Interacting SQG Vortices and Passive Scalar Transport

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. The model can be used to explore the effect on transport of the transition from two-dimensional to three-dimensional mesoscale geophysical flows. On an f -plane with linear stratification, we examine the dynamics of SQG vortices and the resulting three-dimensional flow including contributions at first order in Rossby number going beyond the usual QG equation to compute the velocity. While it is simple to obtain the vertical velocity, finding O(Ro) horizontal flow is more involved. The Finite Time Braiding Entropy (FTBE) of Thiffeault & Budisic is used to quantify the chaotic mixing induced by three point vortices. We also consider the exact SQG vortex solution developed by Dritschel (2011) from the limit of a QG ellipsoid of constant potential vorticity. We examine the interaction of two such vortices and the resulting transport.