Mathematical Modelling of Solitary Oceanographic Vortices

Abstract

One of the most striking things one sees when examining satellite images of the ocean is the abundance of swirls, eddies and other vortex motions. Whether one is examining the rapid destabilization of coastal currents or seemingly lethargic mid-ocean flows, one does not observe the flow of a slow viscous fluid but rather the continuous turbulent interaction of multiple eddies (Figure 13.1.1). It is not too much of an exaggeration to suggest that the large scale transient behaviour in the ocean should be analyzed in terms of eddy dynamics. The principal purpose of this chapter is to provide an introduction to some of the mathematical models that are being used to study various aspects of ocean eddy dynamics. This contribution is not meant to be exhaustive. Readers will find other aspects emphasized in, for example, Flierl (1987). Rather, our survey topics, while attempting to briefly describe some of the central features of the modern theory, do however reflect the author’s personal biases. For example, we will tend to focus exclusively on steadily-travelling, isolated or coherent eddies (in the sense that the area-integrated energy and enstrophy is finite) and ignore steady or topographically-forced ocean eddies. Thus, we will not describe ocean eddies that can be essentially described as a Taylor column (Hide 1961; Swaters and Mysak 1985). We will also not describe the process of eddy formation even though this is a physical process of real interest and complexity.