Resistive Instabilities of a Viscous Fluid with Horizontal Boundary

Abstract

The gravitational instabilities of a system consisting of two homogeneous fluids with horizontal interface, in the presence of a uniform horizontal magnetic field, are investigated. The fluids are incompressible and have finite electrical conductivity and viscosity. The dispersion relation, which is obtained for the general case, is then specialized for a lower fluid of vanishing density, viscosity, and conductivity. In the limit of infinite conductivity in the upper fluid, the resulting dispersion relation corresponds to that previously obtained for a conducting fluid supported by a magnetic field against gravity. For finite conductivity in the upper fluid, this procedure avoids the difficulties involved as a result of diffusion across a supporting magnetic field. The effects of viscosity and resistivity on the Rayleigh-Taylor modes are obtained. In addition, a resistive gravitational interchange instability is found, although magnetic shear is absent. It is further established that a small viscosity diminishes the growth rate of the resistive gravitational instability.