Oscillatory Marangoni convection in a conducting fluid layer with a deformable free surface in the presence of a vertical magnetic field

Linear stability theory is applied to the problem of the onset of oscillatory Marangoni convection in a horizontal layer of electrically conducting fluid heated from below in the presence of a vertical magnetic field. The fluid layer is bounded from below by a rigid boundary and from above by a deformable free surface. The critical Marangoni number M_c, the critical wavenumber a_c and the critical frequency ω_c are obtained for wide ranges of the Prandtl number P₁, the magnetic Prandtl number P₂, the crispation number C_r and the Chandrasekhar number Q. We present numerically a necessary and sufficient condition for oscillatory Marangoni convection to occur.