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Abstract

We examine (i) what sets the vertical stratification in the abyssal ocean, and (ii) the rate of upwelling of water 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, taking into account the bottom-intensified nature of the rate of diapycnal mixing in the ocean. This 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 geometry and conservation equations of this problem can be described as a steady-state filling-box problem. 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 given input parameters, 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. This knowledge is equivalent to knowledge of the area-integrated diffusive buoyancy flux on the buoyancy surfaces in the abyss.