Semiempirical theory of turbulent transfer

Abstract

A closed system of equations is constructed for flow of a nonisotropic character on the assumption that the mixing path length is not small compared with the characteristic dimension of the stream. It is assumed that the velocity pulsation field can be characterized by a multipoint distribution function, which satisfies the continuity equation. This enables equations to be obtained for the one-point and two-point distribution function. A series of assumptions is made concerning the nature of the forces acting on the turbulent formation (“turbule” or vortex) in the stream and concerning the correlation time of the random force with the scale and intensity of the turbulence. Assumptions are also made concerning the expression of the integral in the equation for the one-point distribution function and the expression for the correlation tensor in the isotropic case. After the moments are calculated, a system of Reynolds' equations is obtained in which approximations, usually acceptable from dimensional considerations, follow for a series of terms. Here, this is a consequence of the approximations for the forces in the equation for the distribution function. Closing the system of equations for the moments reduces to solving the equation for the distribution function. It turns out that the integral character of the transfer (diffusion of a nongradient type) is connected with taking third-order moments into account. A series of examples of flow is considered, and values of the empirical constants are determined. The system of equations obtained enables us to consider flow with strong anisotropy of turbulent transfer.