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

TL;DR

This paper extends a stochastic dynamical model of large-scale circulation in Rayleigh-Benard convection to include effects of physical perturbations like tilting and elliptical containers, predicting flow locking, oscillations, and orientation preferences.

Contribution

It introduces an extended model accounting for symmetry-breaking perturbations and validates predictions with experimental measurements.

Findings

Tilt encourages flow alignment and strengthens circulation.

Large tilt angles cause oscillations around the preferred orientation.

Elliptical containers induce flow orientation and oscillations depending on ellipticity.

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-Benard 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 delta and the orientation theta_0 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 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 walls 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.