, within which the turbulent energy dissipation rate $\epsilon $ is determined by the our method described in [46]. Yellow curves are for the theoretical spectra calculated by us using Equation (14) in [46] and the experimental values of $\epsilon $. The purple lines are for the −5/3 Kolmogorov–Obukhov spectra calculated by us using Equation (18) in [46]. The brown vertical lines show the frequencies of IGW-induced quasi-harmonic oscillations of the vertical velocity. Measurements were taken on 6 July 2021.

**Figure 5.**Height–time distributions of the instrumental error of estimation of the radial velocity (

**a**), the variance of the vertical component of the wind velocity vector (

**b**), turbulent kinetic energy (TKE) dissipation rate (

**c**), and the relative error of estimation of the dissipation rate (

**d**) on 6 July 2021. The white rectangle bounds the height–time domain of the IGW observation.

**Figure 6.**Vertical profiles of the horizontal component of wind velocity ${U}_{1}$ obtained from lidar measurements at 02:32 (1), 03:02 (2), 03:32 (3), 04:02 (4), 04:32 (5), and 05:02 (6) LT on 28 May 2022.

**Figure 7.**Height–time distribution (

**a**), time series at a height of 351 m (

**b**), and period of quasi-harmonic oscillations of the vertical velocity as a function of time (

**c**) obtained from lidar measurements on 28 May 2022.

**Figure 8.**Spectra of the vertical component of wind velocity (the black curves with squares) obtained from lidar measurements on 28 May 2022 from 02:30 to 03:00 (

**a**), from 03:30 to 04:00 (

**b**), and from 03:50 to 04:20 LT (

**c**) at a height of 351 m. Noise spectral components are shown by the green dashed lines. The purple arrows indicate the interval, within which the TKE dissipation rate $\epsilon $ was estimated by the method described by us in [46]. The obtained values of the dissipation rate were used by us to calculate the theoretical spectra using Equation (14) in [46], with allowance for noise and averaging over the probing volume (yellow curves) and the −5/3 frequency dependence (purple lines). The brown vertical lines show the frequencies of quasi-harmonic oscillations of the vertical velocity. The blue lines are the results of fitting the power-law dependence to the experimental spectra in the intervals indicated by the blue arrows. For the pink and blue curves, 95 percent confidence intervals are indicated.

**Figure 9.**Time series of the exponent $\alpha $ determined from the fitting of the power dependence to the experimental spectra of vertical wind velocity in the frequency range from 0.006 to 0.05 Hz (

**a**) and the Richardson number (

**b**) (black curves). The data of measurements by the StreamLine lidar and MTP-5 microwave temperature profiler on 28 May 2022 at a height of 351 m are used. The purple line corresponds to the exponent of −5/3.

**Figure 10.**Height–time distributions of the instrumental error of estimation of the radial velocity (

**a**), the variance of the vertical component of the wind velocity vector (

**b**), TKE dissipation rate (

**c**), and relative error of estimation of the dissipation rate (

**d**). The white rectangle bounds the domain of IGW observation. Measurements were taken on 28 May 2022.

**Figure 11.**Spectra of the vertical component of wind velocity (black curves with squares) obtained from lidar measurements on 30 May 2022, from 06:04 to 06:34 LT, at different heights. Noise components of the spectra are shown by green dashed lines. The purple arrows show the range, within which the TKE dissipation rate $\epsilon $ was estimated by the method described by us in [46]. The obtained values of the dissipation rate were used to calculate the theoretical spectra using Equation (14) in [46] with allowance for noise and averaging over the probing volume (yellow curves) and the −5/3 frequency dependence of the spectrum (purple lines). The blue lines are the results of fitting the power-law dependence to the experimental spectra in the intervals indicated by the blue arrows. For the pink and blue curves, 95 percent confidence intervals are indicated.

**Figure 12.**Vertical profiles of the horizontal wind velocity (

**a**), TKE dissipation rate (

**b**), the relative error of lidar estimation of the dissipation rate (

**c**), exponent calculated by fitting the power-law dependence to the experimental spectra of the vertical wind velocity in the frequency range from 0.004 to 0.02 Hz (

**d**), mean air temperature (

**e**), and Richardson number (

**f**). The purple line corresponds to the exponent of −5/3. The measurement data of the StreamLine lidar and the MTP-5 microwave temperature profiler from 06:04 to 06:34 LT on 30 May 2022 were used.

**Figure 13.**A histogram of the exponent $\alpha $ of the spectrum of vertical wind velocity in the low-frequency range during IGW propagation in the stable atmospheric boundary layer.

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**MDPI and ACS Style**

Banakh, V.A.; Smalikho, I.N.
The Impact of Internal Gravity Waves on the Spectra of Turbulent Fluctuations of Vertical Wind Velocity in the Stable Atmospheric Boundary Layer. *Remote Sens.* **2023**, *15*, 2894.
https://doi.org/10.3390/rs15112894

**AMA Style**

Banakh VA, Smalikho IN.
The Impact of Internal Gravity Waves on the Spectra of Turbulent Fluctuations of Vertical Wind Velocity in the Stable Atmospheric Boundary Layer. *Remote Sensing*. 2023; 15(11):2894.
https://doi.org/10.3390/rs15112894

**Chicago/Turabian Style**

Banakh, Viktor A., and Igor N. Smalikho.
2023. "The Impact of Internal Gravity Waves on the Spectra of Turbulent Fluctuations of Vertical Wind Velocity in the Stable Atmospheric Boundary Layer" *Remote Sensing* 15, no. 11: 2894.
https://doi.org/10.3390/rs15112894