Effect of an aligned magnetic field on the instability of two superposed conducting fluids in a porous medium

The effect of aligned magnetic field on the instability of two superposed conducting fluids in porous medium has been investigated. The unstable and stable cases of the resulting dispersion relation have been separately dealt with. In the unstable case, it is shown, for non-porous media, and for horizontal to vertical magnetic field values Lambda <= 1, that no mode of maximum instability exists. However, when Lambda > 1, there is a mode of maximum instability which would assert itself during the initial period of motion. The stability effect holds in the presence of porous medium or when Lambda > 1 is found to be faster than its effect in the corresponding case of non-porous medium or when Lambda < 1, respectively. If the vertical magnetic field dominates, we found that the kinematic viscosity has a stabilizing effect, and both the porosity of porous medium and the medium permeability have destabilizing effects on the considered system. If the horizontal magnetic field dominates, we found that the kinematic viscosity and the medium permeability has a stabilizing and a destabilizing effects, respectively; while the porosity of porous medium has a destabilizing effect (for small wavenumbers) as well as stabilizing effect (for large wavenumbers). In the stable case, it is found that no normal mode solution exists, and that whether the medium is porous or not, the potentially stable configuration remains stable in the presence of an oblique magnetic field.