Effects of General Rotation and a Horizontal Magnetic Field on the Rayleigh–Taylor Instability of Three-Fluid Layer in Porous Media

Abstract

The Rayleigh-Taylor instability of superposed conducting fluids through porous media under the influence of a uniform magnetic field and general rotation was investigated. The system is composed of a middle fluid sheet of finite thickness embedded between two semi-infinite fluids. The fluids are assumed incompressible and perfectly conducting. A dispersion equation is derived by solving the linearized equations of motion using the boundary conditions. The behavior of the growth rate with respect to the horizontal magnetic field, the vertical and horizontal components of rotation, the viscosity, and the permeability of the porous medium are examined numerically. The results show that the system is divided into two modes (two growth rates). The horizontal magnetic field, and the vertical and horizontal components of rotation, viscosity and porosity have a stabilizing effect on the growth rate of an unstable configuration.