UC San Diego

The surface quasi-geostrophic (SQG) equations are a model for low-Rossby number geophysical flows in which the dynamics are governed by potential temperature dynamics on the boundary. We examine point vortex solutions to this model as well as the chaotic flows induced by three point vortices. The chaotic transport induced by these flows is investigated using techniques of Poincaré maps and the Finite Time Braiding Exponent (FTBE). This chaotic transport is representative of the mixing in the flow, and these terms are used interchangeably in this work. Compared with point vortices in two-dimensional flow, the SQG vortices are found to produce flows with higher FTBE, indicating more mixing. Select results are presented for analyzing mixing for arbitrary vortex strengths.