How much Upwelling occurs in the Abyssal Bottom Boundary Layer?

We ask (i) what sets the vertical stratification in the abyssal ocean, and (ii) what sets the upwelling in the bottom boundary layer of the abyssal ocean?

We restrict attention to the bottom-most, densest, 2000m of the ocean and analyse the buoyancy budget in buoyancy coordinates.  The bottom-intensified nature of diapycnal mixing means that the diapycnal velocity in the ocean interior is downwards towards denser fluid, and all the diapycnal upwelling occurs in the first ~50m above the sea floor, with the upwelling transport in this Bottom Boundary Layer often being two or three times the net diapycnal upwelling needed to balance the sinking transport of Antarctic Bottom Water. 

The rate of sinking of dense Antarctic Bottom Water and the area-integrated diffusive buoyancy flux across the upper-most buoyancy surface are both regarded as known, which gives the buoyancy contrast between the sinking Antarctic Bottom Water and the value of buoyancy on this upper-most surface.  We show that the vertical stratification in the interior abyssal ocean is then entirely determined by knowledge of the rate of detrainment (or entrainment) of plume fluid out of (into) the sinking plume and into (out of) the ocean interior.  Importantly, the vertical stratification cannot be determined from knowledge of oceanic diapycnal mixing alone.