Nonlinear compressible magnetoconvection. I  Travelling waves and oscillations
Abstract
Twodimensional compressible convection in a polytropic layer with an imposed vertical magnetic field is studied in a series of numerical experiments which consider a shallow layer, spanning only a fraction of a scale height in density, and increase the ratio (1/beta) of the magnetic to the thermal pressure in a regime where convection sets in at an oscillatory bifurcation. Initially, there are stable periodic oscillations (standing wave solutions). For moderate values of beta the only deviations from Boussinesq behavior are where the field is locally intense but as beta is decreased magnetic pressure fluctuations become increasingly important. When beta is of order unity at the top of the layer standing waves become unstable at higher Rayleigh numbers and traveling waves are preferred. This is an essentially compressible effect in which magnetic pressure plays a crucial role. The associated bifurcation structure is investigated in some detail.
 Publication:

Journal of Fluid Mechanics
 Pub Date:
 October 1989
 DOI:
 10.1017/S0022112089002703
 Bibcode:
 1989JFM...207..587H
 Keywords:

 Boussinesq Approximation;
 Compressible Fluids;
 Magnetic Field Configurations;
 Magnetoacoustic Waves;
 Stellar Magnetic Fields;
 Traveling Waves;
 Rayleigh Number;
 Standing Waves;
 Stellar Envelopes;
 Plasma Physics