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The Breakup of Dense Filaments

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  • 1 Department of Oceanography and Geophysical Fluid Dynamics Institute, The Florida state University, Tallahassee, Florida
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Abstract

The breakup of a long strip of dense fluid flowing over a sloping bottom is examined with the aid of a nonlinear two-layer analytical model. The inviscid strip is bounded by the sloping bottom from below and an interface (that intersects the bottom along the two edges) from the top. The infinitely deep upper layer in which the filament is embedded contains a uniform flow and is taken to be passive. Such flows represent an idealization of currants that result from various outflows and deep water spreading.

It is shown analytically that a dense filament can break up to a discrete set or closely packed anticyclonic eddies (lenses) propagating steadily along the isobaths. The lenses are arranged in a zig-zag manner with the e4cs of each tens touching its neighboring tens. Such a pattern results from the fact that the eddies are too large to fit into the area freed by the straight filament so that they push each other to the sides during the breakup. The solution for this pack of eddies is computed without solving for the detailed breakup process. As in other adjustment problems, the final and initial states are connected via known conservation properties even though the problem is highly nonlinear. Specifically, conservation of potential vorticity, integrated angular momentum and mass am applied. These conservation laws illustrate that about 10% of the initial energy is ,radiated away (via long gravity waves) during the breakup.

The theory suggest that some of the actual filaments in the ocean, such as the Mediterranean outflow, may not consist at a single continuous flow but rather of a stream of closely packed lenses translating steadily along the bottom.

Abstract

The breakup of a long strip of dense fluid flowing over a sloping bottom is examined with the aid of a nonlinear two-layer analytical model. The inviscid strip is bounded by the sloping bottom from below and an interface (that intersects the bottom along the two edges) from the top. The infinitely deep upper layer in which the filament is embedded contains a uniform flow and is taken to be passive. Such flows represent an idealization of currants that result from various outflows and deep water spreading.

It is shown analytically that a dense filament can break up to a discrete set or closely packed anticyclonic eddies (lenses) propagating steadily along the isobaths. The lenses are arranged in a zig-zag manner with the e4cs of each tens touching its neighboring tens. Such a pattern results from the fact that the eddies are too large to fit into the area freed by the straight filament so that they push each other to the sides during the breakup. The solution for this pack of eddies is computed without solving for the detailed breakup process. As in other adjustment problems, the final and initial states are connected via known conservation properties even though the problem is highly nonlinear. Specifically, conservation of potential vorticity, integrated angular momentum and mass am applied. These conservation laws illustrate that about 10% of the initial energy is ,radiated away (via long gravity waves) during the breakup.

The theory suggest that some of the actual filaments in the ocean, such as the Mediterranean outflow, may not consist at a single continuous flow but rather of a stream of closely packed lenses translating steadily along the bottom.

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