Reynolds-number dependence of line and surface stretching in turbulence: folding effects
Reynolds-number dependence of line and surface stretching in turbulence: folding effects
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DOI：
10.1017/s0022112007007240
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发表时间：
2007-09-10
影响因子：
3.7
通讯作者：
Kida, Shigeo
中科院分区：
文献类型：
--
作者：
Goto, Susumu;Kida, Shigeo
在统计上稳定的均匀各向同性湍流中，充分伸展的物质线和物质面的拉伸率（用柯尔莫哥洛夫时间的倒数进行归一化）取决于雷诺数，这与传统观点（即物质对象变形的统计特性仅由柯尔莫哥洛夫尺度的涡旋决定）形成对比。充分伸展的物质对象拉伸率的这种雷诺数依赖性在二维和三维湍流中都通过数值方法得到了验证，尽管无穷小物质对象的归一化拉伸率被证实与雷诺数无关。这些数值结果可以从以下三个事实来理解。首先，指数级快速拉伸导致有限尺寸物质对象快速多次折叠，但无穷小对象不会发生折叠。其次，由于局部折叠程度与局部拉伸率正相关，且在有限尺寸对象上非均匀分布，所以折叠提高了有限尺寸对象的拉伸率。第三，物质对象的无穷小部分的拉伸由柯尔莫哥洛夫尺度的涡旋控制，而有限尺寸物质对象的折叠由小于对象空间尺度的所有涡旋控制。换句话说，物质对象无穷小部分拉伸的时间尺度与柯尔莫哥洛夫时间成正比，而充分伸展的物质对象折叠的时间尺度可以与最大涡旋的周转时间一样长。物质对象无穷小部分拉伸的短时间尺度和整个对象折叠的长时间尺度相结合，产生了雷诺数依赖性。论文的在线版本附有相关视频。
The stretching rate, normalized by the reciprocal of the Kolmogorov time, of sufficiently extended material lines and surfaces in statistically stationary homogeneous isotropic turbulence depends on the Reynolds number, in contrast to the conventional picture that the statistics of material object deformation are determined solely by the Kolmogorov-scale eddies. This Reynolds-number dependence of the stretching rate of sufficiently extended material objects is numerically verified both in two- and three-dimensional turbulence, although the normalized stretching rate of infinitesimal material objects is confirmed to be independent of the Reynolds number. These numerical results can be understood from the following three facts. First, the exponentially rapid stretching brings about rapid multiple folding of finite-sized material objects, but no folding takes place for infinitesimal objects. Secondly, since the local degree of folding is positively correlated with the local stretching rate and it is non-uniformly distributed over finite-sized objects, the folding enhances the stretching rate of the finite-sized objects. Thirdly, the stretching of infinitesimal fractions of material objects is governed by the Kolmogorov-scale eddies, whereas the folding of a finite-sized material object is governed by all eddies smaller than the spatial extent of the objects. In other words, the time scale of stretching of infinitesimal fractions of material objects is proportional to the Kolmogorov time, whereas that of folding of sufficiently extended material objects can be as long as the turnover time of the largest eddies. The combination of the short time scale of stretching of infinitesimal fractions and the long time scale of folding of the whole object yields the Reynolds-number dependence. Movies are available with the online version of the paper.