Constitutive theory of inhomogeneous turbulent flow based on two-scale Lagrangian formalism

TL;DR

This paper develops a closure theory for inhomogeneous turbulent flow using a two-scale Lagrangian formalism, enabling systematic derivation of constitutive relations without empirical parameters.

Contribution

It introduces a novel two-scale Lagrangian formalism and renormalized-perturbation approach for inhomogeneous turbulence, avoiding empirical assumptions.

Findings

Derivation of turbulence constitutive relations systematically.

Incorporation of convective integration in a covariant manner.

Framework applicable to complex inhomogeneous flows.

Abstract

A closure theory is developed for inhomogeneous turbulent flow, which enables a systematic derivation of the turbulence constitutive relations without relying on any empirical parameters. Renormalized-perturbation approximation is performed in the convective coordinate frame based on the mean flow, successfully incorporating the convective integration in generally covariant manner.