A new Eulerian theory of turbulence constrained by random Galilean invariance

TL;DR

This paper introduces a novel Eulerian turbulence theory that enforces random Galilean invariance, resulting in a set of equations that better capture the effects of random sweeping in homogeneous, isotropic turbulence.

Contribution

It presents a new Eulerian turbulence framework incorporating random Galilean invariance constraints, offering a potential approach to improve closure models for turbulence correlations.

Findings

Exact solutions for a random oscillator model

Provides a new set of equations for turbulence propagators

Suggests a method to include random sweeping effects

Abstract

We propose a new Eulerian turbulence theory to obtain a closed set of equations for homogeneous, isotropic turbulent velocity field correlations and propagator functions by incorporating constraints of random Galilean invariance. This incorporation generates a few different equations for propagator and the present theory suggests a way to utilize them into the closure solutions of two-time and single-time velocity correlations' equations so as to properly account for random sweeping phenomena. The present theory yields exact solutions when applied to simple model problem of random oscillator.