Small-Scale Statistics and Structure of Turbulence – in the Light of High Resolution Direct Numerical Simulation
Small-Scale Statistics and Structure of Turbulence – in the Light of High Resolution Direct Numerical Simulation
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DOI：
10.1017/cbo9781139032810.002
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发表时间：
2012-12
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影响因子：
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通讯作者：
Y. Kaneda;K. Morishita
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作者：
Y. Kaneda;K. Morishita
引言充分发展的湍流是一种涉及大量动力学自由度的现象。湍流流体的运动对流动条件的微小差异很敏感，因此，尽管后者看起来是相同的，但它们可能会引起运动的巨大差异。在某种意义上，这个困难类似于我们在处理由阿伏伽德罗数的分子组成的系统时所面临的困难，在这个系统中，不可能预测所有分子的运动。然而，我们知道，在压力、体积和温度等少数变量之间的某些关系，如理想气体定律，对分子的运动、形状、碰撞过程等的差异不敏感。有鉴于此，很自然地要问在湍流中是否存在这样的关系。在这方面，我们记得流体运动是由流动条件（例如边界条件和强迫）决定的。运动不可能对这些条件的差异不敏感，特别是在大尺度上。然而，人们也倾向于假定，在充分发展的湍流中，在足够高的雷诺数和远离流动边界的足够小的尺度上的统计中，存在着某些类型的关系式，它们在对大尺度流动条件的细节不敏感的意义上是通用的。事实上，这一思想是Kolmogorov理论（Kolmogorov，1941 a，以下简称K41）的基础，也是许多现代湍流研究的核心。在下文中，这种意义上的普遍性被称为K41意义上的普遍性
Introduction Fully developed turbulence is a phenomenon involving huge numbers of degrees of dynamical freedom. The motions of a turbulent fluid are sensitive to small differences in flow conditions, so though the latter are seemingly identical they may give rise to large differences in the motions.1 It is difficult to predict them in full detail. This difficulty is similar, in a sense, to the one we face in treating systems consisting of an Avogadro number of molecules, in which it is impossible to predict the motions of them all. It is known, however, that certain relations, such as the ideal gas laws, between a few number of variables such as pressure, volume, and temperature are insensitive to differences in the motions, shapes, collision processes, etc. of the molecules. Given this, it is natural to ask whether there is any such relation in turbulence. In this regard, we recall that fluid motion is determined by flow conditions, such as boundary conditions and forcing. It is unlikely that the motion would be insensitive to the difference in these conditions, especially at large scales. It is also tempting, however, to assume that, in the statistics at sufficiently small scales in fully developed turbulence at sufficiently high Reynolds number, and away from the flow boundaries, there exist certain kinds of relation which are universal in the sense that they are insensitive to the detail of large-scale flow conditions. In fact, this idea underlies Kolmogorov's theory (Kolmogorov, 1941a, hereafter referred as K41), and has been at the heart of many modern studies of turbulence. Hereafter, universality in this sense is referred to as universality in the sense of K41