The Effects of Nonrectangular Cross Section, Friction, and Barotropic Fluctuations on the Exchange through the Strait of Gibraltar

Myriam Bormans Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada

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Chris Garrett Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada

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Abstract

The inviscid two-layer hydraulic model of Farmer and Armi has two types of solution in the eastern end of the Strait of Gibraltar for flow that is critical at Camarinal Sill. The solution corresponding to maximal exchange has a fast supercritical flow with a shallow interface whereas the solutions corresponding to submaximal exchange show a much slower subcritical flow with a rather deep interface. We extend their model to include physically important effects such as nonrectangular cross section, friction and barotropic fluctuations. Allowing for realistic cross sections reduces the exchange and raises the interface everywhere along the strait. Realistic interfacial friction has little influence on the exchange but lateral friction at the sloping sides of the cross sections has a significant effect on the flow and brings the two solutions (supercritical and subcritical) closer together. The effect of the earth's rotation is also summarized but dealt with in more detail in a companion paper by Bormans and Garrett.

Low-frequency barotropic fluctuations significantly alter the volume flux and the interface depth everywhere along the strait and so should be taken into account in any comparison between theory and observations. They also affect sea-level differences across and along the strait, with a ratio of these that is positive for maximal exchange and negative for submaximal exchange. This provides a useful diagnostic using sea level data alone.

It appears that the exchange through the Strait of Gibraltar alternates between periods of maximal and submaximal exchange, although we do not yet know the frequency of, or conditions for, each state.

Abstract

The inviscid two-layer hydraulic model of Farmer and Armi has two types of solution in the eastern end of the Strait of Gibraltar for flow that is critical at Camarinal Sill. The solution corresponding to maximal exchange has a fast supercritical flow with a shallow interface whereas the solutions corresponding to submaximal exchange show a much slower subcritical flow with a rather deep interface. We extend their model to include physically important effects such as nonrectangular cross section, friction and barotropic fluctuations. Allowing for realistic cross sections reduces the exchange and raises the interface everywhere along the strait. Realistic interfacial friction has little influence on the exchange but lateral friction at the sloping sides of the cross sections has a significant effect on the flow and brings the two solutions (supercritical and subcritical) closer together. The effect of the earth's rotation is also summarized but dealt with in more detail in a companion paper by Bormans and Garrett.

Low-frequency barotropic fluctuations significantly alter the volume flux and the interface depth everywhere along the strait and so should be taken into account in any comparison between theory and observations. They also affect sea-level differences across and along the strait, with a ratio of these that is positive for maximal exchange and negative for submaximal exchange. This provides a useful diagnostic using sea level data alone.

It appears that the exchange through the Strait of Gibraltar alternates between periods of maximal and submaximal exchange, although we do not yet know the frequency of, or conditions for, each state.

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