Nonlocal Form of the Rapid Pressure-Strain Correlation in Turbulent Flows

TL;DR

This paper introduces a new nonlocal formulation for the rapid pressure-strain correlation in turbulent flows, accounting for spatial variations in mean velocity gradients, aiming to improve turbulence anisotropy predictions in inhomogeneous flows.

Contribution

A fundamentally-based explicit nonlocal formulation of the rapid pressure-strain correlation derived via Taylor expansion, incorporating spatial variations in mean velocity gradients.

Findings

Derived series expansion for high- and low-Reynolds numbers

Expressed nonlocal correlation as Laplacians of mean strain rate tensor

Proposed a nonlocal transport equation for turbulence anisotropy

Abstract

A new fundamentally-based formulation of nonlocal effects in the rapid pressure-strain correlation in turbulent flows has been obtained. The resulting explicit form for the rapid pressure-strain correlation accounts for nonlocal effects produced by spatial variations in the mean-flow velocity gradients, and is derived through Taylor expansion of the mean velocity gradients appearing in the exact integral relation for the rapid pressure-strain correlation. The integrals in the resulting series expansion are solved for high- and low-Reynolds number forms of the longitudinal correlation function $f(r)$, and the resulting nonlocal rapid pressure-strain correlation is expressed as an infinite series in terms of Laplacians of the mean strain rate tensor. The new formulation is used to obtain a nonlocal transport equation for the turbulence anisotropy that is expected to provide improved predictions of the anisotropy in strongly inhomogeneous flows.