论文标题
倾斜对湍流雷利 - b {é}的大规模循环方向动力学的影响
Effects of tilt on the orientation dynamics of the large-scale circulation in turbulent Rayleigh-B{é}nard convection
论文作者
论文摘要
我们通过实验测试倾斜湍流的雷利 - b {é}对流单元对大规模循环（LSC）方向的动力学的影响$θ_0$。测量$θ_0$的概率分布，并用于获得倾斜诱导的电位作用于$θ_0$，该$θ_0$用于$θ_0$的低维模型中。电势的形式是$θ_0$中的正弦曲线，而小倾斜角的倾斜角度线性，这是由作用于LSC的平均浮力力的矢量方向的简单几何模型来解释的。但是，发现倾斜诱导的强迫的大小比以前预测的大两个数量级。当将此参数调整为从$θ_0$的概率分布获得的匹配值时，扩散模型可以定量预测倾斜对$θ_0$的影响。尤其是，倾斜会导致立方细胞相邻角之间的潜在屏障高度发生变化，并且预测$θ_0$的屏障率变化以$ \ pm30 \％$的准确性预测。由于圆柱形细胞被倾斜，倾斜诱导的电势提供了恢复力，在超过阻尼强度时会诱导振荡。预测在20 \％以内的临界倾斜角度，预测与测得的振荡频率一致。这些观察结果表明，可以扩展一个自洽的低维模型，以包括由于倾斜而引起的$θ_0$的动力学。但是，倾斜对$θ_0$的效果的低估值为重新审查预测幅度。
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.
