Small-scale statistics in high-resolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics
Small-scale statistics in high-resolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics
复制标题
DOI：
10.1017/s0022112007008531
复制
发表时间：
2007-12-10
影响因子：
3.7
通讯作者：
Uno, A.
中科院分区：
文献类型：
--
作者：
Ishihara, T.;Kaneda, Y.;Uno, A.
通过分析高分辨率直接数值模拟（DNS）的数据，在一个周期性的盒子，高达4096 3网格点的湍流的速度梯度和欧拉和拉格朗日加速度的一点统计进行了研究。DNS由两个系列的运行组成;一个是k（max）eta类似于1（系列1），另一个是k（max）eta类似于2（系列2），其中k（max）是最大波数，eta是柯尔莫哥洛夫长度尺度。最大泰勒微尺度雷诺数R-lambda在系列1中约为1130，在系列2中约为675。特别注意的是可能的雷诺数（Re）的统计依赖。强涡区的可视化显示表明，高雷诺数下湍流场由一组小的强涡区组成，其结构与小涡区不同。速度梯度概率分布函数对Re的可能依赖性通过偏斜度和平坦度因子（S和F）对R-lambda的依赖性来分析。DNS数据表明，纵向速度梯度的S和F的R-λ依赖关系符合简单的幂律：S近似于-0.32R（λ）（0.11），F近似于1.14（λ）（0.34），与以前的实验数据相当吻合。他们还表明，所有的四阶矩的速度梯度的比例与R-λ相似，彼此在R-λ> 100，而不是R-λ < 100。关于时间导数的统计，对于欧拉和拉格朗日速度，湍流速度的二阶时间导数比一阶时间导数更间歇，并且湍流速度的拉格朗日时间导数比欧拉时间导数更间歇，正如所预期的那样。拉格朗日加速度的平坦因子在R-lambda近似为430时高达90。欧拉和拉格朗日加速度的平坦度因子随着R-lambda的增加而增加，分别与R-lambda（alpha E）和R-lambda（alpha L）大致成比例，其中alpha（E）接近0.5，alpha（L）接近1.0，而欧拉和拉格朗日速度的二阶时间导数的平坦度因子分别与R-lambda（beta E）和R-lambda（beta L）大致成比例地增加，其中β（E）近似为1.5，β（L）近似为3.0。
One-point statistics of velocity gradients and Eulerian and Lagrangian accelerations are studied by analysing the data from high-resolution direct numerical simulations (DNS) of turbulence in a periodic box, with up to 4096 3 grid points. The DNS consist of two series of runs; one is with k(max)eta similar to 1 (Series 1) and the other is with k(max)eta similar to 2 (Series 2), where k(max) is the maximum wavenumber and eta the Kolmogorov length scale. The maximum Taylor-microscale Reynolds number R-lambda in Series 1 is about 1130, and it is about 675 in Series 2. Particular attention is paid to the possible Reynolds number (Re) dependence of the statistics. The visualization of the intense vorticity regions shows that the turbulence field at high Re consists of clusters of small intense vorticity regions, and their structure is to be distinguished from those of small eddies. The possible dependence on Re of the probability distribution functions of velocity gradients is analysed through the dependence on R-lambda of the skewness and flatness factors (S and F). The DNS data suggest that the R-lambda dependence of S and F of the longitudinal velocity gradients fit well with a simple power law: S similar to -0.32R(lambda)(0.11) and F similar to 1.14(lambda)(0.34), in fairly good agreement with previous experimental data. They also suggest that all the fourth-order moments of velocity gradients scale with R-lambda similarly to each other at R-lambda > 100, in contrast to R-lambda < 100. Regarding the statistics of time derivatives, the sccond-order time derivatives of turbulent velocities are more intermittent than the first-order ones for both the Eulerian and Lagrangian velocities, and the Lagrangian time derivatives of turbulent velocities are more intermittent than the Eulerian time derivatives, as would be expected. The flatness factor of the Lagrangian acceleration is as large as 90 at R-lambda approximate to 430. The flatness factors of the Eulerian and Lagrangian accelerations increase with R-lambda approximately proportional to R-lambda(alpha E) and R-lambda(alpha L), respectively, where alpha(E) approximate to 0.5 and alpha(L) approximate to 1.0, while those of the second-order time derivatives of the Eulerian and Lagrangian velocities increases approximately proportional to R-lambda(beta E) and R-lambda(beta L), respectively, where beta(E) approximate to 1.5 and beta(L) approximate to 3.0.