Instability of superposed streaming fluids through a porous medium

This paper treats the Kelvin-Helmholtz instability arising at the interface separating 2 superposed, viscous, electrically conducting fluids through a porous medium in the presence of a uniform 2D horizontal magnetic field. The stability motion was also assumed to be uniform, 2D, and horizontal. By applying the normal mode technique to the linearized perturbation equations, the dispersion relation was derived. The stability analysis was carried out for fluids of high kinematic viscosities. It was found that both viscosity and porosity suppressed the stability, while streaming motion had a destabilizing influence.