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Abstract The Indo-Pacific Ocean appears exponentially stratified between 1- and 3-km depth with a decay scale on the order of 1 km. In his celebrated paper “Abyssal recipes,” W. Munk proposed a theoretical explanation of these observations by suggesting a pointwise buoyancy balance between the upwelling of cold water and the downward diffusion of heat. Assuming a constant upwelling velocity w and turbulent diffusivity κ , the model yields an exponential stratification whose decay scale is consistent with observations if κ ∼ 10 −4 m 2 s −1 . Over time, much effort has been made to reconcile Munk’s ideas with evidence of vertical variability in κ , but comparably little emphasis has been placed on the even stronger evidence that w decays toward the surface. In particular, the basin-averaged w nearly vanishes at 1-km depth in the Indo-Pacific. In light of this evidence, we consider a variable-coefficient, basin-averaged analog of Munk’s budget, which we verify against a hierarchy of numerical models ranging from an idealized basin-and-channel configuration to a coarse global ocean simulation. Study of the budget reveals that the decay of basin-averaged w requires a concurrent decay in basin-averaged κ to produce an exponential-like stratification. As such, the frequently cited value of 10 −4 m 2 s −1 is representative only of the bottom of the middepths, whereas κ must be much smaller above. The decay of mixing in the vertical is as important to the stratification as its magnitude . Significance Statement Using a combination of theory and numerical simulations, it is argued that the observed magnitude and shape of the global ocean stratification and overturning circulation appear to demand that turbulent mixing increases quasi-exponentially toward the ocean bottom. Climate models must therefore prescribe such a vertical profile of turbulent mixing in order to properly represent the heat and carbon uptake accomplished by the global overturning circulation on centennial and longer time scales. 

Abstract A toy model for the deep ocean overturning circulation in multiple basins is presented and applied to study the role of buoyancy forcing and basin geometry in the ocean’s global overturning. The model reproduces the results from idealized general circulation model simulations and provides theoretical insights into the mechanisms that govern the structure of the overturning circulation. The results highlight the importance of the diabatic component of the meridional overturning circulation (MOC) for the depth of North Atlantic Deep Water (NADW) and for the interbasin exchange of deep ocean water masses. This diabatic component, which extends the upper cell in the Atlantic below the depth of adiabatic upwelling in the Southern Ocean, is shown to be sensitive to the global area-integrated diapycnal mixing rate and the density contrast between NADW and Antarctic Bottom Water (AABW). The model also shows that the zonally averaged global overturning circulation is to zeroth-order independent of whether the ocean consists of one or multiple connected basins, but depends on the total length of the southern reentrant channel region (representing the Southern Ocean) and the global ocean area integrated diapycnal mixing. Common biases in single-basin simulations can thus be understood as a direct result of the reduced domain size.