柯尔莫哥洛夫微尺度

柯尔莫哥洛夫微尺度湍流中最小的尺度。在柯尔莫哥洛夫尺度上,粘度占主导地位,湍流动能消散为热量。它们由[1]定义

柯尔莫哥洛夫长度尺度
柯尔莫哥洛夫时间尺度
柯尔莫哥洛夫速度标度

其中是每单位质量的湍流动能的平均耗散率,和是流体的运动粘度。 柯尔莫哥洛夫长度尺度的典型值,对于大气运动,其中对于千米级的大涡流,尺度范围大约从 0.1 到 10 毫米;对于较小的流,例如在实验室系统中的流, 可能要小得多。 [2]

柯尔莫哥洛夫在他1941年发表的理论中称,最小尺度的湍流是普遍的(对于每一个湍流都相似),并且它们只依赖于 。 柯尔莫哥洛夫微尺度的定义可以通过这种理论和量纲分析得到。由于运动粘度的维度是长度2 /时间,单位质量的能量耗散率的维度是长度2 /时间3 ,所以唯一具有时间维度的组合是这是柯尔莫罗戈夫时间尺度。同样,柯尔莫哥洛夫长度尺度是唯一的组合具有长度尺寸。


或者,可以从均方应变率张量的倒数中获得柯尔莫哥洛夫时间尺度的定义, 这也给出了使用单位质量的能量耗散率的定义 .那么柯尔莫哥洛夫长度尺度可以得到雷诺数等于1的尺度, .

柯尔莫哥洛夫 1941 理论是一种平均场理论,因为它假设相关的动态参数是平均能量耗散率。在流体湍流中,能量耗散率随空间和时间波动,因此可以将微尺度视为也在空间和时间上变化的量。但是,标准做法是使用平均场值,因为它们代表给定流量中最小尺度的典型值。

另见

参考文献

  1. ^ M. T. Landahl; E. Mollo-Christensen. Turbulence and Random Processes in Fluid Mechanics 2nd. Cambridge University Press. 1992: 10. ISBN 978-0521422130. 
  2. ^ George, William K. "Lectures in Turbulence for the 21st Century." Department of Thermo and Fluid Engineering, Chalmers University of Technology, Göteborg, Sweden (2005).p 64 [online] http://www.turbulence-online.com/Publications/Lecture_Notes/Turbulence_Lille/TB_16January2013.pdf页面存档备份,存于互联网档案馆

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