A Generalizable Theory for the Reynolds Stress, Based on the Lagrangian Turbulence Transport

TL;DR

This paper develops a comprehensive Lagrangian-based theory for Reynolds stress transport, validated with DNS data, applicable to complex turbulent flows including boundary layers and swirling pipe flows.

Contribution

It introduces a generalized formalism for turbulence transport equations based on Lagrangian momentum transport, extending to complex flow configurations.

Findings

Good agreement with DNS data across flow types

Validates the transport equations for all Reynolds stress components

Demonstrates application to turbulent jet flows

Abstract

Using the Lagrangian transport of momentum, the Reynolds shear stress can be expressed in terms of basic turbulence parameters. In this view, the Reynolds stress gradient represents the lateral transport of streamwise momentum, balanced by the u2 transport, pressure and shear force terms in the momentum equation. We extend this formalism to other turbulence parameters such as diagonal components of the Reynolds stress, and also to more complex flows (boundary layer flows with adverse pressure gradients and pipe flows with swirl). Data from direct numerical simulations (DNS) are used to validate this full set of turbulent transport equations, exhibiting a good degree of consistency and agreement for all of the components and across different geometries. An example of the use of this full set of turbulence transport equations is shown for turbulent jet flows.