ORDER-PARAMETER EQUATION AND MODEL EQUATION FOR HIGH PRANDTL NUMBER -RAYLEIGH-BENARD CONVECTION IN A ROTATING LARGE ASPECT RATIO SYSTEM

We derive the order parameter equation which describes the evolution o f spatio-temporal patterns close to the Benard instability in a rotati ng large aspect ratio system for high Prandtl number fluids. Since thi s order parameter equation contains rather complicated nonlinear terms we present a model equation which can be obtained from the order para meter equation by suitable simplification of the nonlinearity. For thi s model equation we calculate the family of roll solutions and investi gate their stability with respect to long scale instabilities and exam ine the onset of the Kuppers-Lortz instability. Then we present spatio temporal patterns which are obtained from a numerical evaluation of th e model equation.