Wall-function-based weak imposition of Dirichlet boundary condition for stratified turbulent flows

Abstract

Wall-function-based weak imposition of Dirichlet boundary condition (WFWD) has seen success in maintaining numerical accuracy with reduced near-wall resolution for modeling wall-bounded turbulent flows. In this work, we extend the formulation of WFWD to stably stratified flows. The performance of the extended formulation is validated with two canonical numerical experiments, namely stratified turbulent channel flow and stable atmospheric boundary layer, demonstrating its effectiveness and potential in modeling wall-bounded stratified turbulent flows. Comparisons are made against results of the original formulation of weak imposition of Dirichlet boundary condition (WD), as well as direct numerical or large-eddy simulations whenever available. Our results show that WFWD with a smooth wall function offers improved accuracy over its WD counterpart in predicting one-point statistics of the turbulent channel flow at various degrees of stratification. Furthermore, on account of adopting a rough wall function WFWD successfully predicts the occurrence of super-geostrophic jet as well as statistics that are in good agreement with highly-resolved large-eddy simulations. Our findings suggest that formulating the weak imposition of Dirichlet boundary condition based on wall functions could mitigate shortcomings of WD when factors like roughness play a non-negligible role.