Nonlinear atmospheric gravity waves in the Earth’s isothermal atmosphere

Heading: 
Space Physics
1Cheremnykh, OK, Lashkin, VM, 1Cheremnykh, SO, 1Fedorenko, AK
1Space Research Institute under NAS and National Space Agency of Ukraine, Kyiv, Ukraine
Kinemat. fiz. nebesnyh tel (Online) 2025, 41(6):3-15
https://doi.org/10.15407/kfnt2025.06.003
Language: Ukrainian
Abstract: 

Modern experimental and theoretical studies of atmospheric gravity waves (AGW) indicate the need for a nonlinear consideration of these processes. First of all, this is due to the exponential growth of the amplitudes of gravity waves with height in the atmosphere, which significantly limits the possibility of applying the linear theory. In the work, analytical solutions of the system of nonlinear equations describing the propagation of atmospheric gravity waves in the isothermal atmosphere were obtained. To find the solutions, we used nonlinear equations obtained earlier in the model of two-dimensional motion of an ideal atmospheric gas in the Boussinesq approximation. The nonlinear components in these equations have the form of Poisson brackets. We found the solutions of the nonlinear equations in the form of plane waves. For this type of solution, the Poisson brackets are converted to zero. This approach allowed us to obtain analytical solutions that describe various types of nonlinear gravity waves in an isothermal atmosphere. In the linear theory of AGW, solutions in the form of plane waves are in the assumption of small amplitudes of perturbations. Unlike the linear consideration, the solutions of the nonlinear equations we obtained do not have restrictions on the amplitude. Within the framework of the specified simplifying assumptions, solutions were obtained from the system of nonlinear equations for: 1) freely propagating internal gravity waves, 2) horizontal (evanescent) atmospheric gravity waves, and 3) important special cases of evanescent wave modes. The energy conditions for the realization of the obtained types of wave perturbations in an isothermal atmosphere were analyzed. The specified nonlinear solutions 1)—3) are non-divergent, since when obtaining them, a system of nonlinear equations was used, written in the assumption of zero velocity divergence. At the same time, in the linear theory, the assumption of zero velocity divergence singles out only one f-mode from the entire AGW spectrum. That is, the application of nonlinear theory when considering gravitational waves, even with significant simplifications in the original system of nonlinear equations, significantly expands the class of wave solutions in comparison with the linear theory.
Keywords: evanescent wave modes, isothermal atmosphere, nonlinear atmospheric gravity waves

Full text (PDF)

References: 

1. Cheremnykh O. K., Cheremnykh S. O., Vlasov D. I. (2022).The Influence of the Earth's Atmosphere Rotation on the Spectrum of Acoustic-Gravity Waves Kinematika i fizika nebesnyh til. 38(3). 3-19.
https://doi.org/10.15407/kfnt2022.03.003

2. Cheremnykh O. K., Fedorenko A. K., Kryuchkov E. I., Klymenko Y. O., Zhuk I. T. (2024). Developing the Models of Acoustic-Gravity Waves in the Upper Atmosphere (Review). Kinematika i fizika nebesnyh til. 40 (1). 3-23.
https://doi.org/10.15407/kfnt2024.01.003

3. Cheremnykh O. K., Fedorenko A. K., Kryuchkov E. I., Selivanov Y. A. (2019). Evanescent acoustic-gravity modes in the isothermal atmosphere: systematization, applications to the Earth's and Solar atmospheres. Ann. Geophys. 37. 1-11.
https://doi.org/10.5194/angeo-2019-1

4. Cheremnykh O., Fedorenko A., Selivanov Y., Cheremnykh S. (2021). Continuous spectrum of evanescent acoustic-gravity waves in an isothermal atmosphere. Mon. Notic. Roy. Astron. Soc. 503(4). 5545-5553.
https://doi.org/10.1093/mnras/stab845

5. Cheremnykh O., Kaladze T., Selivanov Y., Cheremnykh S. (2022). Evanescent acoustic-gravity waves in a rotating stratified atmosphere. Adv. Space Res. 69. 1272- 1280.
https://doi.org/10.1016/j.asr.2021.10.050

6. Fedorenko A. K., Kryuchkov E. I., Cheremnykh O. K., Klymenko Yu. O., Yampolski Yu. M. (2018). Peculiarities of acoustic-gravity waves in inhomogeneous flows of the polar thermosphere. J. Atmos. and Solar-Terr. Phys. 178. 17-23.
https://doi.org/10.1016/j.jastp.2018.05.009

7. Fritts D. C., Laughman B., Lund T. S., Snively J. B. (2015). Self-acceleration and instability of gravity wave packets: 1. Effects of temporal localization. J. Geophys. Res. Atmos. 120. 8783-8803.
https://doi.org/10.1002/2015JD023363

8. Huang C. S., Li J. (1992). Interaction of atmospheric gravity solitary waves with ion acoustic solitary waves in the ionospheric F-region. J. Atmos. and Terr. Phys. 54. 951-956.
https://doi.org/10.1016/0021-9169(92)90060-X

9. Huang K. M., Zhang S. D., Yi F., Huang C. M., Gan Q., Gong Y., Zhang Y. H. (2014). Nonlinear interaction of gravity waves in a nonisothermal and dissipative atmosphere. Ann. Geophys. 32. 263-275.
https://doi.org/10.5194/angeo-32-263-2014

10. Jones W. L. (1969). Non-divergent oscillations in the Solar Atmosphere. Solar Phys. 7. 204-209.
https://doi.org/10.1007/BF00224898

11. Jovanovi D., Stenflo L., Shukla P. K. (2001). Acoustic gravity tripolar vortices. Phys. Lett. A. 279. 70-74.
https://doi.org/10.1016/S0375-9601(00)00796-9

12. Jovanovi D., Stenflo L., Shukla P. K. (2002). Acoustic-gravity nonlinear structures. Nonlin. Proc. Geophys. 9. 333-339.
https://doi.org/10.5194/npg-9-333-2002

13. Kaladze T. D., Pokhotelov O. A., Shan H. A., Shan M. I., Stenflo L. (2008). Acoustic-gravity waves in the Earth's ionosphere. J. Atmos. and Solar-Terr. Phys. 70. 1607-1616.
https://doi.org/10.1016/j.jastp.2008.06.009

14. Kaladze T. D., Misra A. P., Roy A., Chatterjee D. (2022). Nonlinear evolution of internal gravity waves in the Earth's ionosphere: Analytical and numerical approach. Adv. Space Res. 69. 3374-3385.
https://doi.org/10.1016/j.asr.2022.02.014

15. Lashkin V. M., Cheremnykh O. K. (2023). Acoustic-gravity waves in quasiisothermal atmospheres with a random vertical temperature profile. Wave Motion. 119. 103140.
https://doi.org/10.1016/j.wavemoti.2023.103140

16. Lashkin V. M., Cheremnykh O. K. (2024). Nonlinear internal gravity waves in the atmosphere: Rogue waves, breathers and dark solitons. Commun. Nonlinear Sci. and Numerical Simulation. 130. 107757. https://doi.org/10.1016/j.cnsns.2023.107757.

17. Lashkin V. M., Cheremnykh O. K. (2024). Modulational instability and collapse of internal gravity waves in the atmosphere. Phys. Rev. E. 10. 024216.
https://doi.org/10.1103/PhysRevE.110.024216

18. Mixa T., Fritts D., Lund T., Laughman B., Wang L., Kantha L. (2019). Numerical simulations of high-frequency gravity wave propagation through fine structures in the mesosphere. J. Geophys. Res. Atmos. 124. 9372-9390.
https://doi.org/10.1029/2018JD029746

19. Onishchenko O., Pokhotelov O., Fedun V. (2013). Convective cells of internal gravity waves in the earth's atmosphere with finite temperature gradient. Ann. Geophys. 31. 459-462.
https://doi.org/10.5194/angeo-31-459-2013

20. Roy A., Roy S., Misra A. P. (2019). Dynamical properties of acoustic-gravity waves in the atmosphere. J. Atmos. and Solar-Terr. Phys. 186. 78-81.
https://doi.org/10.1016/j.jastp.2019.02.009

21. Snively J. B. (2017). Nonlinear gravity wave forcing as a source of acoustic waves in the mesosphere, thermosphere, and ionosphere. Geophys. Res. Lett. 44. 12020- 12027.
https://doi.org/10.1002/2017GL075360

22. Stenflo L. (1987). Acoustic solitary waves. Phys. Fluids. 30. 3297-3299.
https://doi.org/10.1063/1.866458

23. Stenflo L. (1990). Acoustic gravity vortices. Phys. Scripta. 41. 641-642.

DOI 10.1088/0031-8949/41/5/001.

24. Stenflo L., Shukla P. K. (2009). Nonlinear acoustic-gravity waves. J. Plasma Physics. 75. 841-847.
https://doi.org/10.1017/S0022377809007892

25. Sutherland B. R. (2015). Internal Gravity Wave, Cambridge University Press.

26. Vadas S. L., Fritts M. J. (2005). Thermospheric responses to gravity waves: Influences of increasing viscosity and thermal diffusivity. J. Geophys. Res. 110(D15103).
https://doi.org/10.1029/2004JD005574

27. Waltercheid R. L., Hecht J. H. (2003). A reexamination of evanescent acoustic-gravity waves: Special properties and aeronomical significance. J. Geophys. Res. 108 (D11). 4340.
https://doi.org/10.1029/2002JD002421

28. Whitham G. B. (1974). Linear and nonlinear waves. A Wiley-Interscience Publications.

29. Yiit E., Aylward A. D., Medvedev A. S. (2008). Parameterization of the effects of vertically propagating gravity waves for thermosphere general circulation models: Sensitivity study. J. Geophys. Res. 113 (D19106).
https://doi.org/10.1029/2008JD010135

30. Zhang S. D., Yi F. (2002). A numerical study of propagation characteristics of gravity wave packets propagating in a dissipative atmosphere. J. Geophys. Res. 107(D14). 1-9.
https://doi.org/10.1029/2001JD000864