A nonlinear one and a half-layer model is considered to examine the collision of isolated eddies with vertical walls. The round undisturbed eddies are allowed to have relatively large amplitudes; they are bounded by a free streamline beyond which the ocean is stagnant. The inviscid interaction is examined by, conceptually, “cutting” the eddies with a straight vertical wall. The resulting events are studied using a perturbation expansion in ε, the nondimensional penetration of the wall into the vortices, i.e., “weak” interactions are examined. Two class of eddies are considered. The first consists of linear quasi-geostrophic eddies (i.e., small amplitude and slow circulation) that are weakly interacting with a wall whereas the second involves moderately nonlinear eddies (i.e., relatively high amplitude and fast speed) that again are weakly interacting with the wall. Analytical solutions for times of 0 (ƒ–1) (where ƒ is the Coriolis parameter) and an infinitely deep lower layer are constructed by applying the conservation of potential vorticity, energy and integrated momentum. It is found that the first class of eddies (linear quasi-geostrophic eddies) leak fluid as they interact with the wall. When a quasi-geostrophic anticyclonic vortex interacts with a wall, it leaks fluid from its right-hand side (looking off-shore in the northern hemisphere) whereas a quasi-geostrophic cyclonic vortex leaks from its left-hand side. Qualitatively, these results are similar to those found in an earlier study of purely barotropic eddies (Nof, 1987). Surprisingly, the second class of eddies (moderately nonlinear eddies) behave in a very different way. Due to the high inertia of these eddies, the leakage associated with a weak interaction is completely blocked and the adjustment to the presence of the wall is confined to the contact area. This bizarre behavior stems from the high speeds along the eddies' rim which choke the leaked flow. When these high speeds are relaxed the leakage re-appears. Simple qualitative experiments on a rotating table support the conclusion that eddies with small speeds along the edge leak. It is speculated that the interaction of warm-core rings with the Gulf Stream has some similarities to the interaction of an anticyclonic vortex with a solid wall. Furthermore, it is speculated that the loss of mass observed during such ring-Stream interactions is a result of the leakage predicted by our theory and experiment.
Nof, Doron. 1988. "Eddy-wall interactions." Journal of Marine Research 46, (3). https://elischolar.library.yale.edu/journal_of_marine_research/1900