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Effects of tilt on the orientation dynamics of the large-scale circulation in turbulent Rayleigh-B{é}nard convection

We experimentally test the effects of tilting a turbulent Rayleigh-B{é}nard convection cell on the dynamics of the large-scale circulation (LSC) orientation $θ_0$. The probability distribution of $θ_0$ is measured, and used to obtain a tilt-induced potential acting on $θ_0$, which is used in a low-dimensional model of diffusion of $θ_0$ in a potential. The form of the potential is sinusoidal in $θ_0$, 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 values obtained from the probability distribution of $θ_0$, the diffusive model can quantitatively predict effects of tilt on $θ_0$. 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 $θ_0$ to escape a corner are predicted with an accuracy of $\pm30\%$. As a cylindrical cell is tilted, the tilt-induced potential provides a restoring force which induces oscillations when it exceeds the strength of damping; this critical tilt angle is predicted within 20\%, and the prediction is consistent with measured oscillation frequencies. These observations show that a self-consistent low-dimensional model can be extended to include the dynamics of $θ_0$ due to tilt. However, the underprediction of the effect of tilt on $θ_0$ warrants revisiting the predicted magnitude.