Diapycnal transport near a sloping bottom boundary

Abstract

The diapycnal motion in the stratified ocean near a sloping bottom boundary is studied using analytical solutions from one-dimensional boundary layer theory. Bottom-intensification of the diapycnal mixing intensity ensures that in the Stratified Mixing Layer (SML), where isopycnals are relatively flat, the diapycnal motion is downward toward denser fluid. In contrast, convergence of the diffusive buoyancy flux near the seafloor drives diapycnal upwelling in what we define as the Bottom Boundary Layer (BBL). Much of the one-dimensional BBL is characterized by a stratification only slightly reduced from that in the SML because the maximum in the buoyancy flux at the top of the BBL, where the diapycnal velocity changes sign, must occur in well-stratified fluid. The diapycnal upwelling in the BBL is determined by variations not only in the magnitude of the buoyancy gradient but also in the curvature of isopycnals. The net diapycnal upwelling is concentrated in the bottom half of the BBL where the magnitude of the buoyancy gradient changes most rapidly. The curvature effect drives upwelling near the seafloor that only makes a significant contribution to the net upwelling for steep slopes. The structure of the diapycnal velocity in this stratified BBL differs from the case of a turbulent well-mixed BBL that has been assumed in some recent theoretical studies on bottom-intensified mixing (e.g. McDougall and Ferrari 2017). This work therefore extends recent theories in a way that should be more applicable to abyssal ocean observations where well-mixed BBLs are not common.