Chaotic advection by a vortex in a polygonal bay

This talk discusses the motion of a point vortex in the presence of a bay and a coastal current, as well as the ensuing water exchange between the bay and the open sea. The bay is either a rectangle or a polygonal idealization of Todos Santos Bay in northwestern Mexico; the coastal current is uniform and parallel to the coast. Complex variable theory was used to compute the path function of the point vortex and the stream function of the flow. In the rectangular bay the path function exhibits five different topologies depending on the aspect ratio of the bay and the relative intensity of the vortex. Wide bays efficiently trap vortices, even strong ones: most initial conditions inside the bay result in periodic trajectories entirely contained in the bay. Narrow bays are ineffective vortex traps: most initial conditions inside the bay lead to infinite trajectories with the vortex moving upstream along the coast. Todos Santos Bay, with its irregular coastline, exhibits a variety of path-function topologies, but it is in general an ineffective vortex trap. The exchange of water between the bay and the open sea was studied using classical dynamical systems theory. With parameter values realistic for Todos Santos Bay, a vortex whose orbital radius is εc, where c is the square root of the bay area, produces a water exchange of about 1.4εc² during each period of the vortex motion.