Magnetohydrodynamic Waves in Rotating Stratified Fows of Astrophysical Plasma in the Boussinesq Approximation

Abstract:

Taking into account stratification in magnetohydrodynamic models of rotating plasma is important for the analysis of many astrophysical objects, for example it expands the possibilities for interpreting the available observational data of large-scale Rossby waves on the Sun. Magnetohydrodynamic waves in rotating stratified flows of astrophysical plasma in the Boussinesq approximation are studied. Coriolis force is taken into account in four different approximations: traditional f -plane, non-traditional f-plane (taking into account the horizontal component of the Coriolis force), traditional beta-plane, and non-traditional beta-plane. Dispersion relations for linear waves in f-plane approximations (both traditional and non-traditional) describe three-dimensional magnetic inertia-gravity waves and three-dimensional magnetostrophic waves. Dispersion relations for linear waves in beta-plane approximations (both traditional and non-traditional) describe two-dimensional magnetic gravity waves, magneto-Rossby waves and one dimensional magnetic inertia-gravity and magnetostrophic waves. Equivalence of the low-frequency mode of the magneto-Rossby wave in the Boussinesq approximation and in the magnetohydrodynamic shallow water approximation is shown. By use of qualitative analysis of dispersion curves all types of three-waves interactions are found. For waves on a non-traditional f-plane the influence of the horizontal component of the Coriolis force on the existence of various types of three-wave interactions is shown. By use of multiscale expansions method amplitude equations for interacting waves and the increments of two types of instability in the system (decay and amplification) are obtained. The difference in the coefficients and differential operators in the three-wave interaction system is shown for each of the found types of three-wave interactions. This research was supported by the Russian Foundation for Basic Research (project no. 19-02-00016) and the the Basis Foundation for Development of Theoretical Physics and Mathematics.