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Transport in time-dependent dynamical systems: finite-time coherent sets
Authors:Froyland Gary  Santitissadeekorn Naratip  Monahan Adam
Institution:School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales 2052, Australia.
Abstract:We study the transport properties of nonautonomous chaotic dynamical systems over a finite-time duration. We are particularly interested in those regions that remain coherent and relatively nondispersive over finite periods of time, despite the chaotic nature of the system. We develop a novel probabilistic methodology based upon transfer operators that automatically detect maximally coherent sets. The approach is very simple to implement, requiring only singular vector computations of a matrix of transitions induced by the dynamics. We illustrate our new methodology on an idealized stratospheric flow and in two and three-dimensional analyses of European Centre for Medium Range Weather Forecasting (ECMWF) reanalysis data.
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