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Nonlinear wave interactions in shallow water magnetohydrodynamics of astrophysical plasma

  • D. A. Klimachkov
  • A. S. Petrosyan
Nuclei, Particles, Fields, Gravitation, and Astrophysics

Abstract

The rotating magnetohydrodynamic flows of a thin layer of astrophysical and space plasmas with a free surface in a vertical external magnetic field are considered in the shallow water approximation. The presence of a vertical external magnetic field changes significantly the dynamics of wave processes in an astrophysical plasma, in contrast to a neutral fluid and a plasma layer in an external toroidal magnetic field. There are three-wave nonlinear interactions in the case under consideration. Using the asymptotic method of multiscale expansions, we have derived nonlinear equations for the interaction of wave packets: three magneto- Poincare waves, three magnetostrophic waves, two magneto-Poincare and one magnetostrophic waves, and two magnetostrophic and one magneto-Poincare waves. The existence of decay instabilities and parametric amplification is predicted. We show that a magneto-Poincare wave decays into two magneto-Poincare waves, a magnetostrophic wave decays into two magnetostrophic waves, a magneto-Poincare wave decays into one magneto-Poincare and one magnetostrophic waves, and a magnetostrophic wave decays into one magnetostrophic and one magneto-Poincare waves. There are the following parametric amplification mechanisms: the parametric amplification of magneto-Poincare waves, the parametric amplification of magnetostrophic waves, the amplification of a magneto-Poincare wave in the field of a magnetostrophic wave, and the amplification of a magnetostrophic wave in the field of a magneto-Poincare wave. The instability growth rates and parametric amplification factors have been found for the corresponding processes.

References

  1. 1.
    T. V. Zaqarashvili, R. Oliver, J. L. Ballester, and B. M. Shergelashvili, Astron. Astrophys. 470, 815 (2007).ADSCrossRefGoogle Scholar
  2. 2.
    K. Heng and A. Spitkovsky, Astrophys. J. 703, 1819 (2009).ADSCrossRefGoogle Scholar
  3. 3.
    N. A. Inogamov and R. A. Sunyaev, Astron. Lett. 36, 848 (2010).ADSCrossRefGoogle Scholar
  4. 4.
    K. Heng and A. P. Showman, Ann. Rev. Earth Planet. Sci. 43, 509 (2015).ADSCrossRefGoogle Scholar
  5. 5.
    K. Heng and J. Workman, Astrophys. J. Suppl. Ser. 213, 27 (2014).ADSCrossRefGoogle Scholar
  6. 6.
    P. A. Gilman, J. Atmosph. Sci. 24, 101 (1967).ADSCrossRefGoogle Scholar
  7. 7.
    S. M. Tobias, P. H. Diamond, and D. W. Hughes, Astrophys. J. Lett. 667, L113 (2007).ADSCrossRefGoogle Scholar
  8. 8.
    A. M. Balk, Astrophys. J. 796, 143 (2014).ADSCrossRefGoogle Scholar
  9. 9.
    P. A. Gilman, Astrophys. J. Lett. 544, L79 (2000).ADSCrossRefGoogle Scholar
  10. 10.
    K. V. Karelsky, A. S. Petrosyan, and S. V. Tarasevich, J. Exp. Theor. Phys. 113, 530 (2011).ADSCrossRefGoogle Scholar
  11. 11.
    K. V. Karelsky, A. S. Petrosyan, and S. V. Tarasevich, Phys. Scripta 155, 014024 (2013).CrossRefGoogle Scholar
  12. 12.
    K. V. Karelsky, A. S. Petrosyan, and S. V. Tarasevich, J. Exp. Theor. Phys. 119, 311 (2014).CrossRefGoogle Scholar
  13. 13.
    H. de Sterck, Phys. Plasmas 8, 3293 (2001).ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    P. J. Dellar, Phys. Plasmas 10, 581 (2003).ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    V. Zeitlin, Nonlin. Proc. Geophys. 20, 893 (2013).ADSCrossRefGoogle Scholar
  16. 16.
    G. K. Vallis, Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation (Cambridge Univ. Press, Cambridge, 2006).CrossRefGoogle Scholar
  17. 17.
    J. Y.-K. Cho, Phil. Trans. R. Soc. London A 366, 4477 (2008).ADSCrossRefGoogle Scholar
  18. 18.
    L. Ostrovsky, Asymptotic Perturbation Theory of Waves (World Scientific, Singapore, 2014).CrossRefMATHGoogle Scholar
  19. 19.
    G. Falkovich, Fluid Mechanics: A Short Course for Physicists (Cambridge Univ. Press, Cambridge, 2011).CrossRefMATHGoogle Scholar
  20. 20.
    E. A. Kuznetsov, Nonlinear Waves (Novosib. Gos. Univ., Novosibirsk, 2015), Pt. 1 [in Russian].Google Scholar
  21. 21.
    E. N. Pelinovskii, V. E. Fridman, Yu. K. Engel’brekht, Nonlinear Evolution Equations (Valgus, Tallin, 1984) [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Inc. 2016

Authors and Affiliations

  1. 1.Space Research InstituteRussian Academy of SciencesMoscowRussia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyi, Moscow oblastRussia

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