Hydromagnetic instability of a continuously stratified fluid layer in a porous medium with a variable oblique magnetic field.

Abstract

The effect of a general oblique magnetic field with linearly varying horizontal components on the stability of a continuously stratified fluid layer in a porous medium has been investigated. The solution is characterized by a variational principle. The exact solution and stability conditions are obtained for such a system in the case of a nonporous medium. Numerical results, for a porous medium, indicate that the inclination angle of the oblique magnetic field has a dual role on the stability of the considered system, while the inclination angle of the wavenumber has a stabilizing effect. It is also found that the porosity of the porous medium has a stabilizing effect, while the kinematic viscosity has a destabilizing effect for a small wavenumber range and a stabilizing effect for other wavenumber values. The medium permeability has a stabilizing effect in the same wavenumber range and a destabilizing effect for other wavenumber values. The buoyancy forces have stabilizing effects on the considered system, which is unstable in absence of buoyancy forces. The density stratification has a destabilizing effect, while the variable horizontal component of the magnetic field has a stabilizing effect on the considered system. The cases of both horizontal and vertical magnetic fields have also been considered, and the obtained results are compared to the case of an oblique magnetic field. The obtained results for the cases of vertical magnetic field and transverse disturbance are found to be almost similar.