Generalized logarithmic law for high-order moments in turbulent boundary layers
Generalized logarithmic law for high-order moments in turbulent boundary layers
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DOI：
10.1017/jfm.2013.61
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发表时间：
2013-02
影响因子：
3.7
通讯作者：
C. Meneveau;I. Marusic
中科院分区：
文献类型：
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作者：
C. Meneveau;I. Marusic
本文分析了湍流边界层中的高雷诺数资料，以检验流向速度起伏的统计矩。以前的工作已经表明，在惯性亚层内，变化随到表面的距离呈现对数行为。在这里，我们将这些观察结果推广到偶数阶矩。我们证明了$2p阶矩的幂为$1/p的$2p$阶矩也遵循如下的对数行为：$\langop{({u}^{\素数+}){}^{2p}\Rangle}\NoLimits^{1/p}={B}_{p}-{A}_{p}\ln(z/\Delta)$，其中${u}^{\素数+}$是由摩擦速度归一化的速度涨落，$\Delta$是外部长度刻度，而${B}_{p}$是非通用常量。对数区的斜率${A}_{p}$对雷诺数非常不敏感，这与壁面有界流动的普遍行为一致。斜率不同于假设高斯统计的预测，而是与亚高斯行为一致。
Abstract High-Reynolds-number data in turbulent boundary layers are analysed to examine statistical moments of streamwise velocity fluctuations ${u}^{\prime } $ . Prior work has shown that the variance of ${u}^{\prime } $ exhibits logarithmic behaviour with distance to the surface, within an inertial sublayer. Here we extend these observations to even-order moments. We show that the $2p$ -order moments, raised to the power $1/ p, $ also follow logarithmic behaviour according to $\langle \mathop{({u}^{\prime + } ){}^{2p} \rangle }\nolimits ^{1/ p} = {B}_{p} - {A}_{p} \ln (z/ \delta )$ , where ${u}^{\prime + } $ is the velocity fluctuation normalized by the friction velocity, $\delta $ is an outer length scale and ${B}_{p} $ are non-universal constants. The slopes ${A}_{p} $ in the logarithmic region appear quite insensitive to Reynolds number, consistent with universal behaviour for wall-bounded flows. The slopes differ from predictions that assume Gaussian statistics, and instead are consistent with sub-Gaussian behaviour.