Regimes of thermocline scaling: The interaction of wind stress and surface buoyancy

The role of the relative geometry of mechanical forcing (wind stress) and buoyancy forcing (prescribed surface temperature) in the maintenance of the main thermocline is explored. In particular, the role of the wind stress curl in enhancing or suppressing the generation of baroclinic eddies is studied in simplified domains. The dependence of key quantities, such as the depth of the thermocline and the maximum heat transport, on the external parameters such as diapycnal mixing and dissipation rate is examined. Qualitatively different regimes are found depending on the relative phase of the wind stress and surface buoyancy distribution. The most efficient arrangement for eddy generation has Ekman pumping (suction) in conjunction with high (low) surface buoyancy. This corresponds to the situation found in the midlatitudes, where the surface Ekman flow carries heat toward the warmer region (i.e., upgradient of the surface temperature). In this case, strong eddy fluxes are generated in order to counteract the upgradient heat transport by the Ekman cell. The result is a thermocline whose depth is independent of the diapycnal diffusivity. However, the competition between these opposing heat fluxes leads to a weak net heat transport, proportional to the diffusivity responsible for the diabatic forcing. This arrangement of wind stress provides a large source of available potential energy on which eddies can grow, so the mechanical energy balance for the eddies is consistent with a substantial eddy heat flux. When the same surface temperature distribution is paired with the opposite wind stress curl, the mean flow produces a sink, rather than a source, of available potential energy and eddies are suppressed. With this arrangement, typical of low latitudes and the subpolar regions, the Ekman overturning cell carries heat downgradient of the surface temperature. Thus, the net heat transport is almost entirely due to the Ekman flow and is independent of the diapycnal diffusivity. At the same time the thermocline is a thin, diffusive boundary layer. Quantitative scalings for the thermocline depth and the poleward heat transport in these two limiting cases are contrasted and successfully compared with eddy-resolving computations.