Resonant interactions of magneto-Poincaré and magneto-Rossby waves in quasi-two-dimensional rotating astrophysical plasma

Abstract

ABSTRACT Increased interest in research of non-linear resonant interactions of waves in rotating astrophysical plasma has taken place in recent years. This is due to the discovering solar magneto-Rossby waves and the emergence of new data on the effect of three-wave interactions of magneto-Rossby waves on solar activity. In context of large-scale magnetohydrodynamic flows in presence of rotation, magneto-Poincaré waves and magneto-Rossby waves are highlighted. The β-plane approximation is developed to simplify the theory of spherical Rossby waves. Nevertheless, the representation of the Coriolis force in this approximation contains a latitude-independent term that ensures the existence of magneto-Poincaré waves on β-plane along with magneto-Rossby waves. In this paper, it is shown that they satisfy the phase matching condition, which leads to emergence of new non-linear interactions mechanisms of waves: two magneto-Poincaré waves and one magneto-Rossby wave; two magneto-Rossby waves and one magneto-Poincaré. Complete dispersion equations on β-plane in quasi-two-dimensional magnetohydrodynamic approximation is analysed both for homogeneous and stratified astrophysical plasma with vertical magnetic field. New dispersion relations for magneto-Poincaré waves on β-plane are obtained. Detailed qualitative analysis of the phase matching condition is carried out, and new types of three-wave interactions of magneto-Poincaré waves and magneto-Rossby waves are found. Three-wave interactions are studied and instabilities of the decay and amplification type are investigated.