Mean velocity profile in stably stratified turbulent channel flow

TL;DR

This paper evaluates the applicability of Monin-Obukhov Similarity Theory to stably stratified turbulent channel flows, proposing a new scaling parameter and closure relation validated by DNS data to predict velocity profiles and skin friction.

Contribution

It extends MOST to confined, stratified flows by identifying key scaling parameters and providing a closure relation validated through DNS simulations.

Findings

The ratio of half-channel height to Obukhov length governs flow regions.

A closure relation estimates this ratio from $Re_{\tau}$ and $Ri_{\tau}$.

Velocity profiles accurately predict skin friction in stratified flows.

Abstract

The Monin-Obukhov Similarity Theory (MOST) is a cornerstone of atmospheric science for describing turbulence in stable boundary layers. Extending MOST to stably stratified turbulent channel flows, however, is non-trivial due to confinement by solid walls and the much smaller turbulent length scales involved. In this study, we investigate the applicability of MOST in closed channels and identify where and to what extent the theory remains valid. A key finding is that the ratio of the half-channel height to the Obukhov length serves as a governing parameter for identifying distinct flow regions and determining the scaling of the mean velocity within them. Hence, we propose a closure relation to estimate this ratio directly from the governing input parameters: friction Reynolds and friction Richardson numbers ($Re_{\tau}$ and $Ri_{\tau}$). The framework is tested against a series of direct numerical simulations (DNS) across a range of $Re_{\tau}$ and $Ri_{\tau}$. The reconstructed velocity profiles enable accurate prediction of the skin friction coefficient crucial for quantifying pressure losses in stratified flows in engineering applications.