Identifying finite-time coherent sets from limited quantities of Lagrangian data

Chaos
Matthew O WilliamsClarence W Rowley

Abstract

A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into coherent pairs, which are sets of initial conditions chosen to minimize the number of trajectories that "leak" from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by solving an optimization problem to obtain a pair of functions whose signs determine set membership. From prior experience with synthetic, "data rich" test problems, and conceptually related methods based on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. We exploit this property by using the basis sets associated with spectral or "mesh-free" methods, and as a result, our approach has the potential to more accurately approximate these functions given a fixed amount of data. In practice, this could enable better approximations of the coherent pairs in problems with relatively limited quantities of Lagrangian data, which is usually the case with experimental geophysical data. We apply this method to three ...Continue Reading

References

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Aug 7, 2007·Physical Review Letters·Gary FroylandAnne Marie Treguier
Apr 8, 2010·Chaos·Steven L Brunton, Clarence W Rowley
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Jan 3, 2013·Chaos·Marko BudisićIgor Mezić
Aug 20, 2014·Proceedings of the National Academy of Sciences of the United States of America·Andrew C PojeArthur J Mariano

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Citations

Jul 15, 2016·Physical Review. E·Alireza HadjighasemGeorge Haller
Jun 4, 2017·Chaos·Alireza HadjighasemGeorge Haller
Sep 18, 2018·Journal of Nonlinear Science·Péter Koltai, D R Michiel Renger
Jul 4, 2019·Chaos·Ralf BanischKathrin Padberg-Gehle

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