On the Magnetic Rayleigh-Bénard problem for compressible fluids

The linear stability of the magnetic Rayleigh Bénard problem for a general compressible horizontal layer of an electrically conducting Newtonian fluid is studied and a comparison of the stability results with the classical magnetic Bénard problem in the Boussinesq approximation is presented. In particular, the physical cases of mercury, liquid sodium and solar plasma have been considered. We find a stabilizing effect of the magnetic field, a dependence of the critical instability parameters on the depth of the layer (as in the case of fluids without magnetic field) and a good agreement with the experiments and the classical results of Chandrasekhar.