Scaling relations in stably stratified channel flow with secondary motions induced by heterogeneous surface temperature

Recent studies have demonstrated that large streamwise-aligned secondary circulations can be generated in stratified flows over thermally heterogeneous surfaces with spanwise length scales in the order of the boundary layer depth. These mean secondary flow structures significantly affect time-averaged profiles of velocity and temperature in turbulent boundary layers, through the dispersive or coherent fluxes. In order to investigate this, we performed a series of Direct Numerical Simulations of stably stratified channel flow with spanwise heterogeneous temperature strips of both finite and infinite length, at Re_τ=180 and Re_τ=550. We analyzed the penetration depth of the heterogeneity into the outer layer and assessed accuracy of existing flux-profile scaling relations. Although the blending height strongly depends on the geometry of the surface temperature patches, mean velocity and temperature profiles of all cases collapse if an outer-layer scaling based on displacement thickness is applied. Comparison of the high-Reynolds cases with temperature patches of finite length to local Monin-Obukhov Similarity Theory (MOST) reveals that the similarity functions for temperature and velocity gradients agree with empirical linear relations in the region far above the surface, where dispersive fluxes are negligible. Profiles of the canonical case with infinitely long spanwise heterogeneity, which has been mostly studied in the context of secondary motions, do not follow local MOST at any height.