论文标题
由立方容器引起的湍流对流的大规模循环的温度曲线振荡
Oscillation in the temperature profile of the large-scale circulation of turbulent convection induced by a cubic container
论文作者
论文摘要
我们列出了湍流雷利-b {é} Nard对流的大规模循环（LSC）温度轮廓形状的振荡观察。温度测量值分解为傅立叶矩作为$θ-θ_0$的函数，其中$θ$是高度中的水平平面中的方位角角度，而$θ_0$是LSC方向。振荡结构以三阶正弦矩和三阶余化力矩在立方细胞中的主导。相比之下，没有发现这些时刻在圆柱细胞中振荡。这种与几何相关的行为可以通过一个模型来解释，该模型假设LSC从热边界层进行了LSC的热量，并且与LSC的路径长沿顶部和底板的边界层成正比。在非圆形横截面单元格中，LSC取向$θ_0$的振荡在LSC的参考框架中导致容器形状的振荡，从而导致在给定的$θ-θ_0$上以LSC的路径长度振荡。在平方横截面单元中，该模型可预测使用$θ_0$作为输入的振幅振幅时，在测量值的50 \％以内的幅度为50 \％以内的幅度为50 \％。圆柱电池是特殊的，因为路径长与$θ_0$无关，因此不会诱导这些振荡矩。在圆柱形细胞中，该模型以宽度振荡为主的正弦曲线温度曲线再现由第二阶正弦矩占主导地位，这与该几何形状的先前观察结果一致。
We present observations of oscillations in the shape of the temperature profile of the large-scale circulation (LSC) of turbulent Rayleigh-B{é}nard convection. Temperature measurements are broken down into Fourier moments as a function of $θ-θ_0$, where $θ$ is the azimuthal angle in a horizontal plane at mid-height, and $θ_0$ is the LSC orientation. The oscillation structure is dominated by a 3rd order sine moment and 3rd order cosine moment in a cubic cell. In contrast, these moments are not found to oscillate in a cylindrical cell. This geometry-dependent behavior can be explained by a model that assumes that the heat transported by the LSC is conducted from the thermal boundary layers, and is proportional to pathlength of the LSC along boundary layers at the top and bottom plates. In a non-circular cross-section cell, oscillations of the LSC orientation $θ_0$ result in an oscillation in the container shape in the reference frame of the LSC, resulting in an oscillation in the pathlength of the LSC at a given $θ-θ_0$. In a square-cross-section cell, this model predicts the dominant 3rd order sine moment and 3rd order cosine moment with magnitudes within 50\% of measured values, when using the amplitude of the oscillation of $θ_0$ as input. A cylindrical cell is special in that the pathlength is independent of $θ_0$, and so these oscillating moments are not induced. In a cylindrical cell, the model reproduces the sinusoidal mean temperature profile with a sloshing oscillation dominated by the 2nd order sine moment, consistent with previous observations in that geometry.
