Mixing and dissipation in a geostrophic buoyancy-driven circulation

Turbulent mixing and energy dissipation have important roles in the global circulation but are not resolved by ocean models. We use direct numerical simulations of a geostrophic circulation, resolving turbulence and convection, to examine the rates of dissipation and mixing. As a starting point, we focus on circulation in a rotating rectangular basin forced by a surface temperature difference but no wind stress. Emphasis is on the geostrophic regime for the horizontal circulation, but also on the case of strong buoyancy forcing (large Rayleigh number), which implies a turbulent convective boundary layer. The computed results are consistent with existing scaling theory that predicts dynamics and heat transport dependent on the relative thicknesses of thermal and Ekman boundary layers, hence on the relative roles of buoyancy and rotation. Scaling theory is extended to describe the volume-integrated rate of mixing, which is proportional to heat transport and decreases with increasing rotation rate or decreasing temperature difference. In contrast, viscous dissipation depends crucially on whether the thermal boundary layer is laminar or turbulent, with no direct Coriolis effect on the turbulence unless rotation is extremely strong. For strong forcing, in the geostrophic regime, the mechanical energy input from buoyancy goes primarily into mixing rather than dissipation. For a buoyancy-driven circulation in a basin comparable to the North Atlantic we estimate that the total rate of mixing accounts for over 95% of the mechanical energy supply, implying that buoyancy is an efficient driver of mixing in the oceans.