 
Summary: Azimuthal asymmetries of the largescale circulation in turbulent
RayleighBénard convection
Eric Browna
and Guenter Ahlers
Department of Physics and iQCD, University of California, Santa Barbara, California 93106, USA
Received 24 April 2008; accepted 26 August 2008; published online 28 October 2008
Previously we published a dynamical model E. Brown and G. Ahlers, Phys. Fluids 20, 075101
2008 for the largescalecirculation LSC dynamics of RayleighBénard convection in
cylindrical containers. The model consists of a pair of stochastic ordinary differential equations,
motivated by the NavierStokes equations, one each for the strength and the orientation 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 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
