Large-Scale Hydrodynamic Flows in Media with Variable Thermodynamic Characteristics

A theory of large-scale flows in a rotating astrophysical plasma under conditions of non-trivial properties of the physical medium, which are not described by the classical hydrodynamic theory of plasma, is developed. As a first step, the theory is developed within a neutral fluid model to describe astrophysical plasma, with a subsequent generalization in mind to take into account magnetic effects. Such a model is of independent importance for studying turbulent dynamo in star-forming regions in galaxies and hydrodynamic instabilities in poorly ionized disks, for describing meridional flows below convective zones in low-mass stars and on the Sun, as well as for studying oscillations of the Sun and stars. Therefore, the results obtained have a wider application, e.g., for describing geophysical currents. The theory is based on two key ideas developed in plasma astrophysics: the use of a shallow water model with large-scale compressibility and the use of a two-layer shallow water model. Equations for two-layer shallow water are derived taking into account rotation and the effect of flow sphericity on rotation, in which the effects of large-scale compressibility are taken into account in the upper layer. For a rotating system, dispersion relations are obtained for Poincaré waves in two-layer shallow water, taking into account large-scale compressibility; similar dispersion relations for Poincaré waves are obtained in the high-frequency limit taking into account the effect of sphericity on rotation; in the low-frequency limit, a dispersion relation is obtained for Rossby waves. It is shown that the dispersion relations for Poincaré waves, taking into account the sphericity of the flow, have a qualitatively different form, which leads to three-wave interactions of Poincaré waves and the interaction of two Poincaré waves with a Rossby wave, which are not observed in a single-layer flow of a compressible fluid. All types of three-wave interactions for the flows under consideration are studied using the method of multiscale expansions.