Galilean invariance and homogeneous anisotropic randomly stirred flows

TL;DR

This paper derives Ward-Takahashi identities from Galilean invariance in the context of randomly forced Navier-Stokes flows, analyzing implications for vertex renormalization in turbulence models.

Contribution

It explicitly derives WT identities for incompressible flows with mean and fluctuating velocities, linking Galilean invariance to vertex renormalization in turbulence theory.

Findings

Derived WT identities for incompressible flow

Analyzed implications for vertex renormalization

Connected Galilean invariance to turbulence modeling

Abstract

The Ward-Takahashi (WT) identities for incompressible flow implied by Galilean invariance are derived for the randomly forced Navier-Stokes equation (NSE), in which both the mean and fluctuating velocity components are explicitly present. The consequences of Galilean invariance for the vertex renormalization are drawn from this identity.