Wave Processes in Rotating Compressible Astrophysical Plasma Flows with Stable Stratification

Abstract

The wave processes in a rotating layer of compressible astrophysical plasma with a stable stratification and a linear entropy profile are studied theoretically. The compressibility is taken into account in the anelastic approximation. In this approximation the acoustic waves are filtered out, the system contains terms with a potential temperature (entropy), and the continuity equation contains an initial stratified density profile. The Coriolis force in the magnetohydrodynamic equations for a compressible astrophysical plasma is considered in four different approximations: a traditional f-plane, a nontraditional f-plane (given the horizontal component of the Coriolis force), a traditional β-plane, and a nontraditional β-plane. Linear and nonlinear theories of wave processes have been developed for each Coriolis force approximation under consideration. New types of waves have been found, with the rotation, magnetic field, gravity, and compressibility serving as their restoring mechanisms. The compressibility effects are represented in the new dispersion equations by the Brunt–Vaisala frequency for compressible stratified flows dependent on both initial density and pressure profiles. All of the realizable types of three-wave interactions have been revealed through a qualitative analysis of the dispersion curves. A system of equations for the amplitudes of interacting waves and the growth rates of parametric instabilities have been derived by the multiscale expansion method.