Velocity statistics in turbulent channel flow up to $Re_{\tau }=4000$
Velocity statistics in turbulent channel flow up to $Re_{\tau }=4000$
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DOI：
10.1017/jfm.2013.674
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发表时间：
2014-02
影响因子：
3.7
通讯作者：
M. Bernardini;S. Pirozzoli;P. Orlandi
中科院分区：
文献类型：
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作者：
M. Bernardini;S. Pirozzoli;P. Orlandi
摘要采用大尺度直接数值模拟方法研究了不可压槽道湍流的高雷诺数特性。实现了雷诺数（$Re_{\tau } = h/\delta _v \approx 4000$，其中$h$是通道半高，$\delta _v$是粘性长度尺度），在该理论预测的渐近雷诺数制度的典型现象的发病，即一个敏感层的平均速度分布的对数变化，和柯尔莫哥洛夫缩放的速度谱。虽然在实验中可以达到更高的雷诺数，目前DNS研究的主要优势是获得完整的三维流场。与细化的重叠参数一致（Afzal & Yajnik，J. Fluid Mech.vol.61，1973，pp. 23-31; Jiménez & Moser，Phil.横河Soc. Lond. A，第365卷，2007年，第365页。715-732），我们的结果表明，平均速度分布从来没有达到真正的对数分布，对数诊断功能，而不是表现出在外层的斜率随雷诺数下降的线性变化。冯卡门常数的外推值为$k \约0.41$。如汤森附加涡流假设所预测的那样，在展向速度变化中观察到一个接近对数层，而流向变化似乎呈现出一个肩部，可能仍然受到低雷诺数效应的影响。与以前的DNS数据在较低的雷诺数的比较表明，增强的近壁区域的外层涡的印记效果。这种机制与外层中过量湍流动能的产生有关，并且它反映在流动可视化和流向速度谱中，这些速度谱在外层中表现出尖锐的峰值。与外部能源生产网站，我们发现证据的Kolmogorov惯性范围内，仅限于展向谱密度的$u$，而幂律与不同的指数被发现的其他频谱。最后，参数给出来解释的'奇'标度的流向速度的方差，基于动能产生项的分析。
Abstract The high-Reynolds-number behaviour of the canonical incompressible turbulent channel flow is investigated through large-scale direct numerical simulation (DNS). A Reynolds number is achieved ( $Re_{\tau } = h/\delta _v \approx 4000$ , where $h$ is the channel half-height, and $\delta _v$ is the viscous length scale) at which theory predicts the onset of phenomena typical of the asymptotic Reynolds number regime, namely a sensible layer with logarithmic variation of the mean velocity profile, and Kolmogorov scaling of the velocity spectra. Although higher Reynolds numbers can be achieved in experiments, the main advantage of the present DNS study is access to the full three-dimensional flow field. Consistent with refined overlap arguments (Afzal & Yajnik, J. Fluid Mech. vol. 61, 1973, pp. 23–31; Jiménez & Moser, Phil. Trans. R. Soc. Lond. A, vol. 365, 2007, pp. 715–732), our results suggest that the mean velocity profile never achieves a truly logarithmic profile, and the logarithmic diagnostic function instead exhibits a linear variation in the outer layer whose slope decreases with the Reynolds number. The extrapolated value of the von Kármán constant is $k \approx 0.41$ . A near logarithmic layer is observed in the spanwise velocity variance, as predicted by Townsend’s attached eddy hypothesis, whereas the streamwise variance seems to exhibit a shoulder, perhaps being still affected by low-Reynolds-number effects. Comparison with previous DNS data at lower Reynolds number suggests enhancement of the imprinting effect of outer-layer eddies onto the near-wall region. This mechanisms is associated with excess turbulence kinetic energy production in the outer layer, and it reflects in flow visualizations and in the streamwise velocity spectra, which exhibit sharp peaks in the outer layer. Associated with the outer energy production site, we find evidence of a Kolmogorov-like inertial range, limited to the spanwise spectral density of $u$ , whereas power laws with different exponents are found for the other spectra. Finally, arguments are given to explain the ‘odd’ scaling of the streamwise velocity variances, based on the analysis of the kinetic energy production term.