An Isopycnal View of Near-Boundary Mixing and Associated Flows

Abstract

The effectiveness of mixing near a sloping boundary is reduced not just by the ratio of the stratification there to that in the interior but by the square of this ratio. This result has previously been derived and interpreted by invoking the upgradient vertical buoyancy flux associated with secondary circulation as this opposes the downgradient vertical diffusive flux. Here it is shown that the result may be derived very simply by considering the diffusive flux across an isopycnal, rather than a horizontal, surface. The reduction in the buoyancy flux comes from the increased isopycnal spacing and the reduced distance to the boundary. Derivation of the secondary circulation in the isopycnal/diapycnal framework is more subtle, however, as it involves allowing for the curvilinear nature of the coordinates.