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

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 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....