On the Rayleigh-Taylor problem in magneto-hydrodynamics with finite resistivity

Abstract

In order to elucidate the importance of the infinite conductivity assumption in MHD a simple problem has been studied. This is a Rayleigh-Taylor problem of two superposed fluids under gravity partially stabilized by a uniform, horizontal magnetic field. It is found that the inclusion of a small, but finite resistivity introduces new and unexpected solutions. For instance, moderately long, stabilized’ waves are now found to grow aperiodically and unexpectedly rapidly at a rate ∝ ($\rm {resistivity}^{\frac{1}{3}$). Other modes are found to be periodic and damped at a rate ∝ ($\rm {resistivity}^{\frac{1}{3}$).