Natural convection in a rotating fluid layer with deformable free surface

Abstract

Abstract In this paper we investigate the stationary thermoconvective instability of a rotating fluid layer with a deformable free surface. In order to understand phenomena which could appear in planetary and stellar systems, a variety of mechanical and thermal boundary conditions is considered, which give upper and lower stability bounds to all possible physical situations. It is shown that rotation is stabilizing when surface deformation is present, for large values of G[sgrave], the product of the Galileo and Prandtl numbers, which appears due to surface deflection. Moreover, it is shown that for certain boundary conditions the interaction between rotation and gravity through surface deformation leads to an increase in convection cell size (decrease in wavenumber) and destabilization of the system when the Taylor number Ta increases and G[sgrave] 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[sgrave] and Ta corresponding to the limits of this approximation are given along with analytical expressions for the corresponding Rayleigh numbers.