The squeezing of eddies through gaps

Abstract

The islands of the Lesser Antilles present a porous meridional barrier to North Brazil Current (NBC) rings. To better understand if, when, and how a NBC ring could be squeezed into the Caribbean Sea through such a gappy barrier, the encounter of a westward drifting eddy with a porous meridional wall is considered. First an eddy encountering a single aperture is modeled. To do so, both an analytical model and a reduced-gravity primitive equations numerical model are used. This was followed by numerical experiments that explored eddy collisions with barriers containing many gaps. In all of these models, the collisions were forced by either β or a steady advection through the gap(s). Using integrated constraints, an analytical solution was constructed for a zero potential vorticity lens passing through a single gap on a β plane. The solution involves a small parameter ε, the ratio of the short timescale associated with the f-plane adjustment, and the long encounter timescale due to β. It is found that, throughout the encounter, the lens remains axisymmetric and is drained by wall jets. Ultimately, the lens diameter adapts to the gap width so that the eddy loses contact with the walls and drifts slowly into the interior of the western basin. Numerical simulations are in good agreement with this theory. Numerical experiments also revealed that, just like a lens forced by β, an intense advected lens remained axisymmetric as it was slowly drained by wall jets. These intense lenses were "stiff" in the sense that they were not distorted by the strain resulting from the convergence of the advecting flow as it passed through the gap. Because of the stiffness of the eddy, it "stalled" and traveled through the gap more slowly than the underlying fluid. By contrast, weak lenses were "slaves" in the sense that they were squeezed through the gap with the advecting flow. No wall jets were present in this weak lens case. Numerical simulations of the analogous multiple gap problem revealed that, in contrast to most of the single gap problems, all the fluid from the approaching eddy penetrated into the interior of the western basin. This was true for both β and advection. Circulation (accounted for by nonlinear flow separations) developed around the individual islands. When the individual islands were small compared to the eddy (e.g., L/Ri = 0.3, where Ri is the initial radius of the lens and L is the island scale), the lens reformed in the lee of the gaps and thus entered the western basin as a single, albeit weakened, vortex. Lenses exhibited signs of breaking when they encountered islands of intermediate size (e.g., L/Ri = 0.5). The presence of β greatly enhanced the tendency of the eddy to break in this particular case. Eddies that encountered large islands (e.g., L/Ri = 1.5) due to either β or advection almost always broke up into a number of smaller offspring. Many of the islands of the Lesser Antilles (LA) have spatial scales of L/Ri = 0.5 (assuming a "typical" NBC radius of 150 km), but there are also some larger obstructions (such as the Grenadines) that are closer to L/Ri = 1.5. Since both β and advection are present in the ocean, these single and multiple gap experiments suggest that the NBC rings/LA collision is in a sensitive regime where NBC rings are often, but not always, shattered as they are forced to squeeze through the passages. Counter-intuitively, smaller, more intense NBC rings are broken up by the islands of the LA, whereas larger and weaker eddies are pushed into the Caribbean Sea as coherent structures, particularly if they collide with the relatively smaller islands to the north of the Grenadines.