Limitation of large-scale ocean transport by small-scale mixing

We prove that the ocean heat transport is strongly constrained by small-scale mixing. The implications of these constraints are analyzed in the context of an eddy-resolving, rapidly rotating primitive-equation flow driven by specified surface temperature and wind-stress, with isotropic diffusion and bottom-drag. The statistical equilibrium is characterized by several quantities, for which we propose scaling-laws as a function of the external parameters. The mean stratification, measured by 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 latter equilibrate at an amplitude which depends to leading order on the bottom-drag. The net poleward heat transport instead depends to leading order on the diapycnal mixing.