On effects of viscosity and magnetic fields on the largest growth rate of linear Rayleigh–Taylor instability

Abstract

In this article, we investigate the effect of viscosity on the largest growth rate in the linear Rayleigh–Taylor (RT) instability of a three-dimensional nonhomogeneous incompressible viscous flow in a bounded domain. By adapting a modified variational approach and careful analysis, we show that the largest growth rate in linear RT instability tends to zero as the viscosity coefficient goes to infinity. Moreover, the largest growth rate increasingly converges to one of the corresponding inviscid fluids as the viscosity coefficient goes to zero. Applying these analysis techniques to the corresponding viscous magnetohydrodynamic fluids, we can also show that the largest growth rate in linear magnetic RT instability tends to zero as the strength of horizontal (or vertical) magnetic field increasingly goes to a critical value.