A Method for Determination of the Reynolds Stress and Turbulence Structure in Wall-Bounded Flows

TL;DR

This paper introduces a new method to determine turbulence structure in wall-bounded flows by combining Reynolds stress transport equations with structure-based u2 profile reconstruction, validated against DNS data.

Contribution

It presents an innovative approach that integrates Reynolds stress transport equations with structure-based u2 profile reconstruction for turbulence analysis.

Findings

Good agreement with DNS data for turbulence profiles

Reynolds stress gradient expression enhances turbulence modeling

Method enables full turbulence structure reconstruction

Abstract

Using the Lagrangian transport of momentum, the Reynolds stress can be expressed in terms of basic turbulence parameters. The Reynolds stress gradient represents the lateral transport of stream-wise momentum, balanced by the u2 transport, pressure and shear force terms in the momentum equation. Data from direct numerical simulations (DNS) have been used to validate this approach, with a good degree of consistency and agreement. This expression for the Reynolds stress gradient adds a transport equation to the Reynolds-averaged Navier-Stokes (RANS) equation, so that the turbulence structure can be determined if the third unknown variable, u2, can be determined. Here, we consider alternative structure-based methods for reconstruction of u2 profiles for wall-bounded flows. The input of u2 profile, in conjunction with the two transport equations (RANS and the current Reynolds stress equation), allows for full reconstruction of the turbulent structure in wall-bounded flows, with reasonable agreement with DNS data.