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

摘要

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 omega(c) are obtained for wide ranges of the Prandtl number P-1, the magnetic Prandtl number P-2, the crispation number C-r and the Chandrasekhar number Q. We present numerically a necessary and sufficient condition for oscillatory Marangoni convection to occur. [References: 26]