The role of secondary circulation in boundary mixing

Abstract

Enhanced mixing near a sloping boundary reduces the stratification and hence the vertical diffusive buoyancy transport. An additional advective buoyancy flux, however, is associated with the bidirectional secondary flow driven by buoyancy forces near the boundary. Some integral relations and simple physical arguments show that, while advection increases the downslope buoyancy transport, it decreases the vertical transport; the overall effectiveness of boundary mixing involves the square of the reduction factor that would occur for the diffusive flux alone in a region of reduced stratification. The secondary circulation may increase the effectiveness of boundary mixing, indirectly, however, by restoring the stratification, and hence the diffusive fluxes, unless this restratification also suppresses the mixing. Integral relations are also derived for the along‐slope flow which is part of the solution rather than arbitrary, and the relationship of the theory to Ekman layer dynamics is discussed.