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Pure and Applied Geophysics

, Volume 175, Issue 8, pp 3023–3035 | Cite as

A Wave Diagnostics in Geophysics: Algorithmic Extraction of Atmosphere Disturbance Modes

  • S. Leble
  • S. Vereshchagin
Article
  • 34 Downloads

Abstract

The problem of diagnostics in geophysics is discussed and a proposal based on dynamic projecting operators technique is formulated. The general exposition is demonstrated by an example of symbolic algorithm for the wave and entropy modes in the exponentially stratified atmosphere. The novel technique is developed as a discrete version for the evolution operator and the corresponding projectors via discrete Fourier transformation. Its explicit realization for directed modes in exponential one-dimensional atmosphere is presented via the correspondent projection operators in its discrete version in terms of matrices with a prescribed action on arrays formed from observation tables. A simulation based on opposite directed (upward and downward) wave train solution is performed and the modes’ extraction from a mixture is illustrated.

Notes

Acknowledgements

This work was supported by the Ministry of Education and Science of Russian Federation (contract 3.1127.2014/K).

References

  1. Anthony, J., & Kettle, A. (2014). Diagnostic diagram to understand atmosphere-ocean dynamics in the southern north sea at high wind speeds. Energy Procedia, 5, 1–8.Google Scholar
  2. Arfken, G. (1985) Mathematical methods for physicists. In 14.6 discrete orthogonality–discrete Fourier transform (3rd ed., pp. 787–792). Orlando: Academic Press. ISBN: 978-0-12-059820-5. https://www.elsevier.com/books/mathematical-methods-for-physicists/arfken/978-0-12-059820-5
  3. Bessarab, F., Kshevetskij, S., & Leble, S. (1987). On the Acoustic–Gravity waves interaction in atmosphere. In V. Kedrinskii (Ed) Problems of nonlinear acoustics. Proceedings of IUPAP, IUTAM symposium on nonlinear acoustics, AN USSR, Siberian Division, Novosibirsk, 1987. AN USSR, Siberian DivisionGoogle Scholar
  4. Brekhovskikh, L. M., & Godin, O. (1999). Acoustics of layered media II: Point sources and bounded beams. Berlin: Springer. (ISBN 9783540655923).CrossRefGoogle Scholar
  5. Chu, B.-T., & Kovasznay, L. S.G. (1958). Non-linear interactions in a viscous heat-conducting compressible gas. Journal of Fluid Mechanics, 3, 494–514.  https://doi.org/10.1017/S0022112058000148.CrossRefGoogle Scholar
  6. Fedorenko, A. (2009). Recovery of characteristics of atmospheric gravity waves in polar regions based on mass spectrometric satellite measurements. Radio Physics and Radio Astronomy, 14, 254–265.Google Scholar
  7. Fedorenko, A., & Kryuchkov, E. (2013). Wind control of the propagation of acoustic gravity waves in the polar atmosphere. Geomagnetism and Aeronomy, 53(3), 377–388.  https://doi.org/10.1134/S0016793213030055.CrossRefGoogle Scholar
  8. Fleck, B., Straus, T., & Wedemeyer, S. (2016). Testing wave propagation properties in the solar chromosphere with ALMA and IRIS. In SPD meeting, vol. 47, American Astronomical Society.Google Scholar
  9. Gaikovich, K. (2004). Inverse problems in physical diagnostics. Hauppauge: Nova Science Publishers, Inc.Google Scholar
  10. Godin, O. A., Zabotin, N. A., & Bullett, T. W. (2015). Acoustic-gravity waves in the atmosphere generated by infragravity waves in the ocean. Earth, Planets and Space, 67(1), 47.  https://doi.org/10.1186/s40623-015-0212-4..CrossRefGoogle Scholar
  11. Gordin, A. (1987). Mathematical problems of hydrodynamical weather prediction. Analytical aspects. Saint Petersburg: Gydrometeoizdat.Google Scholar
  12. Holton, J. R. (1971). A diagnostic model for equatorial wave disturbances: the role of vertical shear of the mean zonal wind. Journal of Atmospheric Sciences 28, 55–64. doi:10.1175/1520-0469(1971)028<0055:ADMFEW>2.0.CO;2Google Scholar
  13. Karpov, I., Bessarab, F. & Leble, S. (2008). Projection operators for the planetary Poincare and Rossby waves in the atmosphere (pp. 32–37). Kaliningrad: Vestnik BFU im. Kanta IKBFUGoogle Scholar
  14. Leble, S. (1991). Nonlinear waves in waveguides: With stratification. Berlin: Springer.  https://doi.org/10.1007/978-3-642-75420-3. (ISBN 978-3-642-75420-3).CrossRefGoogle Scholar
  15. Leble, S. (1988). Theory of thermospheric waves and their ionospheric effects. Pure and Applied Geophysics, 127(2), 491–527.  https://doi.org/10.1007/BF00879823.CrossRefGoogle Scholar
  16. Leble, S., Perelomova, A. (2013). Problem of proper decomposition and initialization of acoustic and entropy modes in a gas affected by the mass force. Applied Mathematical Modelling 37(3), 629–635.  https://doi.org/10.1016/j.apm.2012.02.037. http://www.sciencedirect.com/science/article/pii/S0307904X12001205
  17. Leble, S., & Vereshchagina, I. (2014). On inverse problem of waves identification by measurements at one point vicinity. ArXiv e-prints. arXiv:1412.7926.
  18. Leble, S., & Vereshchagina, I. (2016). Problem of disturbance identification by measurement in the vicinity of a point. Task Quarterly, 20(2), 131–141Google Scholar
  19. Leble, S., & Zaitsev, A. (1987). Novye Methody v Teorii Nelinejnych Voln. Kaliningrad: Kalingrad State University.Google Scholar
  20. Leble, S. (2016). General remarks for the dynamic projection method. Task Quarterly, 20(2), 113–130.Google Scholar
  21. Makhlouf, U., Dewan, E., Isler, J. R., & Tuan, T. F. (1990). On the importance of the purely gravitationally induced density, pressure, and temperature variations in gravity waves: Their application to airglow observations. Journal of Geophysical Research: Space Physics, 95(A4), 4103–4111.  https://doi.org/10.1029/JA095iA04p04103.CrossRefGoogle Scholar
  22. Pedlosky, J. (1987). Geophysical fluid dynamics. Berlin: Springer.  https://doi.org/10.1007/978-1-4612-4650-3.CrossRefGoogle Scholar
  23. Perelomova, A. (1998). Nonlinear dynamics of vertically propagating acoustic waves in a stratified atmosphere. Acta Acustica United with Acustica, 84(6), 1002–1006. http://www.ingentaconnect.com/content/dav/aaua/1998/00000084/00000006/art00004
  24. Perelomova, A. (2000). Nonlinear dynamics of directed acoustic waves in stratified and homogeneous liquids and gases with arbitrary equation of state. Archives of Acoustics, 25(4). http://acoustics.ippt.pan.pl/index.php/aa/article/view/382
  25. Perelomova, A. (1993). Construction of directed disturbances in one-dimensional isothermal atmosphere model. The Journal Izvestiya, Atmospheric and Oceanic Physics, 29(1), 47–50.Google Scholar
  26. Souffrin, P., & Spiegel, E. A. (1967). An overstability of gravity waves. Annales d’Astrophysique, 30, 985.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Immanuel Kant Baltic Federal UniversityKaliningradRussia

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