A Dynamical Systems Approach to Lagrangian Transport in a Double-Gyre

Chad Coulliette, Control & Dynamical Systems, Caltech

The flow obtained from a 3-layer, eddy-resolving quasi-geostrophic circulation model subject to an applied wind stress curl. For this model we will consider transport between the northern and southern "gyres" separated by a jet. We will focus on the importance of invariant manifolds in forming geometric structures that govern transport. By "govern," we mean they can be used to compute Lagrangian transport quantities, such as the flux across the jet. We will consider periodic, quasi-periodic, and chaotic velocity fields, and thus assess the effectiveness of dynamical systems techniques in flows with progressively more spatio-temporal complexity. The numerical methods necessary to implement the dynamical systems techniques and the significance of invariant manifolds as signatures of specific "events," such as rings pinching off from a meandering jet, will also be discussed.