On One Possibility of Closuring the Chain of Equations for Statistical Moments in Turbulence Theory

• 作者: Edward V. Teodorovich
• 来源期刊: 现代物理(英文)
• 学科: 数学
• 关键词: Random Velocity Field STATISTICAL DESCRIPTION Characteristic Functional CHAIN of EQUATIONS for MOMENTS Problem of Closuring
• 年，卷（期）: 2013,（1）
• 页码范围: 56-63
• 页数: 8页
• 分类号: O1

摘要

The paper concerns the problem on statistical description of the turbulent velocity pulsations by using the method of characteristic functional. The equations for velocity covariance and Green’s function, which describes an average velocity response to external force action, have been obtained. For the nonlinear term in the equation for velocity covariance, it has been obtained an exact representation in the form of two terms, which can be treated as describing a momentum transport due to turbulent viscosity and action of effective random forces (within the framework of traditional phenomenological description, the turbulent viscosity is only accounted for). Using a low perturbation theory approximation for high statistical moments, a scheme of closuring the chain of equations for statistical moments is proposed. As the result, we come to a closed set of equations for velocity covariance and Green’s function, the solution to which corresponds to summing up a certain infinite subsequence of total perturbation series.