Stable channel flow with spanwise heterogeneous surface temperature

Recent studies have demonstrated that large secondary motions are excited by surface roughness with dominant spanwise length scales of the order flow's outer scale. Inspired this, we explore effect heterogeneous temperature in weakly to strongly stratified closed channel flow (at $Ri_\tau =120$ , 960; $Re_\tau = 180$ 550) direct numerical simulations. The configuration consists equally sized strips high and low at lower upper boundaries, while an overall stable stratification is induced imposing average difference between top bottom. We consider influence width ( ${\rm \pi} /8 \leq \lambda /h 4{\rm $ ), Reynolds number, stability boundary condition on mean structure, skin friction heat transfer. Results indicate flows excited, alternating high- low-momentum pathways vortices, similar patterns roughness. find impact heterogeneity layer depends scale temperature. Comparison uniform reveals increases global coefficient reduces Nusselt number most cases. However, for high-Reynolds cases $\lambda \geq {\rm /2$ a reduction coefficient. At stronger stability, vertical extent vortices reduced momentum transfer smaller.