INTERACTION OF VORTICES WITH TOPOGRAPHY

Irregular topography is a prevalent ocean feature, appearing in the shape of the ocean bottom, along the coastline, and on the shelves and slopes that connect the coast to the deep abyss. Strong jet-like currents, with considerable variability and enhanced mixing, are often observed near topography, implying that the continental shelves and slopes, ridges and seamounts exert a strong dynamical oceanic influence. Past studies have illustrated the complicated nature of vortex-topography interaction in which smaller-scale vortices are often produced; thatis, topography catalyzes a forward cascade in the mesoscale fields and may provide important routes to dissipation.The interaction of an ocean vortex with the continental shelf and slope is one aspect of a more general problem about wave-vortex interactions in a variable medium. A crucial parameter here is the ratio of the shelf width to the vortex size, which is typically small. In order to develop adequate mathematical models, and to clarify the basic physical mechanisms, we propose a thorough investigation of the evolution of a strong vortex in the vicinity of confined shelf-like topography. The first stage, when the vortex approaches the shelf from the open ocean, will be analyzed theoretically to determine the coastally-trapped waves forced by an approaching eddy. Since a proper description of ocean dynamics over a steep continental slope adjacent to the deep-water side of a shelf-break requires baroclinic effects to be taken into account, we propose using a two-layer model in the deep area matched with a barotropic model in the shallow area, where the ocean depth is smaller than the interface depth. Such a combination of a barotropic-baroclinic model should capture the most essential elements of current variability in the littoral zone, which remain presently relatively unexplored.At the next stage, the on-shelf advection of shelf water with high potential vorticity into the open ocean results in the development of a vortex sheet around the intense eddy. The subsequent rolling-up into smaller-scale cyclonic vortices will be studied numerically using a certain equation set which captures the essential dynamical processes. The results of the analysis will be compared with numerical simulations and observational data for a range of the relevant parameters. Our general aim is to construct a mathematical model for the process of vortex-shelf interaction, which can provide an adequate description of variability and mixing near confined topography.