Magnetogravitational Vortex-Sheet Instability of Two Superposed Conducting Fluids in Porous Medium Under Strong Magnetic Field

Abstract

The instability of two superposed homogeneous streaming uids is discussed under gravitational force and uniform magnetic eld in porous medium. The two streams are moving in opposite directions with equal velocities parallel to the horizontal plane. The solution has been obtained through the normal mode technique, and the most gen- eral dispersion relation has been obtained as 20th-order equation for the growth rate with quite complicated coe¢ cients. Solving numeri- caly the dispersion relation for appropriate boundary conditions with high Alfvén and sound velocities, it is found that uid velocities and porosity of porous medium have stabilizing e¤ects, and Alfvén and sound velocities have destabilizing e¤ects, while medium permeabil- ity has a slightly stabilizing e¤ect, and the dynamic viscosities have slightly destabilizing e¤ect. The limiting cases of non-porous medium have also been studied for both streaming and stationary uids.

Key words: Hydrodynamic stability; Conducting uids; Flows through porous media; Gravitational force; Magnetohydrodynamics