The Relationship between Water Mass Formation and the Surface Buoyancy Flux, with Application to Phillips’ Red Sea Model

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Abstract
A buoyancy flux across the sea surface between the outcropping of isopycnals must be balanced by a subsurface diapycnal buoyancy flux. If this flux were only advective, its derivative with respect to buoyancy would provide a direct estimate of the buildup of volume between isopycnals or rate of water mass formation. A diapycnal velocity, however, requires diapycnal mixing which also causes a diapycnal buoyancy flux, and it is shown that there is no reason to expect a simple relationship between the advective and diffusive fluxes. For a surface layer with vigorous vertical mixing and weak horizontal mixing, however, the diapycnal diffusive flux of buoyancy is small, and the flow through the base of the mixed layer can be derived from the derivative of the surface buoyancy flux with respect to buoyancy. These points are illustrated by examination of the Phillips similarity solution for the convective circulation driven in a channel by a uniform surface buoyancy loss.
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