Two-frequency propagation mode of acoustic-gravity waves in the earth atmosphere

1Cheremnykh, OK, 1Kryuchkov, YI, 1Fedorenko, AK, 1Cheremnykh, SO
1Space Research Institute under NAS and National Space Agency of Ukraine, Kyiv, Ukraine
Kinemat. fiz. nebesnyh tel (Online) 2020, 36(2):34-57
Start Page: Dynamics and Physics of Solar System Bodies
Language: Ukrainian

As known from long-term theoretical and experimental studies of acoustic-gravity waves (AGW), they largely determine the dynamics and energy balance of the atmospheres of planets and the Sun. Linear wave perturbations in the atmosphere can be described using a system of second-order equations for the vertical and horizontal components of the perturbed velocity. It follows from this system that small perturbations in the atmosphere can be considered as oscillations of coupled oscillators with two degrees of freedom. This suggests the idea of a more detailed study of linear acoustic-gravitational wave modes in the atmosphere using well-developed methods of the oscillations theory. To study small perturbations in the Earth's atmosphere, the methods of the theory of coupled oscillatory systems are used. It is shown that acoustic-gravity waves in an isothermal atmosphere can be considered as a superposition of oscillations that occur simultaneously at two natural frequencies: acoustic and gravitational. Equations are obtained for the natural oscillation's frequencies, as well as for the components of the perturbed velocity under given initial conditions. Changes in the components of the perturbed velocity as a function of time are analyzed and new features of their behavior are discovered. All solutions are presented using real values only. This is more convenient for comparison with observational data than the complex representation commonly used in the theory of acoustic-gravity waves. The conditions are studied under which the usual single-frequency oscillation mode can be realized in the atmosphere. The results of the work can be used to explain some features of satellite observations of wave disturbances in the Earth's atmosphere, which do not fit into the framework of the known theoretical concepts.

Keywords: acoustic-gravitational wave, coupled oscillators, Earth's atmosphere

1. V. I. Arnold, Mathematical Methods of Classical Mechanics (Nauka, Moscow, 1979; Springer-Verlag, New York, 1980).

2. G. Bateman, MHD Instabilities (MIT Press, Cambridge, MA, 1978; Energoizdat, Moscow, 1982).

3. E. E. Gossard and W. H. Hooke, Waves in the Atmosphere: Atmospheric Infrasound and Gravity Waves: Their Generation and Propagation (Elsevier, Amsterdam, 1975; Mir, Moscow, 1978).

4. N. V. Karlov and N. A. Kirichenko, Oscillations, Waves, Structures (Fizmatlit, Moscow, 2003) [in Russian].

5. E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations (McGraw-Hill, New York, 1955; Inostrannaya. Literatura., Moscow, 1958).

6. E. I. Kryuchkov, A. K. Fedorenko, O. K. Cheremnykh. Influence of the upper atmosphere inhomogeneity on acoustic-gravity wave propagation, Kosm. Nauka Tekhnol. 18 (4), 30–36 (2012).

7. E. I. Kryuchkov, O. K. Cheremnykh, and A. K. Fedorenko. Properties of acoustic-gravity waves in the Earth’s polar thermosphere, Kinematics Phys. Celestial Bodies 33, 122–129 (2017).

8. Yu. P. Ladikov-Roev and O. K. Cheremnykh, Mathematical Models of Continuous Media (Naukova Dumka, Kyiv, 2010) [in Russian].

9. Yu. P. Ladikov-Roev, O. K. Cheremnykh, A. K. Fedorenko, and V. E. Nabivach. Acoustic-gravity waves in a vortex polar thermosphere, Probl. Upr. Inf., No. 5, 74–84 (2015).

10. L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 1: Mechanics (Nauka, Moscow, 1965; Pergamon, Oxford, 1969).

11. L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 6: Fluid Dynamics (Nauka, Moscow, 1986; Pergamon, Oxford, 1987).

12. K. Magnus, Vibrations (Blackie, London, 1965; Mir, Moscow, 1982).

13. R. Priest, Solar Magnetohydrodynamics (Reidel, Dordrecht, 1982; Mir, Moscow, 1985).

14. M. I. Rabinovich and D. I. Trubetskov, Introduction to the Theory of Oscillations and Waves (Nauka, Moscow, 1984) [in Russian].

15. A. N. Tikhonov, A. B. Vasil’eva, and A. G. Sveshnikov, Differential Equations (Nauka, Moscow, 1985; Springer-Verlag, Berlin, 1985).

16. P. Hartman, Ordinary Differential Equations (Wiley, New York, 1964; Mir, Moscow, 1970).

17. O. K. Cheremnykh, Yu. A. Selivanov, and I. V. Zakharov. The influence of compressibility and non-isothermality of the atmosphere on the propagation of acoustic-gravity waves, Kosm. Nauka Tekhnol. 16 (1), 9–19 (2010).

18. A. V. Bespalova, A. K. Fedorenko, O. K. Cheremnykh, and I. T. Zhuk. Satellite observations of wave disturbances caused by moving solar terminator, J. Atmos. Sol.-Terr. Phys. 140, 79–85 (2016).

19. O. K. Cheremnykh, A. K. Fedorenko, E. I. Kryuchkov, and Y. A. Selivanov. Evanescent acoustic-gravity modes in the isothermal atmosphere: Systematization and applications to the Earth and solar atmospheres, Ann. Geophys. 37, 401–415 (2019).

20. A. K. Fedorenko, E. I. Kryuchkov, O. K. Cheremnykh, Yu. O. Klymenko, and Yu. M. Yampolski. Peculiarities of acoustic-gravity waves in inhomogeneous flows of the polar thermosphere, J. Atmos. Sol.-Terr. Phys. 178, 17–23 (2018).

21. A. K. Fedorenko, A. V. Bespalova, O. K. Cheremnykh, and E. I. Kryuchkov. A dominant acoustic-gravity mode in the polar thermosphere, Ann. Geophys. 33, 101–108 (2015).

22. C. O. Hines. Internal gravity waves at ionospheric heights, Can. J. Phys. 38, 1441–1481 (1960).

23. K. M. Huang, S. D. Zhang, F. Yi, C. M. Huang, Q. Gan, Y. Gong, and Y. H. Zhang. Nonlinear interaction of gravity waves in a nonisothermal and dissipative atmosphere, Ann. Geophys. 32, 263–275 (2014).

24. D. Jovanovic, L. Stenflo, and P. K. Shukla. Acoustic-gravity nonlinear structures, Nonlinear Process. Geophys. 9, 333–339 (2002).

25. T. D. Kaladze, O. A. Pokhotelov, H. A. Shan, M. I. Shan, and L. Stenflo. Acoustic-gravity waves in the Earth ionosphere, J. Atmos. Sol.-Terr. Phys. 70, 1607–1616 (2008).

26. A. K. Nekrasov, S. L. Shalimov, P. K. Shukla, and L. Stenflo. Nonlinear disturbances in the ionosphere due to acoustic gravity waves, J. Atmos. Terr. Phys. 57, 732–742 (1995).

27. Yu. G. Rapoport, O. K. Cheremnykh, Yu. A. Selivanov, A. K. Fedorenko, V. M. Ivchenko, V. V. Grimalsky, and E. N. Tkachenko. Modeling AGW and PEMW in inhomogeneous atmosphere and ionosphere, in Proc. 14th Int. Conf. on Mathematical Methods in Electromagnetic Theory (MMET), Kharkiv, Ukraine, Aug. 28–30,2012 (IEEE, Piscataway, NJ, 2012), pp. 577–580, paper no. 6331225.

28. P. H. Roberts, An Introduction to Magnetohydrodynamics (Longmans, London, 1967).

29. A. Roy, S. Roy, and A. P. Misra. Dynamical properties of acoustic-gravity waves in the atmosphere, J. Atmos. Sol.-Terr. Phys. 186, 78–81 (2019).

30. L. Stenflo. Nonlinear equations for acoustic gravity waves, Phys. Lett. A. 222, 378–380 (1996).

31. L. Stenflo and P. K. Shukla. Nonlinear acoustic-gravity waves, J. Plasma Phys. 75, 841–847 (2009).

32. I. Tolstoy. The theory of waves in stratified fluids including the effect of gravity and rotation, Rev. Mod. Phys. 35, 207–230 (1963).

33. B. A. Trubnikov. Dynamical principle of stability for magnetohydrostatic systems, Phys. Fluids 5, 184–191 (1962).

34. S. L. Vadas and D. C. Fritts. Thermospheric responses to gravity waves: Influences of increasing viscosity and thermal diffusivity, J. Geophys. Res.: Atmos. 110, D15103 (2005).

35. W. A. Whitaker. Heating of the solar corona by gravity waves, Astrophys. J. 137, 914–930 (1963).

36. G. Worrall. Oscillations in an isothermal atmosphere: The solar five-minute oscillations, Astrophys. J. 172, 749–753 (1972).

37. K. C. Yeh and C. H. Liu. Acoustic-gravity waves in the upper atmosphere, Rev. Geophys. Space Phys. 12, 193–216 (1974).