Nonlinear hydromagnetic waves in a thermally stratified cylindrical fluid: Exact helically symmetric solutions

The propagation of nonlinear hydromagnetic waves in a highly conducting, self‐gravitating fluid in a cylindrical 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 case when the physical quantities are helically symmetric in cylindrical coordinates. The solutions represent waves propagating helically on the cylindrical surfaces, under the influence of the helical magnetic and velocity fields and the convective forces. The solutions may be applicable to the hydromagnetic waves in the Earth’s fluid core and the solar convection zone with suitable modifications to account for spherical geometry.