Logarithmic scaling of turbulence in smooth- and rough-wall pipe flow
Logarithmic scaling of turbulence in smooth- and rough-wall pipe flow
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DOI：
10.1017/jfm.2013.255
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发表时间：
2013-07
影响因子：
3.7
通讯作者：
M. Hultmark;Margit Vallikivi;Sean C. C. Bailey-Sean-C.-C.-Bailey-2243995599;Alexander Smits
中科院分区：
文献类型：
--
作者：
M. Hultmark;Margit Vallikivi;Sean C. C. Bailey-Sean-C.-C.-Bailey-2243995599;Alexander Smits
摘要在一个前所未有的雷诺数范围内，对充分发展的光滑和粗糙管流中湍流脉动的流向分量进行了测量。对于雷诺数R{e}_{\tau } \gt 20\hspace{0.167em} 000$，流向雷诺应力与平均速度剖面的比例密切相关，与粗糙度无关，并且在相同的空间范围内。这一观察结果扩展了Hultmark，Vallikivi和Smits（Phys. Rev. Lett.，Vol.108，2012）以包括粗糙流。对数区域的起始点位于壁距离等于柯尔莫哥洛夫长度尺度的100倍的位置，这标志着惯性尺度的足够尺度分离。此外，在对数区域中，四阶矩的平方根也显示出对数行为，这与观察到的基本概率密度函数在该区域中接近高斯分布相一致。
Abstract Measurements of the streamwise component of the turbulent fluctuations in fully developed smooth and rough pipe flow are presented over an unprecedented Reynolds number range. For Reynolds numbers $R{e}_{\tau } \gt 20\hspace{0.167em} 000$ , the streamwise Reynolds stress closely follows the scaling of the mean velocity profile, independent of the roughness, and over the same spatial extent. This observation extends the findings of a logarithmic law in the turbulence fluctuations as reported by Hultmark, Vallikivi & Smits (Phys. Rev. Lett., vol. 108, 2012) to include rough flows. The onset of the logarithmic region is found at a location where the wall distance is equal to ∼100 times the Kolmogorov length scale, which then marks sufficient scale separation for inertial scaling. Furthermore, in the logarithmic region the square root of the fourth-order moment also displays logarithmic behaviour, in accordance with the observation that the underlying probability density function is close to Gaussian in this region.