EFFECT OF SURFACE ROUGHNESS ON KELVIN-HELMHOLTZ INSTABILITY IN PRESENCE OF MAGNETIC FIELD

We study the effect of surface roughness on Kelvin-Helmholtz instability (KHI) in a fluid layer above by a porous layer and below by a rigid surface in presence of transverse magnetic field. A simple theory based on fully developed flow approximations is used to derive the dispersion relation with surface roughness for the growth rate of KHI. We replace the effect of boundary layer with Beavers and Joseph slip condition as well as roughness condition at the rigid surface. The dispersion relation is derived using suitable boundary and surface conditions and results are discussed graphically. The magnetic field is found to be stabilizing and the influence of the various parameters involved in the problem on the interface stability is thoroughly analyzed.