Transition to the ultimate turbulent regime in stratified inclined duct flow

Stratified inclined duct (SID) flows are a canonical model for sustained buoyancy-driven exchange flows between two reservoirs with fluids at different densities through a long tilted channel, Experiments can access the highly turbulent regime but lack resolution, while direct numerical simulations (DNS) at realistically high Prandtl number Pr=7 have not achieved sufficiently high Reynolds numbers. We conduct three-dimensional DNS up to Re ≈ 8000 for a flow with temperature stratification in water (Pr = 7). We observe the transition to the so-called ultimate regime of turbulent convection as evidenced by the Nusselt number scaling Nu ∼ Ra^1/2. We further report that the shear Reynolds number surpasses the threshold range around Re^*_s ≈ 420 for turbulent kinetic boundary layers with the emergence of logarithmic velocity profiles. Our work connects SID flows with the broader class of wall-bounded turbulent convection flows and gives insight into mixing and transport in oceanography and industrial flow.