Mean velocity equation for turbulent flow

TL;DR

This paper derives a mean velocity equation for turbulent flow using statistical mechanics, addressing the turbulence closure problem by calculating higher-order force terms through multilinear mode coupling theory.

Contribution

It introduces a new turbulence equation derived from N-particle statistical mechanics, including detailed calculations of third-order force terms.

Findings

Derived a mean velocity equation for turbulent flow

Calculated third-order friction force terms using mode coupling theory

Expressed force as a convolution integral with velocity gradients

Abstract

The hydrodynamic equation derived by N-particle statistical mechanics is investigated. This is an attempt to provide additional information concerning the closure problem of turbulence theory. The equation is interpreted as mean velocity equation for turbulent fluid flow. The third-order term of the friction force is calculated. Multilinear mode coupling theory is applied in order to obtain formulas for the third- und fourth-order equilibrium time correlation functions appearing in the expression. The force term is obtained as a convolution integral containing higher order gradients of the velocity field.