Hydrothermal wave instability of thermocapillary driven convection in a plane layer subjected to a uniform magnetic field

Thermocapillary driven motion is considered in a horizontal electrically conducting fluid layer heated from the side and exposed to a magnetic field coplanar to the layer. The hydrothermal wave instability and its control by the magnetic field is studied by a linear stability analysis. The special assumption of disturbances traveling crosswise the basic flow allows an analytical solution of the problem. For a particular class of perturbations considered here, the critical Marangoni number and the wavelength of the most unstable mode increase directly with the strength of the applied magnetic field.