Turbulence Momentum Transport and Prediction of the Reynolds Stress in Canonical Flows

TL;DR

This paper introduces a novel method for calculating Reynolds stress in canonical turbulent flows using a control volume approach and differential transforms, aligning well with experimental and DNS data.

Contribution

It provides a new physics-based explicit formula for Reynolds stress, enabling better understanding and potential application to complex turbulent flows.

Findings

Good agreement with experimental and DNS data

Reynolds stress expressed explicitly in terms of turbulence parameters

Potential for extending to complex turbulent flows

Abstract

We present a unique method for solving for the Reynolds stress in turbulent canonical flows, based on the momentum balance for a control volume moving at the local mean velocity. A differential transform converts this momentum balance to a solvable form. Comparisons with experimental and computational data in simple geometries show quite good agreements. An alternate picture for the turbulence momentum transport is offered, as verified with data, where the turbulence momentum is transported by the mean velocity while being dissipated by viscosity. The net momentum transport is the Reynolds stress. This turbulence momentum balance is verified using DNS and experimental data. Implications of this work are that the Reynolds stress can be written explicitly in terms of basic turbulence parameters in a simple form, derived from pure fluid physics, and that potential exists for applications of this concept to more complex turbulent flows.