Rotating Rayleigh–Bénard convection: asymmetric modes and vortex states

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.

Vortex structure in rotating Rayleigh-Bénard convection

“…[9], with thermal boundary layer effects suppressing Ekman pumping in the core of the vortex and thus leading to formation of a narrow zone of upwelling flow near the core and a ring-shaped downwelling region surrounding it. The structure of the boundary layer vortices may prove important in understanding recent heat transport results which show an enhancement by rotation of the amount of heat transported by convection [6,7]. Previous suggestions on the mechanism for this enhancement have been that Ekman pumping is more effective at extracting heat from the boundary layer than buoyancy alone.…”

“…Despite the early roots of these types of investigations in the pioneering theoretical and experimental studies of ChandrasekharLl] and Nakagawa and Frenzen [2], there has been remarkably little quantitative work on the flow structures and in particular the velocity field in rotating convection. The primary tools of past work have been global heat transport measurements, local temperature probes, and qualitative flow visualization with dye, aluminum flakes, streak photography, and shadowgraph [2][3][4][5][6][7]. A semi-quantitative investigation of the vertical temperature structure of a transient thermal plume in the presence of rotation indicated a complex three-dimensional form for non-axially-concentric vortices [8].…”

A model for vortical plumes in rotating convection

“…5 and 6. Experiments with visualizations [7][8][9][10][11] showed indeed a flow structuring consisting of many columnar vortices. In numerical studies 12,13 these columnar vortices were also observed.…”

Prandtl-, Rayleigh-, and Rossby-Number Dependence of Heat Transport in Turbulent Rotating Rayleigh-Bénard Convection

“…However, at modest rotation rates, experiments [9][10][11] and numerical simulations [12][13][14][15] have shown that under certain conditions the heat transport can also be enhanced, before it rapidly decreases for stronger rotation. This enhancement has been ascribed to Ekman pumping [13,[16][17][18]: Because of the rotation, rising or falling plumes of hot or cold fluid are stretched into vertical vortices that suck fluid out of the thermal boundary layers (BL) adjacent to the bottom and top plates.…”