Exact Resummations in the Theory of Hydrodynamic Turbulence: 0. Line-Resummed Diagrammatic Perturbation Approach
Exact Resummations in the Theory of Hydrodynamic Turbulence: 0. Line-Resummed Diagrammatic Perturbation Approach
复制标题
水动力湍流理论的精确恢复：0. 线恢复图解摄动方法
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
I. Procaccia
中科院分区：
文献类型：
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作者：
V. L’vov;I. Procaccia
在莱舒什暑期学校，我们之一（IP）所做的讲座涉及流体流动中高雷诺数湍流的标度特性。所提供的结果可在文献中获得，没有真实的需要在此重现。恰恰相反，该领域的一些基本工具和理论技术在教学格式中是不可用的，为了感兴趣的学生的利益，在这里展示它们似乎是值得的。我们开始与天真的扰动理论的详细阐述的系综平均的流体动力学观测值（平均速度，响应函数和相关函数）。在这种理论中，有效膨胀参数是雷诺数（Re）;因此，需要进行无限次迭代来改变有效膨胀参数。我们详细介绍了Dyson-Wyld线重定，它允许一个穿着的传播子，并改变有效的扩展参数从Re到O（1）。接下来，我们开发了图解系列的“修饰顶点”表示。最后，我们详细讨论了湍流统计理论的路径积分公式，并证明了它与Dyson-Wyld理论是等价的。根据这里提供的材料，人们可以顺利地阅读这一领域的最新发展。
The lectures presented by one of us (IP) at the Les Houches summer school dealt with the scaling properties of high Reynolds number turbulence in fluid flows. The results presented are available in the literature and there is no real need to reproduce them here. Quite on the contrary, some of the basic tools of the field and theoretical techniques are not available in a pedagogical format, and it seems worthwhile to present them here for the benefit of the interested student. We begin with a detailed exposition of the naive perturbation theory for the ensemble averages of hydrodynamic observables (the mean velocity, the response functions and the correlation functions). The effective expansion parameter in such a theory is the Reynolds number (Re); one needs therefore to perform infinite resummations to change the effective expansion parameter. We present in detail the Dyson-Wyld line resummation which allows one to dress the propagators, and to change the effective expansion parameter from Re to O(1). Next we develop the ``dressed vertex" representation of the diagrammatic series. Lastly we discuss in full detail the path-integral formulation of the statistical theory of turbulence, and show that it is equivalent order by order to the Dyson-Wyld theory. On the basis of the material presented here one can proceed smoothly to read the recent developments in this field.