Heat and Momentum Transfer in Stably Stratified Channel Flow with Spanwise Heterogeneous Surface Temperature

Recent studies have demonstrated that large secondary flows are excited by spanwise heterogeneous surface roughness with dominant length scales of the order of the boundary layer height. Inspired by this, we explore the effect of spanwise heterogeneous surface temperature on stably stratified closed channel flow (Ri_τ =120 - 960, Re_τ = 180 - 550) with DNS. The configuration consists of high- and low temperature strips at the bottom and top boundaries, while a vertical temperature difference across the channel induces overall stable stratification. Results show similar secondary flow patterns as for heterogeneous roughness, with alternating high- and low-momentum pathways and in-plane vortices. By systematically varying the width of the strips (π/8 < λ/h <4π) we find that the impact of the surface heterogeneity on the outer layer depends strongly on this spanwise length scale. Comparison to homogeneous stable channel flow reveals that in most cases, heterogeneous surface temperatures lead to increased friction coefficients. However for the high-Re cases and λ/h > π/2, we find a reduction of the friction coefficient. In contrast, the Nusselt number was reduced for all heterogeneous cases, though a clear dependence on λ/h is present.