The effect of a uniform vertical magnetic field on the onset of oscillatory Marangoni convection in a horizontal layer of conducting fluid

In this paper we use classical linear stability theory to undertake a detailed investigation of the effect of a uniform vertical magnetic field on the onset of oscillatory thermocapillary-driven Marangoni convection in a horizontal layer of quiescent, electrically conducting fluid healed from below. For simplicity we restrict our attention to the simplest case of a fluid layer with a non-deformable free surface and perfectly electrically conducting boundaries in which the onset of convection is always steady in the absence of the magnetic field. The present numerical calculations show that the presence of the magnetic field can cause the preferred mode of instability to be oscillatory rather than steady convection. Nevertheless, in all the cases investigated the effect of the magnetic field is always to stabilise the layer relative to the case of no magnetic field.