A Note on Thermocapillary Instability in the Presence of a Magnetic Field

We formulate the asymptotic theory of thermocapillary instability in a planar fluid layer heated from below in the presence of a strong magnetic field corresponding to high Hartmann number. Explicit asymptotic expressions are derived for the velocity perturbation, temperature perturbation and electric current density. Their spatial structure is characterized in terms of Hartmann boundary layers - a concept which permits a physical understanding of more complicated situations involving surface deformation, buoyancy and thermoelectric effects. The physical nature of large scale instabilities in the case of a deformable surface is clarified.