Finite-time Partitions for Lagrangian Structure Identification in Gulf Stream Eddy Transport

We develop a methodology to identify finite-time Lagrangian structures from data and models using an extension of the Koopman operator-theoretic methods developed for velocity fields with simple (periodic, quasi-periodic) time-dependence. To achieve this, the notion of the Finite Time Ergodic (FiTER) partition is developed and rigorously justified. In combination with a clustering-based approach, the methodology enables identification of the temporal evolution of Lagrangian structures in a classic, benchmark, oceanographic transport problem, namely the cross-stream flux induced by the interaction of a meso- scale Gulf Stream Ring eddy with the main jet. We focus on a single mixing event driven by the interaction between an energetic cold core ring (a cyclone), the strong jet, and a number of smaller scale cyclones and anticyclones. The new methodology enab les reconstruction of Lagrangian structures in three dimensions and analysis of their time-evolution.