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.

中文翻译：

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Boussinesq逼近中旋转等离子体的三维分层流中的波动过程

摘要

用Boussinesq近似研究了重力场中分层旋转等离子体中的磁流体动力学（MHD）波。非传统f平面上f平面上的流动理论（在科里奥利力的水平分量上），在β平面上以及在非传统的β平面上开发了平面。在每种情况下，都获得了描述Boussinesq逼近中的三维MHD方程组的线性解，这些解描述了磁引力惯性波，磁化营养波和Rossby磁波。使用色散方程可以找到所有现有类型的三波相互作用。在β平面近似中的磁性罗斯比波的情况下，可以看出，在Boussinesq近似中，磁性罗斯比波的低频模式与浅水MHD近似中的等效。通过多尺度展开法，可以建立一个相互作用波的振幅方程组以及系统中发生的两种类型的不稳定性（衰减和放大）的增量，获得。对于每种类型的三波相互作用，表明在三波相互作用的系统中，系数和微分算子存在差异。