Abstract

The Navier–Stokes equation in the presence of external regular and random forces is considered. The statistical solution is described in terms of the characteristic functional obeying the equation in functional derivatives. The representations of corrections to the viscosity and the variance of external random forces due to turbulent mixing have been derived. A relation between the vertices of different types has been found that enables one to take into account the contribution to the physical characteristics of turbulence for vertices of all types.

中文翻译：

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湍流统计理论的功能表述

摘要

考虑存在外部规则和随机力的Navier–Stokes方程。根据特征函数服从函数导数方程来描述统计解。得出了由于湍流混合而引起的粘度校正和外部随机力变化的表示。已经发现不同类型的顶点之间的关系，使得人们能够考虑所有类型的顶点对湍流的物理特性的贡献。