Applied Maths Seminar: Froyland -- Identification and tracking of coherent features in oceanic and atmospheric flows

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.