Buoyancy-driven Abyssal Circulation in a Circumpolar Ocean

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  • 1 Department of Mathematics, University of Exeter, Exeter, United Kingdom
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Abstract

Simple models are developed to describe the abyssal circulation in a circumpolar ocean driven by localized annual sources of water representing convection events. Models are based on a geostrophic reduced-gravity formulation and are located on a zonally periodic beta plane.

Nonlinear analytical solutions are first obtained for the evolution of an initially prescribed water mass distribution in the presence of a zonal mean flow and topography that is a function of the meridional coordinate only. For large time, our model suggests that diffusion results in a zonally uniform interface height with associated geostrophic currents if the initial water mass has nontrivial zonally averaged meridional structure. Possible influence of neglected effects on this large time behavior are discussed. Solutions are also presented for the evolution of an abyssal water mass introduced into an area where no equally dense water existed previously, and for a water mass added to a preexisting abyssal layer of equal density. The examples help clarify the varying roles of planetary and topographic beta as well as the role of horizontal diffusion. The initial value problem is then extended to allow for repeated additions of abyssal water. The resulting complicated flow field is discussed in terms of simple principles. For large times the active layer depth and the zonally averaged zonal current grow without bound in this model, pointing to the need for a loss of abyssal water if a statistical equilibrium is to be achieved.

Finally a quasi-linear model is developed that includes water loss parameterized by a Newtonian damping term and allows for more general bottom topography and background flow. Horizontal diffusion is not included in this model so wave breaking can occur, after which time the model is invalid. The model is used to investigate the influence of a meridional ridge on the abyssal circulation.

Abstract

Simple models are developed to describe the abyssal circulation in a circumpolar ocean driven by localized annual sources of water representing convection events. Models are based on a geostrophic reduced-gravity formulation and are located on a zonally periodic beta plane.

Nonlinear analytical solutions are first obtained for the evolution of an initially prescribed water mass distribution in the presence of a zonal mean flow and topography that is a function of the meridional coordinate only. For large time, our model suggests that diffusion results in a zonally uniform interface height with associated geostrophic currents if the initial water mass has nontrivial zonally averaged meridional structure. Possible influence of neglected effects on this large time behavior are discussed. Solutions are also presented for the evolution of an abyssal water mass introduced into an area where no equally dense water existed previously, and for a water mass added to a preexisting abyssal layer of equal density. The examples help clarify the varying roles of planetary and topographic beta as well as the role of horizontal diffusion. The initial value problem is then extended to allow for repeated additions of abyssal water. The resulting complicated flow field is discussed in terms of simple principles. For large times the active layer depth and the zonally averaged zonal current grow without bound in this model, pointing to the need for a loss of abyssal water if a statistical equilibrium is to be achieved.

Finally a quasi-linear model is developed that includes water loss parameterized by a Newtonian damping term and allows for more general bottom topography and background flow. Horizontal diffusion is not included in this model so wave breaking can occur, after which time the model is invalid. The model is used to investigate the influence of a meridional ridge on the abyssal circulation.

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