Self-Diffusion by Multivariate-Normal Turbulent Velocity Field

Abstract

A closed set of \textit{exact} equations describing statistical theory of turbulent self-diffusion by multivariate-normal turbulent velocity field is derived. In doing so, we first suggest exact formulas for correlations $<f_i(p)f_j(p^{\prime })R[\mathbf{f}]>$, $<g(p)R[\mathbf{f}]>$ and $<g(p)f_j(p^{\prime })R[\mathbf{f}]>$ when the functional $R[\mathbf{f}]$ is functional of functions $f_i$'s having multivariate-normal distribution, $g$ and $f_i$'s have joint normal distribution and zero mean values.

8 pages