Rayleigh-Benard convection-with rotation at small Prandtl numbers

We present experimental and theoretical results near the onset of the Rayleigh-Benard convection with rotation about a vertical axis in a fluid with a Prandtl number sigma close to 0.18. In the experiment we used a H-2-Xe gas mixture with a separation ratio Psi=0.22 and a Lewis number L= 1.22 at various pressures and dimensionless rotation rates Omega up to 400. On the basis of a standard weakly nonlinear stability analysis, we found a supercritical, stationary bifurcation for Omega less than or similar to13, which became subcritical over the range 13less than or similar toOmega less than or similar to160. For Omegagreater than or similar to160 a supercritical Hopf bifurcation precedes the stationary instability of the uniform state. Following the unstable straight-roll fixed point in the subcritical regime by Galerkin methods we determined the location of the saddlenode and the stability of the nonlinear two-dimensional straight-roll state. The rolls were found to be unstable to three-dimensional Kuppers-Lortz perturbations for 3.8less than or similar toOmegaless than or similar to160. Theoretical results for a pure fluid with the same sigma were qualitatively similar. Measurements using shadowgraph flow visualization yielded a bifurcation line and an Omega range of subcriticality, which agreed with the stability analysis. In the subcritical range the experiment revealed a discontinuity of the pattern amplitude at onset, but was I unable to find Any hysteresis. Patterns at Onset fluctuated irregularly between the ground state and the finite-amplitude state. In this parameter range the convection pattern further above onset was chaotically time dependent. Investigation of the Hopf bifurcation line was difficult because of a wall mode that, for large Omega, preceded the bulk instability. For Omegasimilar or equal to400, patterns were found in the sample inferior only when the expected Hopf bifurcation was exceeded by about 10%. This is consistent with the convective nature of the bifurcation. However, the observed structure, although time periodic, was spatially disordered and had a frequency that was considerably larger than the expected Hopf frequency. In a separate sample cell with a radial ramp in the spacing no structure was observed at all in the cell interior until the expected stationary instability was reached.