EXACT CALCULATION OF CONVECTION THRESHOLDS IN ROTATING BINARY-LIQUID MIXTURES

The exact sine series method of Stein [Phys. Rev. A 43, 768 (1991)] has been extended to allow the calculation of critical Rayleigh numbers and wave numbers for both stationary and oscillatory convection states of rotating binary mixtures in Rayleigh-Benard geometry. Checks on the accuracy of the method against previous calculations yield good agreement, provided these are multimode. Single-mode methods seriously underestimate R(c) when the convection state is rotation-induced oscillatory. The method is used to obtain a hydrodynamic phase diagram showing a codimension-three point for a hypothetical mixture with Prandtl number 0.2 and Lewis number 0.0266. Threshold state calculations for a realistic He-3-He-4 mixture show that observation of a codimension-three point is impractical through the Prandtl number being too high.