Control of large-scale heat transport by small-scale mixing

The equilibrium of an idealized flow driven at the surface by wind stress and rapid relaxation to non-uniform buoyancy is analyzed in terms of entropy production, mechanical energy balance, and heat transport. The flow is rapidly rotating, and dissipation is provided by bottom drag. Diabatic forcing is transmitted from the surface by isotropic diffusion of buoyancy. The domain is periodic so that zonal averaging provides a useful decomposition of the flow into mean and eddy components. The statistical equilibrium is characterized by quantities such as the lateral buoyancy flux and the thermocline depth; here, scaling laws are proposed for these quantities in terms of the external parameters. The scaling theory predicts relations between heat transport, thermocline depth, bottom drag, and diapycnal diffusivity, which are confirmed by numerical simulations. The authors find that the depth of the thermocline is independent of the diapycnal mixing to leading order, but depends on the bottom drag. This dependence arises because the mean stratification is due to a balance between the large-scale wind-driven heat transport and the heat transport due to baroclinic eddies. The eddies equilibrate at an amplitude that depends to leading order on the bottom drag. The net poleward heat transport is a residual between the mean and eddy heat transports. The size of this residual is determined by the details of the diapycnal diffusivity. If the diffusivity is uniform (as in laboratory experiments) then the heat transport is linearly proportional to the diffusivity. If a mixed layer is incorporated by greatly increasing the diffusivity in a thin surface layer then the net heat transport is dominated by the model mixed layer.