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Effects of tilt on the orientation dynamics of the large-scale circulation in turbulent Rayleigh-B{\'e}nard convection
Fluid Dynamics · Submitted 11 Jun 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim These observations show that a self-consistent low-dimensional model can be extended to include the dynamics of $\theta_0$ due to tilt.
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The abstract, sentence by sentence
We experimentally test the effects of tilting a turbulent Rayleigh-B{\'e}nard convection cell on the dynamics of the large-scale circulation (LSC) orientation $\theta_0$. The probability distribution of $\theta_0$ is measured, and used to obtain a tilt-induced potential acting on $\theta_0$, which is used in a low-dimensional model of diffusion of $\theta_0$ in a potential. The form of the potential is sinusoidal in $\theta_0$, 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 $\theta_0$, the diffusive model can quantitatively predict effects of tilt on $\theta_0$. 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 $\theta_0$ 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 $\theta_0$ due to tilt. However, the underprediction of the effect of tilt on $\theta_0$ warrants revisiting the predicted magnitude.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We experimentally test the effects of tilting a turbulent Rayleigh-B{\'e}nard convection cell on the dynamics of the large-scale circulation (LSC) orientation $\theta_0$. | contribution 0.97 | 0.95 | 0.04 | asserted 0.91 |
| s1 | The probability distribution of $\theta_0$ is measured, and used to obtain a tilt-induced potential acting on $\theta_0$, which is used in a low-dimensional model of diffusion of $\theta_0$ in a potential. | method 0.96 | 0.95 | 0.05 | asserted 1.00 |
| s2 | The form of the potential is sinusoidal in $\theta_0$, 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. | result 0.77 | 0.85 | 0.10 | asserted 1.00 |
| s3 | However, the magnitude of the tilt-induced forcing is found to be two orders of magnitude larger than previously predicted. | result 1.00 | 0.94 | 0.17 | asserted 1.00 |
| s4 | When this parameter is adjusted to match values obtained from the probability distribution of $\theta_0$, the diffusive model can quantitatively predict effects of tilt on $\theta_0$. | result 0.80 | 0.87 | 0.18 | asserted 0.98 |
| s5 | 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 $\theta_0$ to escape a corner are predicted with an accuracy of $\pm30\%$. | result 1.00 | 0.88 | 0.13 | asserted 0.97 |
| s6 | 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. | result 0.98 | 0.89 | 0.10 | asserted 0.78 |
| s7 | These observations show that a self-consistent low-dimensional model can be extended to include the dynamics of $\theta_0$ due to tilt. | interpretation 0.95 | 0.80 | 0.68 | asserted 1.00 |
| s8 | However, the underprediction of the effect of tilt on $\theta_0$ warrants revisiting the predicted magnitude. | limitation 0.51 | 0.47 | 0.10 | asserted 0.70 |
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Original abstract
We experimentally test the effects of tilting a turbulent Rayleigh-B{\'e}nard convection cell on the dynamics of the large-scale circulation (LSC) orientation $\theta_0$. The probability distribution of $\theta_0$ is measured, and used to obtain a tilt-induced potential acting on $\theta_0$, which is used in a low-dimensional model of diffusion of $\theta_0$ in a potential. The form of the potential is sinusoidal in $\theta_0$, 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 $\theta_0$, the diffusive model can quantitatively predict effects of tilt on $\theta_0$. 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 $\theta_0$ 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 $\theta_0$ due to tilt. However, the underprediction of the effect of tilt on $\theta_0$ warrants revisiting the predicted magnitude.
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