Gary Froyland University of New South Wales Identification and tracking of coherent features in oceanic and atmospheric flows Wednesday 12th Aug 14:05-14:55pm, Eastern Avenue Lecture Theatre. Transport and mixing processes play an important role in many natural phenomena, including ocean circulation, atmospheric dynamics, and fluid dynamics. Ergodic theoretic approaches to identifying transport barriers and slowly mixing structures in autonomous systems have been developed around the Perron-Frobenius operator and its eigenfunctions. We describe an extension of these techniques to /general non-autonomous systems/ in which one can observe /mobile, time-dependent/, slowly dispersive structures, which we term coherent sets. We will outline the theory and numerics behind these new approaches and contrast the results with geometric approaches based upon time-dependent invariant manifolds and finite-time Lyapunov exponents (FTLEs). We will show that the latter approach can sometimes not identify the strongest transport barrier. Our new algorithms are based upon a Perron-Frobenius cocycle. We will discuss the structure of the Lyapunov spectrum of this cocycle, state a strengthened version of the Multiplicative Ergodic Theorem for non-invertible matrices, and develop a numerical algorithm to approximate the Oseledets subspaces that describe coherent sets. The underlying ideas and numerical results will be illustrated with case studies from oceanic and atmospheric applications.