Rotating Rayleigh–Bénard convection: asymmetric modes and vortex states

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Abstract
We present optical shadowgraph flow visualization and heat transport measurements of Rayleigh–Bénard convection with rotation about a vertical axis. The fluid, water with Prandtl number 6.4, is confined in a cylindrical convection cell with radius-to-height ratio Γ = 1. For dimensionless rotation rates 150 < Ω < 8800, the onset of convection occurs at critical Rayleigh numbers Rc(Ω) much less than those predicted by linear stability analysis for a laterally infinite system and qualitatively consistent with finite-aspect-ratio, linear-stability calculations of Buell & Catton (1983). As in the calculations, the forward bifurcation at onset is to states of localized flow near the lateral walls with azimuthal periodicity of 3 < m < 8. These states precess in the rotating frame, contrary to the assumptions of Buell & Catton (1983) but in quantitative agreement with recent calculations of Goldstein et al. (1992), with a frequency that is finite at onset but goes to zero as Ω goes to zero. At Ω = 2145 we find primary and secondary stability boundaries for states with m = 4, 5, 6, and 7. Further, we show that at higher Rayleigh number, there is a transition to a vortex state where the vortices form with the symmetry of the existing azimuthal periodicity of the sidewall state. Aperiodic, time-dependent heat transport begins for Rayleigh numbers at or slightly above the first appearance of vortices. Visualization of the formation and interactions of thermal vortices is presented, and the behaviour of the Nusselt number at high Rayleigh numbers is discussed.

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