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Maximizing Buoyancy Flux across Layered Geostrophic Sections

Nelson G. HoggWoods Hole 0ceanographic Institution Woods Hole Massachusetts

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Henry M. StommelWoods Hole 0ceanographic Institution Woods Hole Massachusetts

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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 β-plane, meridional section, to three moving layers and to a moving bottom layer with topography are discussed.

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 β-plane, meridional section, to three moving layers and to a moving bottom layer with topography are discussed.

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