Transition to the ultimate turbulent regime in stratified inclined duct flow

The stratified inclined duct (SID) flow provides a canonical model for sustained, buoyancy-driven exchange between two reservoirs of different density, and emerges as a new 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 (DNS) at realistically high Prandtl number Pr\,=\,7 (for heat in water) have not achieved sufficiently high Reynolds numbers $\reynolds$. We conduct three-dimensional DNS up to $\reynolds= 8000$ and observe the transition to the so-called ultimate regime of turbulent convection as evidenced by the Nusselt number scaling $\nusselt \sim \rayleigh^{1/2}$. We further report that 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. Our work connects SID flow with the broader class of wall-bounded turbulent convection flows and gives insight into mixing in the vigorously turbulent regimes of oceanography and industry.