Nonlinear compressible magnetoconvection Part 1. Travelling waves and oscillations

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Abstract
Two-dimensional compressible convection in a polytropic layer with an imposed vertical magnetic field is studied in a series of numerical experiments. We consider a shallow layer, spanning only a fraction of a scale height in density, and increase the ratio (β−1) 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 β the only deviations from Boussinesq behaviour are where the field is locally intense but as β is decreased magnetic pressure fluctuations become increasingly important. When β is of order unity at the top of the layer standing waves become unstable at higher Rayleigh numbers and travelling 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.

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