A simple convective model of the global overturning circulation, including effects of entrainment into sinking regions

We use a simple conceptual model to examine the roles of vertical mixing and surface buoyancy fluxes in the dynamics of the global overturning circulation that ventilates the deep oceans. In addition to using the Munk [Munk, W.H., 1966. Abyssal recipes. Deep-Sea Research 13, 707-730] advection-diffusion balance in the ocean interior, we close the circulation by including the small high-latitude sinking regions, which are assumed to be turbulent geostrophic gravity currents on gentle topographic slopes. The interior and sinking regions are coupled by turbulent entrainment into the sinking regions and we examine the global influence of this entrainment. An important realization is that the rates of mixing into slope currents, predicted to be very small as a function of along-flow distance, imply rates of entrainment per unit depth of fall that are comparable to the entrainment rate for vertical plumes. The overturning mass flux and ocean density stratification are found as a function of the vertical diffusivity and total heat transport. Given a realistic heat transport and the measured average mixing rate of order 10^-5 m²/s, this simple model yields predictions consistent with data for the increase in volume flux with depth in slope currents, the magnitude of the global overturning circulation, and the averaged top-to-bottom density difference. Despite the absence of other mechanisms thought to be important in the thermocline, the model also gives a realistic thermal boundary layer thickness. As a consequence of entrainment into the dense sinking currents, the linking of abyssal densities to surface fluxes and the assumption of a uniform diffusivity, the model convective flow requires much less energy than the Munk (1966) prediction. The results indicate that the ocean overturning is feasibly a convective one and we suggest there might be no need to search for 'missing' mixing.