Splitting of the wave disturbance spectrum in the isothermal atmosphere due to its rotation
Heading:
| 1Cheremnykh, OK, 1Fedorenko, AK, Cheremnykh, OS, 2Kronberg, EA 1Space Research Institute under NAS and National Space Agency of Ukraine, Kyiv, Ukraine 2Max Planck Institute, Göttingen, Germany |
| Kinemat. fiz. nebesnyh tel (Online) 2023, 39(6):3-23 |
| https://doi.org/10.15407/kfnt2023.06.003 |
| Language: Ukrainian |
Abstract: The influence of the Earth’s rotation on the spectrum of low-frequency wave disturbances in an isothermal atmosphere is investigated. The system of equations for small linear disturbances is obtained in the “traditional” approximation and in the β-plane approximation, taking into account the frequency of rotation of the atmosphere. The found equations differ from the previously obtained ones in that the left parts of the equations depend only on time, whereas the right parts are expressed in terms of disturbed pressure. It is shown that at zero perturbed pressure, taking into account the atmospheric rotation in the equations, leads to the “splitting” of the obtained system into separate equations describing vertical and horizontal perturbations. Compact analytical solutions were obtained for both types of disturbances. It was established that vertical disturbances are realized in the form of Brunt — Vaisaila waves, and horizontal — in the form of Rossby waves and inertial oscillations. |
| Keywords: acoustic-gravity waves, dispersion equation, inertial oscillations, Rossby waves, rotating atmosphere, β-plane approximation |
References:
1. Krystal O. N., Voytsekhovska A. D., Cheremnykh O. K., Cheremnykh S. O. (2023). On one property of the dispersion equation for latitudinal acoustic-gravitational waves. Space Science and Technology. 5 (in print).
2. Kryuchkov E. I., Cheremnykh O. K., Fedorenko A. K. (2017). Properties of acoustic-gravity waves in the Earth's polar thermosphere. Kinematics and Phys. Celestial Bodies. 33(3). 122-129. https://doi.org/10.3103/S0884591317030047
3. Ladykov-Roev Yu. P., Cheremnykh O. K. (2010). Mathematical models of continuous media. Kyiv: Naukova Dumka, 552.
4. 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. Kinematics and Phys. Celestial Bodies. 38(3). 121-131. https://doi.org/10.3103/S0884591322030023
5. Batchelor G. K. (2000). An introduction to fluid dynamics. Cambridge University Press, 615. https://doi.org/10.1017/CBO9780511800955
6. Beer T. (1974). Atmospheric waves. John Wiley, New York, 300.
7. Brekhovskikh L. M., Goncharov V. V. (1982). Introductions are the mechanics of continuous media. Moscow: Nauka. 335.
8. 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(3). 405-415. https://doi.org/10.5194/angeo-37-405-2019
9. 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
10. Cheremnykh O., Kaladze T., Selivanov Yu. A. Cheremnykh S. (2022). Evanescent acoustic-gravity waves in a rotating stratified atmosphere. Adv. Space Res. 69(3). 1272-1280. https://doi.org/10.1016/j.asr.2021.10.050
11. Fedorenko A. K., Bespalova A. V., Cheremnykh O. K., Kryuchkov E. I. (2015). A dominant acoustic-gravity mode in the polar thermosphere. Ann. Geophys. 33(1). 101-108. https://doi.org/10.5194/angeo-33-101-2015
12. 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
13. Gill A. E. (1982). Atmosphere-ocean dynamics, Academic Press, New York, 662 p.
14. Gossard E. E., Hooke W. H. (1975). Waves in the atmosphere: Atmospheric infrasound and gravity waves: Their generation and propagation. Elsevier Scientific Publishing Company, 456 p.
15. Hines C. O. (1960). Internal atmospheric gravity waves at ionospheric heights. Can. J. Phys. 38. 1441-1481. https://doi.org/10.1139/p60-150
16. Kaladze T. D., Pokhotelov O. A., Shan H. A., Shan M. I., Stenflo L. (2008). Acoustic-gravity waves in the Earth ionosphere. J. Atmos. and Solar-Terr. Phys. 70. 1607-1616. https://doi.org/10.1016/j.jastp.2008.06.009
17. Kertz W. (1957). This encyclopedia. 48. Р. 928-981. https://doi.org/10.1007/978-3-642-45881-1_16
18. Kshevetskii S. P., Kurdyaeva Y. A., Gavrilov N. M. (2021). Spectra of acoustic gravity waves in the atmosphere with a quasi-isothermal upper layer. Atmosphere. 12. 818. https://doi.org/10.3390/atmos12070818
19. Lamb H. (1932). Hydrodynamics. Dover, New York, 362 p.
20. Landa P. S. (1977). Nonlinear vibrations and waves. M., Nauka, 496.
21. Lavrova O. Y., Sabinin K. D. (2016). Manifestations of inertial oscillations in satellite images of the sea surface. Sovrem. probl. distantsionnogo zondirovaniya Zemli iz kosmosa. 13. 60-73. https://doi.org/10.21046/2070-7401-2016-13-21-60-73
22. Longuet-Higgins M. S. (1964). Planetary waves on a rotating sphere. P. 1. Proc. Roy. Soc. A. 279. 446-473. https://doi.org/10.1098/rspa.1964.0116
23. Pokhotelov O. A., Kaladze T. D., Shukla P. K., Stenflo L. (2001) Three-dimensional solitary vortex structures in the upper atmosphere. Phys. Scr. 64. 245-252. https://doi.org/10.1238/Physica.Regular.064a00245
24. Priest E. (2014). Magnetohydrodynamics of the Sun. Cambridge University Press. https://doi.org/10.1017/CBO9781139020732
25. Rossby C.-G. (1940). Planetary flow patterns in the atmosphere. Quart. J. Roy. Meteorol. Soc. 66. 68-87.
26. 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
27. Stenflo L., Shukla P. K. (2009). Nonlinear acoustic gravity wave. J. Plasma Phys. 75. 841-847. https://doi.org/10.1017/S0022377809007892
28. Sutherland B. R. (2010). Internal gravity waves. Cambridge University Press, 377. https://doi.org/10.1017/CBO9780511780318
29. Tolstoy I. (1963). The theory of waves in stratified fluids including the effect of gravity and rotation. Rev. Mod. Phys. 35(1). 207-230. https://doi.org/10.1103/RevModPhys.35.207
30. Tolstoy I. (1967). Long-period gravity waves in the atmosphere. J. Geophys. Res. 72(18). 4605-4610. https://doi.org/10.1029/JZ072i018p04605
31. 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
32. Woollings T., Li C., Drouard M., Dunn-Sigouin E., Elmestekawy K. A., Hell M., Hoskins B., Mbengue C., Patterson M., Spengler T. (2023). The role of Rossby waves in polar weather and climate. Weather and Climate Dyn. 4(1). 61-80. https://doi.org/10.5194/wcd-2022-43
33. Zaqarashvili T. V., Albekioni M., Ballester J. L., Bekki Y., Biancofiore L., Birch A. C., Dikpati M., Gizon L., Gurgenashvili E., Heifetz E., Lanza A. F., McIntosh S. W., Ofman L., Oliver R., Proxauf B., Umurhan O. M., Yellin-Bergovoy R. (2021). Rossby waves in astrophysics. Space Sci. Rev. 217(15). 61-80. https://doi.org/10.1007/s11214-021-00790-2