C. Garrett et al., THE RELATIONSHIP BETWEEN WATER MASS FORMATION AND THE SURFACE BUOYANCY FLUX, WITH APPLICATION TO PHILLIPS RED-SEA MODEL, Journal of physical oceanography, 25(7), 1995, pp. 1696-1705
A buoyancy flux across the sea surface between the outcropping of isop
ycnals must be balanced by a subsurface diapycnal buoyancy flux. If th
is this flux were only advective, its derivative with respect to buoya
ncy would provide a direct estimate of the buildup of volume between i
sopycnals or rate of water mass formation. A diapycnal velocity, howev
er, requires diapycnal mixing which also causes a diapycnal buoyancy f
lux, and it is shown that there is no reason to expect a simple relati
onship between the advective and diffusive fluxes. For a surface layer
with vigorous vertical mixing and weak horizontal mixing, however, th
e 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 illus
trated by examination of the Phillips similarity solution for the conv
ective circulation driven in a channel by a uniform surface buoyancy l
oss.