VISCOUS CORRECTIONS FOR THE VISCOUS POTENTIAL FLOW ANALYSIS OF MAGNETO-HYDRODYNAMIC KELVIN-HELMHOLTZ INSTABILITY THROUGH POROUS MEDIA

摘要

Viscous corrections for the viscous potential flow analysis of Kelvin-Helmholtz instability at the interface of two incompressible, viscous, and electrically conducting fluids has been carried out. The fluids are flowing through porous media between two rigid planes and they are subjected to a constant magnetic field parallel to the streaming direction. In viscous potential flow theory, viscosity enters through normal stress balance and the effect of shearing stresses is completely neglected. We include the viscous pressure in the normal stress balance along with irrotational pressure and it is assumed that this viscous pressure will resolve the discontinuity of the tangential stresses at the interface for two fluids. A dispersion relation has been derived and stability is discussed theoretically as well as numerically. The stability criterion is given in terms of a critical value of relative velocity as well as the critical value of applied magnetic field. It has been observed that a tangential magnetic field has a stabilizing effect on the stability of the system while a porous medium destabilizes the interface. Also, it has been found that the effect of irrotational shearing stresses stabilizes the system.