PATTERN DYNAMICS IN ROTATING CONVECTION AT FINITE PRANDTL NUMBER

A Swift-Hohenberg-type model is derived for rotating convection in a B oussinesq fluid at a moderate Prandtl number, for both free-slip and r igid top and bottom boundary conditions. In the former case, a phase d ynamics analysis-is used to relate the skewed-varicose instability, wh ich can occur in the absence of rotation, and the small-angle instabil ity which develops for arbitrary rotation rate and leads to a continuo us rotation of the rolls. Numerical simulations show the ordering effe ct of a moderate rotation which counterbalances the destructuring effe ct of the mean flow. In the free-slip case, this effect induces the fo rmation of coherent targets, associated with large vortices of the sam e sign as the external rotation. In the no-slip case, this leads to a maximum correlation of the patterns for a rotation rate of the order o f the critical value for the onset of the Kuppers-Lortz instability.