MHD instability of two fluids between parallel plates

Abstract

The work focuses on the exact solution of the perturbative model for a plane-parallel flow of two immiscible fluids under constant transversal magnetic field (Hartmann flow). The special case of the perturbation’s symmetry is considered: it is supposed that perturbations intensity depends just on specified two parameters and time. Nevertheless, the considered case seems to be common enough and can be considered as one of the flow stability criteria. To receive exact solution, the governing equation system is analyzed. It is shown that in the considered case, it can be reduced to heat equations for the nontrivial components. The perturbations considered in this work are not necessary of harmonic type and the corresponding equations on the perturbations are not Orr-Sommerfeld equations.