关于湍流中速度随机场的分布
On distributions of velocity random fields in turbulent flows
摘要：
本文推导了湍流速度场单次单点概率密度函数的偏微分方程。PDF偏微分方程是一个高度非线性的抛物输运方程，它依赖于两个具有重要物理意义的条件统计数值。PDF偏微分方程是经典雷诺平均流方程的一般形式，是PDF输运方程的精确形式。PDF偏微分方程为湍流建模提供了一种新的方法。构造了一个显式的算例，虽然这个算例看起来是人为的，但它演示了基于新的PDF偏微分方程的PDF方法。
英文摘要：
The purpose of the present paper is to derive a partial differential equation (PDE) for the single-time single-point probability density function (PDF) of the velocity field of a turbulent flow. The PDF PDE is a highly non-linear parabolic-transport equation, which depends on two conditional statistical numerics of important physical significance. The PDF PDE is a general form of the classical Reynolds mean flow equation, and is a precise formulation of the PDF transport equation. The PDF PDE provides us with a new method for modelling turbulence. An explicit example is constructed, though the example is seemingly artificial, but it demonstrates the PDF method based on the new PDF PDE.
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