Effects of tilt on the orientation dynamics of the large-scale circulation in turbulent Rayleigh–Bénard convection

Abstract

We experimentally test the effects of tilting a turbulent Rayleigh–Bénard convection cell on the dynamics of the large-scale circulation (LSC) orientation θ0. The probability distribution of θ0 is measured and used to obtain a tilt-induced potential acting on θ0, which is used in a low-dimensional model of diffusion of θ0 in a potential. The form of the potential is sinusoidal in θ0 and linear in tilt angle for small tilt angles, which is explained by a simple geometric model of the vector direction of the mean buoyancy force acting on the LSC. However, the magnitude of the tilt-induced forcing is found to be two orders of magnitude larger than previously predicted. When this parameter is adjusted to match the values obtained from the probability distribution of θ0, the diffusive model can quantitatively predict the effects of tilt on θ0. In particular, tilt causes a change in potential barrier height between neighboring corners of a cubic cell, and changes in the barrier-crossing rate for θ0 to escape a corner are predicted with an accuracy of ±30%. As a cylindrical cell is tilted, the tilt-induced potential provides a restoring force that induces oscillations when it exceeds the strength of damping; this critical tilt angle is predicted within 20%, and the prediction is consistent with the measured oscillation frequencies. These observations show that a self-consistent low-dimensional model can be extended to include the dynamics of θ0 due to tilt. However, the underprediction of the effect of tilt on θ0 warrants revisiting the predicted magnitude.