The Bifurcation of Outflows

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  • 1 Department of Oceanography, The Florida Stage University, Tallahassee, FL 32306
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Abstract

The behavior of outflows resulting from channels cutting through broad continents and emptying into wedgelike oceans, or channels cutting in wedgelike continents and emptying into broad oceans, is examined analytically. The model is nonlinear and inviscid, and the vertical structure is approximated by two layers; the upper layer is active and the lower is passive.

Examination of the governing equations shows that, since outflows are externally driven (by gravity and mass flux), there exists an “outflow length scale” in the open ocean. This length scale (l) is given by [gHb/fU0]½, where b is half the emptying channel width, g′ the “reduced gravity,” H the channel depth, f the Coriolis parameter, and U0 the flow speed within the channel. Solutions are constructed using this new length scale and a power series expansion.

It is found that, due to the earth's rotation, an outflow can be deflected toward one of the coasts or bifurcate into two branches, depending on the basin geometry. When the outflow results from a channel cutting through a broad continent and emptying into a wedgelike ocean, there are two possibilities. If the wedge opening is less than 90°, the outflow deflects to the right (looking downstream); if the wedge opening is larger than 90°, the outflow deflects to the left. In contrast, when the channel is cutting through a deltalike continent and emptying into a broad ocean, the outflow bifurcates. If the angle between the two walls bounding the ocean is less than 270°, the outflow splits into a narrow band that flows to the right and a broad current that veers to the left and penetrates into the ocean interior as an isolated ocean. A mirrored picture is established when the angle between the walls is large than 270°.

Possible application of this theory to the two outflow modes observed near the Tsugaru Strait is mentioned.

Abstract

The behavior of outflows resulting from channels cutting through broad continents and emptying into wedgelike oceans, or channels cutting in wedgelike continents and emptying into broad oceans, is examined analytically. The model is nonlinear and inviscid, and the vertical structure is approximated by two layers; the upper layer is active and the lower is passive.

Examination of the governing equations shows that, since outflows are externally driven (by gravity and mass flux), there exists an “outflow length scale” in the open ocean. This length scale (l) is given by [gHb/fU0]½, where b is half the emptying channel width, g′ the “reduced gravity,” H the channel depth, f the Coriolis parameter, and U0 the flow speed within the channel. Solutions are constructed using this new length scale and a power series expansion.

It is found that, due to the earth's rotation, an outflow can be deflected toward one of the coasts or bifurcate into two branches, depending on the basin geometry. When the outflow results from a channel cutting through a broad continent and emptying into a wedgelike ocean, there are two possibilities. If the wedge opening is less than 90°, the outflow deflects to the right (looking downstream); if the wedge opening is larger than 90°, the outflow deflects to the left. In contrast, when the channel is cutting through a deltalike continent and emptying into a broad ocean, the outflow bifurcates. If the angle between the two walls bounding the ocean is less than 270°, the outflow splits into a narrow band that flows to the right and a broad current that veers to the left and penetrates into the ocean interior as an isolated ocean. A mirrored picture is established when the angle between the walls is large than 270°.

Possible application of this theory to the two outflow modes observed near the Tsugaru Strait is mentioned.

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