Effect of Magnetic Field on Kelvin-Helmholtz Instability in a Couple-Stress Fluid Layer Bounded Above by a Porous Layer and Below by a Rigid Surface

Abstract

Kelvin-Helmholtz instability (KHI) appears in stratified two-fluid flow at surface. When the relative velocity is higher than the critical relative velocity, the growth of waves occurs. It is found that magnetic field has a stabilization effect whereas the buoyancy force has a destabilization effect on the KHI in the presence of sharp inter-face. The RT instability increases with wave number and flow shear, and acts much like a KHI when destabilizing effect of sheared flow dominates. It is shown that both of ablation velocity and magnetic field have stabilization effect on RT instability in the presence of continued interface. In this paper, we study the effect of magnetic field on Kelvin-Helmholtz instability (KHI) in a Couple-stress fluid layer above by a porous layer and below by a rigid surface. A simple theory based on fully developed flow approximations is used to derive the dispersion relation for the growth rate of KHI. We replace the effect of boundary layer with Beavers and Joseph slip condition at the rigid surface. The dispersion relation is derived using suitable boundary and surface conditions and results are discussed graphically. The stabilization effect of magnetic field takes place for whole waveband and becomes more significant for the short wavelength. The growth rate decreases as the density scale length increases. The stabilization effect of magnetic field is more significant for the short density scale length.