The effect of a uniform vertical magnetic field on the linear growth rates of steady Marangoni convection in a horizontal layer of conducting fluid

Abstract

In this paper we investigate the effect of a uniform vertical magnetic field on the linear growth (and decay) rates of steady Marangoni convection in a horizontal layer of electrically-conducting fluid heated from below. Explicit analytical expressions for the linear growth rates of both long- and short-wave instability modes are derived for the first time. Numerically-calculated results for the linear growth rates are also presented. In particular, we show that the effect of increasing the magnetic field strength is always to stabilise the layer by decreasing the growth rates of the unstable modes.