Effect of magnetic field on the conducting fluids streaming in porous medium

The Kelvin-Helmholtz instability of two superposed fluids of plasma streaming in opposite directions through porous medium has been investigated in a uniform two dimensional horizontal magnetic field. The medium is assumed to be conducting and incompressible. By applying the normal mode technique, the dispersion relation has been derived. From the dispersion relation the Kelvin-Helmholtz instability condition is obtained. It is observed that the instability condition is modified due to the simultaneous presence of two dimensional horizontal magnetic field, porosity and suspended particles. It is found that the conditions for the Kelvin-Helmholtz instability depends on the magnetic field, on the suspended dust particles and on the relaxation frequency of the particles. Numerical analysis is performed to show the effect of various parameters on the growth rate of Kelvin Helmholtz instability. It is also found that magnetic field, suspended dust particles and medium porosity has a stabilizing effect on the growth rate of unstable K-H mode