Nonlinear hydromagnetic waves in a thermally stratified spherical shell: Exact toroidal field solutions

Abstract

The propagation of nonlinear hydromagnetic waves in a highly conducting, self-gravitating fluid in a spherical geometry, subject to the convective forces produced by a radial temperature gradient, is treated in a Boussinesq approximation. Exact wave solutions of the nonlinear magnetohydrodynamic equations (in the Boussinesq approximation) in the presence of convective forces are obtained for the toroidal velocity and magnetic fields. The solution represents waves propagating along the mean magnetic field with the velocity depending on the mean magnetic (or velocity) field strength and the strength of stratification, under the influence of the azimuthal magnetic and velocity fields and convective forces. The solutions may be applicable to the hydromagnetic waves in the Earth’s core and the solar convection zone.