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Wave Processes in Three-Dimensional Stratified Flows of a Rotating Plasma in the Boussinesq Approximation

  • STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS
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Abstract

Magnetohydrodynamic (MHD) waves in a stratified rotating plasma in a gravitational field are investigated in the Boussinesq approximation. A theory of flows on an f-plane, on a nontraditional f-plane (with regard to the horizontal component of the Coriolis force), on a β-plane, and on a nontraditional β‑plane is developed. In each case, linear solutions to systems of three-dimensional MHD equations in the Boussinesq approximation are obtained that describe magnetic gravito-inertial waves, magnetostrophic waves, and magnetic Rossby waves. All existing types of three-wave interactions are found with the use of dispersion equations. In the case of magnetic Rossby waves in the β-plane approximation, it is shown that the low-frequency mode of a magnetic Rossby wave in the Boussinesq approximation is equivalent to that in the shallow-water MHD approximation. By the multiscale expansion method, a system of amplitude equations for interacting waves and the increments of two types of instability occurring in the system, decay and amplification, are obtained. For each type of three-wave interactions, it is shown that there is a difference in the coefficients and differential operators in the system of three-wave interactions.

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ACKNOWLEDGMENTS

We are grateful to D.A. Klimachkov for useful discussions.

Funding

This work was supported by the Foundation for the Advancement of Theoretical Physics and Mathematics Bazis, by the Russian Foundation for Basic Research (project no. 19-02-00016), and by the Presidium of the Russian Academy of Sciences within the Fundamental Research Program no. 28 “Space: Research of Fundamental Processes and Their Interrelations.” This work was carried out under project KP19-270 “Issues of the origin and evolution of the Universe using ground-based observation and space research methods” within a program of large-scale projects for conducting fundamental research in priority areas defined by the Presidium of the Russian Academy of Sciences.

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Authors and Affiliations

  1. Space Research Institute, Russian Academy of Sciences, 117997, Moscow, Russia

    M. A. Fedotova & A. S. Petrosyan

  2. Moscow Institute of Physics and Technology (State University), 141700, Dolgoprudny, Moscow oblast, Russia

    A. S. Petrosyan

Authors
  1. M. A. Fedotova
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  2. A. S. Petrosyan
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Corresponding author

Correspondence to M. A. Fedotova.

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Translated by I. Nikitin

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Fedotova, M.A., Petrosyan, A.S. Wave Processes in Three-Dimensional Stratified Flows of a Rotating Plasma in the Boussinesq Approximation. J. Exp. Theor. Phys. 131, 337–355 (2020). https://doi.org/10.1134/S1063776120060035

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  • DOI: https://doi.org/10.1134/S1063776120060035

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