Rayleigh-Bénard Convection with Rotation at Small Prandtl Numbers
This paper reviews past results from and future prospects for experimental studies of Rayleigh-Bénard convection with rotation about a vertical axis. At dimensionless rotation rates 0 ≤ Ω ≤ 20 and for Prandtl numbers σ ≃ 1, Küppers-Lortz-unstable patterns offered a unique opportunity to study spatio-temporal chaos immediately above a supercritical bifurcation where weakly-nonlinear theories in the form of Ginzburg-Landau (GL) or Swift-Hohenberg (SH) equations can be expected to be valid. However, the dependence of the time and length scales of the chaotic state on ε ≡ ΔT/ΔT C - 1 was found to be different from the expected dependence based on the structure of GL equations. For Ω ≳ 70 and 0.7 ≲ σ ≲ 5 patterns were found to be cellular near onset with local four-fold coordination. They differ from the theoretically expected Küppers-Lortz-unstable state. Stable as well as intermittent defect-free rotating square lattices exist in this parameter range.
Smaller Prandtl numbers ( 0.16 ≲ σ ≲ 0.7) can only be reached in mixtures of gases. These fluids are expected to offer rich future opportunities for the study of a line of tricritical bifurcations, of supercritical Hopf bifurcations to standing waves, of a line of codimension-two points, and of a codimension-three point.
KeywordsPrandtl Number Hopf Bifurcation Critical Rayleigh Number Tricritical Point Stationary Bifurcation
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