A Theoretical Basis for Determination of the Reynolds Stress in Canonical Turbulent Flows

TL;DR

This paper introduces a novel theoretical method for calculating Reynolds stress in canonical turbulent flows using momentum balance in a moving control volume, validated against experimental and DNS data, with potential applications in aerodynamics.

Contribution

It provides a new theoretical approach for determining Reynolds stress based on momentum balance, offering a closed-form expression and validation with data.

Findings

Good agreement with experimental and DNS data

Offers a new perspective on turbulence momentum transport

Potential applications in complex flow analysis

Abstract

We present a unique method for solving for the Reynolds stress in turbulent canonical flows, which is based on momentum balance for a control volume moving at the local mean velocity. Comparisons with experimental and computational data in simple geometries show quite good agreement. An alternate picture for the turbulence momentum transport is offered, based on the closed-form expression for the Reynolds stress. The turbulence momentum balance is verified using DNS data. This approach has potential applications in aerodynamics, and also represents a possible method for determining the Reynolds stress in more complex flows.