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Universality of probability density distributions in the overlap region in high Reynolds number turbulent boundary layers

机译：高雷诺数湍流边界层重叠区域中概率密度分布的普遍性

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摘要

The probability density functions (PDFs) of the streamwise mean velocity in high Reynolds number turbulent boundary layers have been studied. The hypothesis of self-similar, normalized with the root mean square velocity, PDFs has been tested using the KTH database of high Reynolds number zero pressure-gradient turbulent boundary layer flow. The self-similarity was tested using the Kullback-Leibler divergence measure and it was found that the region of self-similar PDFs extends from about 160 viscous wall units to about 0.3 boundary layer thicknesses (in delta(95)). This region is somewhat larger than the universal overlap region. The PDF shape in the universal overlap region is close to Gaussian allowing for a Gram-Charlier expansion approximation of the measured PDFs. A remarkable collapse was found for 57 normalized PDF distributions for different positions within the universal overlap region and Reynolds numbers based on the momentum-loss thickness between 4300 and 12 600, strongly indicating a high degree of flow universality within the universal overlap region. Within the range studied, the Gram-Charlier expansion coefficients (related to the PDF moments) show no Reynolds number trend further supporting the self-similarity hypothesis. (C) 2004 American Institute of Physics.
机译：研究了高雷诺数湍流边界层中流向平均速度的概率密度函数（PDFs）。已经使用高雷诺数零压力梯度湍流边界层流的KTH数据库测试了用均方根速度归一化的自相似假设。使用Kullback-Leibler散度测度测试了自相似性，发现自相似PDF的区域从大约160个粘性壁单元扩展到大约0.3个边界层厚度（在delta（95）中）。该区域比通用重叠区域大一些。通用重叠区域中的PDF形状接近于高斯，从而可以对所测量的PDF进行Gram-Charlier展开近似。对于通用重叠区域内不同位置的57个归一化PDF分布以及基于4300至12 600之间的动量损失厚度的雷诺数，发现了明显的崩溃，强烈表明通用重叠区域内的流动通用性很高。在所研究的范围内，Gram-Charlier膨胀系数（与PDF矩有关）没有显示雷诺数趋势，进一步支持了自相似性假设。 （C）2004美国物理研究所。

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