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We develop a methodology to identify finite-time Lagrangian structures fromdata and models using an extension of the Koopman operator-theoretic methodsdeveloped 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 aclustering-based approach, the methodology enables identification of thetemporal evolution of Lagrangian structures in a classic, benchmark,oceanographic transport problem, namely the cross-stream flux induced by theinteraction of a meso- scale Gulf Stream Ring eddy with the main jet. We focuson a single mixing event driven by the interaction between an energetic coldcore ring (a cyclone), the strong jet, and a number of smaller scale cyclonesand anticyclones. The new methodology enab les reconstruction of Lagrangianstructures in three dimensions and analysis of their time-evolution.

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