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The Destruction of Lenses and Generation of Wodons

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  • 1 Department of Oceanography, The Florida State University, Tallahassee, Florida
  • | 2 Department of Oceanography and the Geophysical Fluid Dynamics Institute, The Florida State University, Tallahassee, Florida
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Abstract

Since midocean eddies Migrate westward, they eventually reach the western boundaries. It is, therefore, of interest to find out what happens after the eddies collide with the walls. An isopycnic, two-layer, primitive equation model on a β plane and a simple analytical model on an f plane are constructed to investigate the meridional migration of an oceanic eddy along a western wall.

On a β plane, three factors determine the eddy's migration along a western meridional wall. First, the image effect pushes an anticyclonic (cyclonic) eddy northward (southward). Second, the β force (resulting from the larger Coriolis force on the northern side of the eddy) pulls an anticyclonic (cyclonic) eddy southward (northward). Third, after an anticyclonic (cyclonic) eddy collides with the wall, parts of the anticyclonic eddy's interior fluid leak out southward (northward) along the wall forming a thin jet. In an analogy to a rocket, this jet pushes the eddy northward (southward). Our aim is to investigate in which direction the eddy ultimately migrates along the will (i.e., to determine which of the above three processes dominates).

The combined effect of the three processes is a rather complicated process and the results are counterintuitive. For instance, imagine a lenslike anticyclonic eddy situated on a sloping bottom (analogous to β). This highly nonlinear eddy migrates with shallow water on its right (“westward”) and encounters a meridional wall. Intuitively, it is expected that, once the “westward” migration is arrested by the wall, gravity will pull the eddy downhill (southward) so that the eddy will migrate toward deep water (i.e., toward the equator). Surprisingly, however, the authors’ numerical computations show that the eddy migrates uphill. This bizarre behavior results from the leakage along the wall that, in terms of the eddy energy, compensates for the uphill drift. Namely, the leakage plays a crucial role in the eddy-wall interaction process because it allows the uphill migration. Eventually, it causes a destruction of the lens by completely draining its fluid.

The above highly nonlinear experiments are supplemented by quasigeostrophic analytical solutions and iso-pycnic numerical experiments of cyclones and anticyclones. It is found that, in contrast to the situation with the lens, the leakage does not play a crucial role in quasigeostrophic eddies. However, all of these experiments show that the image effect is the most dominant process. It turns out that, as the eddy responds to the presence of the wall, it is transformed into a half-circular shape that is very different from its original preinteraction circular shape. This results from the fact that, even though the westward β-induced speed (forcing the eddy into the wall) is small, it is active over an extended period of time so that its final effect is relatively large. The final half-circular eddy that migrates along the wall is nearly independent of β as long as the eddy is not extremely far from its original latitude. This is demonstrated by both our numerical solution (of the primitive equations) as well as our quasigeostrophic analytical solution. The authors term this final migrating eddy a wodon as it represents a combination of a wall and a modon.

Possible applications of these models to various oceanic situations are discussed.

Abstract

Since midocean eddies Migrate westward, they eventually reach the western boundaries. It is, therefore, of interest to find out what happens after the eddies collide with the walls. An isopycnic, two-layer, primitive equation model on a β plane and a simple analytical model on an f plane are constructed to investigate the meridional migration of an oceanic eddy along a western wall.

On a β plane, three factors determine the eddy's migration along a western meridional wall. First, the image effect pushes an anticyclonic (cyclonic) eddy northward (southward). Second, the β force (resulting from the larger Coriolis force on the northern side of the eddy) pulls an anticyclonic (cyclonic) eddy southward (northward). Third, after an anticyclonic (cyclonic) eddy collides with the wall, parts of the anticyclonic eddy's interior fluid leak out southward (northward) along the wall forming a thin jet. In an analogy to a rocket, this jet pushes the eddy northward (southward). Our aim is to investigate in which direction the eddy ultimately migrates along the will (i.e., to determine which of the above three processes dominates).

The combined effect of the three processes is a rather complicated process and the results are counterintuitive. For instance, imagine a lenslike anticyclonic eddy situated on a sloping bottom (analogous to β). This highly nonlinear eddy migrates with shallow water on its right (“westward”) and encounters a meridional wall. Intuitively, it is expected that, once the “westward” migration is arrested by the wall, gravity will pull the eddy downhill (southward) so that the eddy will migrate toward deep water (i.e., toward the equator). Surprisingly, however, the authors’ numerical computations show that the eddy migrates uphill. This bizarre behavior results from the leakage along the wall that, in terms of the eddy energy, compensates for the uphill drift. Namely, the leakage plays a crucial role in the eddy-wall interaction process because it allows the uphill migration. Eventually, it causes a destruction of the lens by completely draining its fluid.

The above highly nonlinear experiments are supplemented by quasigeostrophic analytical solutions and iso-pycnic numerical experiments of cyclones and anticyclones. It is found that, in contrast to the situation with the lens, the leakage does not play a crucial role in quasigeostrophic eddies. However, all of these experiments show that the image effect is the most dominant process. It turns out that, as the eddy responds to the presence of the wall, it is transformed into a half-circular shape that is very different from its original preinteraction circular shape. This results from the fact that, even though the westward β-induced speed (forcing the eddy into the wall) is small, it is active over an extended period of time so that its final effect is relatively large. The final half-circular eddy that migrates along the wall is nearly independent of β as long as the eddy is not extremely far from its original latitude. This is demonstrated by both our numerical solution (of the primitive equations) as well as our quasigeostrophic analytical solution. The authors term this final migrating eddy a wodon as it represents a combination of a wall and a modon.

Possible applications of these models to various oceanic situations are discussed.

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