Mean velocity profile in stably stratified turbulent channel flow

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. 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 their corresponding mean velocity scaling. Hence, we propose a relation to estimate this ratio directly from the governing input parameters: the friction Reynolds and friction Richardson numbers (Re_τ and Ri_τ). The framework is tested against a series of direct numerical simulations across a range of Re_τ and Ri_τ. The reconstructed velocity profiles enable accurate prediction of the skin-friction coefficient crucial for quantifying pressure losses in stratified flows in engineering applications.