Law of the wall in an unstably stratified turbulent channel flow

TL;DR

This study uses direct numerical simulations to explore how buoyancy influences the boundary layer and velocity profiles in unstably stratified turbulent channel flows, revealing deviations from classical log-law behavior.

Contribution

It introduces a phenomenological model that accurately captures the effects of buoyancy on the velocity profile in turbulent channel flows.

Findings

Buoyancy causes measurable deviations from the classical log-law in velocity profiles.

The proposed model successfully predicts the observed deviations.

Simulations provide detailed profiles of velocity, temperature, and Reynolds stresses under buoyant conditions.

Abstract

We perform direct numerical simulations of an unstably stratified turbulent channel flow to address the effects of buoyancy on the boundary layer dynamics and mean field quantities. We systematically span a range of parameters in the space of friction Reynolds number ($Re_{\tau}$) and Rayleigh number ($Ra$). Our focus is on deviations from the logarithmic law of the wall due to buoyant motion. The effects of convection in the relevant ranges are discussed providing measurements of mean profiles of velocity, temperature and Reynolds stresses as well as of the friction coefficient. A phenomenological model is proposed and shown to capture the observed deviations of the velocity profile in the log-law region from the non-convective case.