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The Influence of the Earth’s Atmosphere Rotation on the Spectrum of Acoustic-Gravity Waves

  • DYNAMICS AND PHYSICS OF BODIES OF THE SOLAR SYSTEM
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Abstract

It was shown in a recent study [11] that taking into account the rotation of the Earth’s atmosphere leads to the appearance of a new region of evanescent waves with a continuous frequency spectrum on the diagnostic diagram of acoustic-gravity waves. The region is located below the lower limit of gravity waves, which is equal to \(2\Omega \) for all wavelengths, where \(\Omega \) is the angular frequency of the atmospheric rotation. This result was obtained for high-latitude regions of the atmosphere in which one can be limited to considering only the vertical component of the Earth’s rotation frequency. This paper shows that taking into account both components of the vector \(\vec {\Omega }\) of the atmospheric rotation frequency \(\vec {\Omega }\)—horizontal, \(\Omega \cos \varphi ,\) where \(\varphi \) is the local latitude, and vertical, \(\Omega \sin \varphi \)—the dominant role in the acoustic-gravity wave propagation is played by the vertical component. It is shown that the horizontal component leads to a negligible modification of the boundaries of the regions of acoustic and gravity waves on the diagnostic diagram. It is also shown that the vertical component of the frequency affects most strongly the lower limit of gravity waves, which depends on the latitude of the observation site for all wavelengths and is equal to 2\(\Omega \sin \varphi \).

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REFERENCES

  1. O. Agapitov and O. K. Cheremnykh, “Natural oscillations of the Earth magnetosphere associated with solar wind sudden impulses,” Ukr. J. Phys. 53, 508–512 (2008).

    Google Scholar 

  2. M. J. Alexander and L. Pfister, “Gravity wave momentum flux in the stratosphere over convection,” Geophys. Res. Lett. 22, 2029–2032 (1995).

    Article  ADS  Google Scholar 

  3. G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge Univ. Press, Cambridge, 2000).

    Book  Google Scholar 

  4. T. Beer, Atmospheric Waves (Wiley, New York, 1974).

    Google Scholar 

  5. 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). https://doi.org/10.1016/j.jastp.2016.02.012

    Article  ADS  Google Scholar 

  6. P. A. Bespalov, V. G. Misonova, and O. N. Savina, “Magnetospheric VLF response to the atmospheric infrasonic waves,” Adv. Space Res. 31, 1235–1240 (2003).

    Article  ADS  Google Scholar 

  7. L. M. Brekhovskikh and V. V. Goncharov, Introduction to the Mechanics of Continuous Media (Nauka, Moscow, 1982) [in Russian].

    Google Scholar 

  8. O. K. Cheremnykh and V. V. Danilova, “Transverse small-scale MHD perturbations in space plasma with magnetic surfaces,” Kinematics Phys. Celestial Bodies 27, 98–108 (2011).

    Article  ADS  Google Scholar 

  9. 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).

    Article  ADS  Google Scholar 

  10. O. K. Cheremnykh, A. K. Fedorenko, Y. A. Selivanov, and S. O. Cheremnykh, “Continuous spectrum of evanescent acoustic-gravity waves in an isothermal atmosphere,” Mon. Not. R. Astron. Soc. 503, 5545–5553 (2021). https://doi.org/10.1093/mnras/stab845

    Article  ADS  Google Scholar 

  11. O. Cheremnykh, T. Kaladze, Yu. A. Selivanov, and S. Cheremnykh, “Evanescent acoustic-gravity waves in a rotating stratified atmosphere,” Adv. Space Res. 69, 1272–1280 (2022).

    Article  ADS  Google Scholar 

  12. O. K. Cheremnykh, Kryuchkov EI, Fedorenko AK, and S. O. Cheremnykh, “Two-frequency propagation mode of acoustic–gravity waves in the Earth’s atmosphere,” Kinematics Phys. Celestial Bodies 36, 64–78 (2020).

    Article  ADS  Google Scholar 

  13. O. K. Cheremnykh and A. S. Parnowski, “Influence of ionospheric conductivity on the ballooning modes in the inner magnetosphere of the Earth,” Adv. Space Res. 37, 599–603 (2006).

    Article  ADS  Google Scholar 

  14. C. Chiuderi and C. Giovanardi, “Wave propagation in a non-isothermal atmosphere and the solar five-minute oscillations,” Sol. Phys. 64, 27–42 (1979).

    Article  ADS  Google Scholar 

  15. A. Ebel, “Contributions of gravity waves to the momentum, heat and turbulent energy budget of the upper mesosphere and lower thermosphere,” J. Atmos. Sol.-Terr. Phys. 46, 727–737 (1984).

    Article  ADS  Google Scholar 

  16. 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). https://doi.org/10.5194/angeo-33-101-2015

    Article  ADS  Google Scholar 

  17. 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).

    Article  ADS  Google Scholar 

  18. S. H. Francis, “Global propagation of atmospheric gravity waves: A review,” J. Atmos. Terr. Phys. 37, 1011–1054 (1975).

    Article  ADS  Google Scholar 

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

    Google Scholar 

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

    Article  ADS  Google Scholar 

  21. W. H. Hooke, “Ionospheric irregularities produced by internal atmospheric gravity waves,” J. Atmos. Sol.-Terr. Phys. 30, 795–823 (1968).

    Article  ADS  Google Scholar 

  22. 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).

    Article  ADS  Google Scholar 

  23. W. L. Jones, “Non-divergent oscillations in the solar atmosphere,” Sol. Phys. 7, 204–209 (1969).

    Article  ADS  Google Scholar 

  24. 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).

    Article  ADS  Google Scholar 

  25. W. Kertz, “Atmosphärische Gezeiten,” in Encyclopedia of Physics (Springer-Verlag, Berlin, 1957), Vol. 48, pp. 928–981.

    Google Scholar 

  26. 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).

    Article  ADS  Google Scholar 

  27. Y. P. Ladikov-Roev, O. K. Cheremnykh, A. K. Fedorenko, and V. E. Nabivach, “Acoustic-gravity waves in whirling polar thermosphere,” J. Autom. Inf. Sci. 47 (9), 10–22 (2015).

    Article  Google Scholar 

  28. H. Lamb, “On atmospheric oscillations,” Proc. R. Soc. London, Ser. A 84, 551–572 (1911). https://doi.org/10.1098/rspa.1911.0008

    Article  MATH  ADS  Google Scholar 

  29. H. Lamb, Hydrodynamics (Dover, New York, 1932).

  30. P. S. Landa, Nonlinear Oscillations and Waves in Dynamical Systems (Nauka, Moscow, 1977; Kluwer, Dordrecht, 1996).

  31. O. Y. Lavrova and K. D. Sabinin, “Manifestations of inertial oscillations in satellite images of the sea surface,” Sovrem. Probl. Distantsionnogo Zondirovaniya Zemli Kosmosa 13 (4), 60–73 (2016).

    Article  Google Scholar 

  32. M. S. Longuet-Higgins, “Planetary waves on a rotating sphere. 1,” Proc. R. Soc., Ser. A. 279, 446–473 (1964);

  33. M. S. Longuet-Higgins, “Planetary waves on a rotating sphere. 2,” Proc. R. Soc., Ser. A. 284, 40–68 (1965).

  34. D. F. Martyn, “Cellular atmospheric waves in the ionosphere and troposphere,” Proc. R. Soc. London, Ser. A 201, 216 (1950).

    Article  MathSciNet  ADS  Google Scholar 

  35. J. C. McWilliams, Fundamentals of Geophysical Fluid Dynamics (Cambridge Univ. Press, Cambridge, 2011).

    MATH  Google Scholar 

  36. N. S. Petrukhin, E. N. Pelinovsky, and T. G. Talipova, “Nonreflected vertical propagation of acoustic waves in a strongly inhomogeneous atmosphere,” Izv., Atmos. Ocean. Phys. 48, 169–173 (2012).

    Article  Google Scholar 

  37. O. A. Pokhotelov, T. D. Kaladze, P. K. Shukla, and L. Stenflo, “Three-dimensional solitary vortex structures in the upper atmosphere,” Phys. Scr. 64, 245–252 (2001).

    Article  ADS  Google Scholar 

  38. 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 PEWM in inhomogenous atmosphere and ionosphere,” in Proc. 14th Int. Conf. on Mathematical Methods in Electromagnetic Theory (MMET), Kharkiv, Ukraine, Aug. 28–30, 2012 (IEEE, Piscataway, N.J., 2012), 577–580. https://doi.org/10.1109/MMET.2012.6331225

  39. C.-G. Rossby, “Relation between variations in the intensity of the zonal circulation of the atmosphere and displacement of the semi-permanents centers of action,” J. Marine Res. 2, 38–55 (1939).

    Article  Google Scholar 

  40. C.-G. Rossby, “Planetary flow patterns in the atmosphere,” Q. J. R. Meteorol. Soc. 66, 68–87 (1940).

    Google Scholar 

  41. 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).

    Article  ADS  Google Scholar 

  42. D. B. Simkhada, J. B. Snively, M. J. Tayler, and S. J. Franke, “Analysis and modeling of ducted and avanescent gravity waves observed in the Havaiian airglow,” Ann. Geophys. 27, 3213–3224 (2009).

    Article  ADS  Google Scholar 

  43. V. M. Somsikov, Solar Terminator and Atmospheric Dynamics (Nauka, Alma-Ata, 1983) [in Russian].

  44. L. Stenflo and P. K. Shukla, “Nonlinear acoustic gravity wave,” J. Plasma Phys. 75, 841–847 (2009). https://doi.org/10.1017/S0022377809007892

    Article  ADS  Google Scholar 

  45. B. R. Sutherland, Internal Gravity Waves (Cambridge Univ. Press, Cambridge, 2015).

    MATH  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  47. I. Tolstoy, “Long-period gravity waves in the atmosphere,” J. Geophys. Res. 72, 4605–4610 (1967).

    Article  ADS  Google Scholar 

  48. I. Tolstoy, Wave Propagation (McGraw-Hill, New York, 1973).

    MATH  Google Scholar 

  49. S. L. Vadas and D. C. Fritts, “Termosphere responses to gravity waves: Influences of incrising viscosity and thermal diffusivity,” J. Geophys. Res.: Atmos. 110, D15103 (2005). https://doi.org/10.1029/2004JD005574

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  52. Y.-L. Lin, Mesoscale Dynamics (Cambridge Univ. Press, New York, 2007).

    Book  Google Scholar 

  53. S. D. Zhang and F. Yi, “numerical study of propagation characteristics of gravity wave packets propagating in a dissipative atmosphere,” J. Geophys. Res.: Atmos. 107, 4222 (2002).

    Article  ADS  Google Scholar 

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Funding

The study was funded by the National Research Foundation of Ukraine, project no. 2020.02/0015 “Theoretical and Experimental Studies of Global Disturbances of Natural and Manmade Origin in the Earth–Atmosphere–Ionosphere System” and the Scientific Program of the National Antarctic Center of the Ministry of Education and Science of Ukraine as well as with the partial support of the Targeted Comprehensive Program of the National Academy of Sciences of Ukraine for Scientific Space Research in 2018–2022. Also authors would like to thank the Volkswagen Foundation (“VWStiftung”) for partial support (grant 97 742).

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Correspondence to O. K. Cheremnykh, S. O. Cheremnykh or D. I. Vlasov.

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Translated by M. Chubarova

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Cheremnykh, O.K., Cheremnykh, S.O. & Vlasov, D.I. The Influence of the Earth’s Atmosphere Rotation on the Spectrum of Acoustic-Gravity Waves. Kinemat. Phys. Celest. Bodies 38, 121–131 (2022). https://doi.org/10.3103/S0884591322030023

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