Transition to the ultimate regime of turbulent convection in stratified inclined duct flow

The stratified inclined duct (SID) provides a canonical setup for sustained, buoyancy-driven exchange flow between two reservoirs of different density, and emerges as a paradigm in geophysical fluid dynamics. Yet, the flow dynamics remain unclear in the highly turbulent regime; laboratory experiments can access this regime but they lack resolution, while direct numerical simulations (DNSs) at realistically high Prandtl number, Pr = 7 (for heat in water), have not achieved sufficiently high Reynolds numbers Re. We conduct three-dimensional DNSs up to Re = 8000 and observe the transition to the so-called ultimate regime of turbulent convection as evidenced by the Nusselt number scaling Nu ∼ Ra¹/², indicating substantially enhanced transport. At the transition, the shear Reynolds number, a key parameter characterizing boundary layer (BL) dynamics, exceeds the threshold range of 420 for turbulent kinetic BLs with the emergence of logarithmic velocity profiles. The nature of the transition toward ultimate SID flow is non-normal-nonlinear, i.e., subcritical and hysteretic, as is typical for the transition to fully turbulent shear flows. Our work connects SID flow with the broader class of wall-bounded turbulent convection flows and gives insight into mixing properties in the vigorously turbulent regime encountered in oceanographic and industrial flows.