Thermosolutal convection in a nonlinear magnetic fluid

Abstract

This work examines the thermosolutal convection of a horizontal layer of an incompressible viscous magnetohydrodynamic fluid of variable permeability for the cases when the fluid is heated and soluted from above, heated and soluted from below, heated from below and soluted from above and heated from above and soluted from below. The model has been proposed by Roberts in the context of neutron stars but the results obtained are also relevant to the area of ferromagnetic fluids. The pressence of the variable magnetic permeability has no effect on the development of instabilities through the mechanism of stationary convection but influences the threshold of overstable convection which is often the preferred mechanism in nonterrestrial applications. In the context of ferromagnetic fluids, both stationary and overstable instability can be expected to be realisable possibilites. When the fluid is heated from above and soluted from below the only possible mode of instability is overstability. However, for the other three cases stationary convection and overstability are possible under some conditions. Numerical results were obtained using series expansion of Chebyshev polynomials.