Azimuthal asymmetries of the large-scale circulation in turbulent Rayleigh–Bénard convection

Abstract

Previously we published a dynamical model [E. Brown and G. Ahlers, Phys. Fluids 20, 075101 (2008)] for the large-scale-circulation (LSC) dynamics of Rayleigh–Bénard convection in cylindrical containers. The model consists of a pair of stochastic ordinary differential equations, motivated by the Navier–Stokes equations, one each for the strength δ and the orientation θ0 of the LSC. Here we extend it to cases where the rotational invariance of the system is broken by one of several physically relevant perturbations. As an example of this symmetry breaking we present experimental measurements of the LSC dynamics for a container tilted relative to gravity. In that case the model predicts that the buoyancy of the thermal boundary layers encourages fluid to travel along the steepest slope, that it locks the LSC in this direction, and that it strengthens the flow, as seen in experiments. The increase in LSC strength is shown to be responsible for the observed suppression of cessations and azimuthal fluctuations. We predict and observe that for large enough tilt angles, the restoring force that aligns the flow with the slope is strong enough to cause oscillations of the LSC around this orientation. This planar oscillation mode is different from coherent torsional oscillations that have been observed previously. The model was applied also to containers with elliptical cross sections and predicts that the pressure due to the side wall forces the flow into a preferred orientation in the direction of the longest diameter. When the ellipticity is large enough, then oscillations around this orientation are predicted. The model shows that various azimuthal asymmetries will lock the LSC orientation. However, only those that act on the δ-equation (such as tilting relative to gravity) will enhance the LSC strength and suppress cessations and other azimuthal dynamics. Those that affect only the θ0 equation, such as an interaction with Earth’s Coriolis force, will align the flow but will not influence its strength and the frequency of cessations.