NATURAL-CONVECTION IN A ROTATING FLUID LAYER WITH DEFORMABLE FREE-SURFACE

In this paper we investigate the stationary thermoconvective instabili ty of a rotating fluid layer with a deformable free surface. In order to understand phenomena which could appear in planetary and stellar sy stems, a variety of mechanical and thermal boundary conditions is cons idered, which give upper and lower stability bounds to all possible ph ysical situations. It is shown that rotation is stabilizing when surfa ce deformation is present, for large values of G sigma, the product of the Galileo and Prandtl numbers, which appears due to surface deflect ion. Moreover, it is shown that for certain boundary conditions the in teraction between rotation and gravity through surface deformation lea ds to an increase in convection cell size (decrease in wavenumber) and destabilization of the system when the Taylor number Ta increases and G sigma is relatively small. The Boussinesq approximation is violated when infinite size convection cells appear in our analysis. Therefore , graphs of the critical values of G sigma and Ta corresponding to the limits of this approximation are given along with analytical expressi ons for the corresponding Rayleigh numbers.