Bénard-Marangoni convection in a rotating fluid with and without surface deformation

This paper deals with Bénard-Marangoni convection in a thin horizontal layer heated from below and rotating uniformly about a vertical axis. The analysis is linear and its objective is to determine the critical temperature drop and the critical wavenumber at the onset of convection. The lower surface of the layer is in contact with an uniformly heated rigid plate and the upper face is deformed and subjected to a temperature-dependent surface tension. Exchange of stability and Boussinesq's approximation are taken for granted. It is shown that rotation has a stabilizing effect while surface deflection plays a stabilizing role at large angular velocity and has an opposite influence at low angular velocity. By increasing the angular velocity, one reinforces the stability, whatever the surface deformation.