Abstract

The impingement of a westward drifting lens-like anticyclonic ring on a meridional boundary is examined analytically and numerically using an (inviscid) layer-and-a-half model. A nonlinear analytical solution is constructed with the aid of a slowly varying perturbation expansion and numerical simulations are performed with the Bleck and Boudra model. It is found that, in contrast to conventional wisdom which implies that an anticyclonic ring encountering a wall moves poleward due to the image effect, the ring stays roughly in a fixed latitude. As it slowly moves into the wall due to β, it gradually leaks fluid toward the equator until it loses all of its mass. As expected, different eddies lose their mass in different rates. The (nondimensional) central thickness of an intense zero potential vorticity ring decays as 1/[1 + β(2g′ Hi)1/2 t/18f]2 where Hi is the initial central thickness, t is time, g′ "reduced gravity," f the Coriolis parameter, and β is the familiar variation of the Coriolis parameter with latitude. Due to the gradually decreasing depth, the ring's westward drift into the wall also gradually slows down; i.e., the ring advances toward the wall and loses mass like "peeling" rate is 2βRd2/9 [where Rd is the instantaneous Rossby radius based on the instantaneous maximum thickness] implying that the eddy migrates toward the wall at a rate that is one-third of the free open ocean rate. Numerical simulations are in excellent agreement with the above solution. As expected, they show that frictional forces decrease the intensity of the leakage and, hence, slow down the draining process. Unfortunately, no analytical solution can be found for weak or moderately strong rings because, for such lenses, there is no known analytical solution even for the nonmigrating state (i.e., rings on an f-plane). Numerical simulations show, however, that such weak or moderately strong rings display (qualitatively) similar characteristics to those of intense zero potential vorticity rings. It is argued that rings such as warm-core Gulf Stream rings, Loop Current rings, Agulhas rings, as well as other eddies (e.g., Meddies) may all experience similar encounters. As the walls that they encounter are subsurface (e.g., the continental rise, the Walvis Ridge and the mid-Atlantic Ridge), the leakages are not expected to be easily detected.

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