Self-Diffusion by Multivariate-Normal Turbulent Velocity Field

TL;DR

This paper derives exact statistical equations for turbulent self-diffusion assuming a multivariate-normal turbulent velocity field, providing a theoretical framework for understanding turbulence-driven mixing.

Contribution

It introduces exact formulas for correlations involving multivariate-normal turbulent velocity fields and functional derivatives, advancing the theoretical understanding of turbulent diffusion.

Findings

Derived exact equations for turbulent self-diffusion.

Formulated formulas for correlations involving Gaussian velocity fields.

Provided a theoretical basis for modeling turbulence-induced mixing.

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 $<f_i(p)f_j(p')R[{\bf f}]>$, $<g(p)R[{\bf f}]>$ and $<g(p)f_j(p')R[{\bf f}]>$ when the functional $R[{\bf f}]$ is functional of functions ${f_i}$'s having multivariate-normal distribution, $g$ and $f_i$'s have joint normal distribution and zero mean values.