Maximizing Buoyancy Flux across Layered Geostrophic Sections

Abstract

For layered analogues of the ocean stratification, the problem of maximizing buoyancy flux across a section with zero mass flux is considered. The two layer situation on an f-plane is particularly simple and it is shown that the buoyancy flux is related to a particular area integral on the D, h plane, D and h being the depths of the lower and upper interfaces, respectively. The maximum buoyancy flux maximizes this area while constraining the layers to have non-negative thickness. Extensions to a ?-plane, meridional section, to three moving layers and to a moving bottom layer with topography are discussed.