Mixing efficiency of buoyancy forced circulation in a rotating basin

We ask whether rotation influences the mixing efficiency in horizontal convection in a rectangular basin. Direct numerical simulations are reported for a rotating $f$-plane ocean with an applied basal temperature differential over a wide range of Ekman number $E_L=6\times10^{-8}-1\times10^{-5}$, with Prandtl number $Pr=5$. Two values of the Rayleigh number are considered which, in the absence of rotation, relate to the viscous ($Ra=7.4\times10^8$) and inertial ($Ra=7.4\times10^{11}$) regimes. The heat flux decreases and boundary layer thickness increases with rotation rate, consistent with geostrophic scaling. At very high rotation rates and the smaller $Ra$ a regime dominated by Ekman pumping is revealed, with strong interior stratification. For the larger $Ra$ turbulent convective plumes in the boundary layer region form cyclonic vortices that extend through the depth, weakening the stratification. The global mixing efficiency $\eta$ is consistent with the theoretical prediction $\eta=1-(HNu/L)^{-1}$ (where $Nu$ is the Nusselt number, $H$ is height and $L$ is length of the domain) for $Nu\gg10$. Independent of rotation, $\eta$ approaches unity at large $Nu$, and therefore at large $Ra$. Laboratory experiments in the inertial regime with an applied heat flux are also considered.