Instability through porous media of three layers superposed conducting fluids

The instability properties of streaming superposed conducting fluids through porous media under the influence of uniform magnetic field have been investigated. The system is composed of a middle fluid sheet of finite thickness embedded between two semi-infinite fluids. The fluids are assumed to be incompressible, perfectly conducting and there are weak viscous stresses on the interfaces. The Rayleigh–Taylor and Kelvin–Helmholtz problems have been studied. Such configurations are of relevance in a variety of astrophysical and space configurations. The solutions of the linearized equations of motion together with the boundary conditions lead to deriving the dispersion equation with complex coefficients. The limiting case of the stability of one interface between two fluids has been discussed. The stability criteria are discussed theoretically and numerically in which stability diagrams are obtained. It has been found that the increase of the viscosity coefficient as well as the porosity plays a regular stabilizing role in the stability behavior, while the increase of the fluid velocity plays a destabilizing influence in the stability criteria.