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

Author(s): Williams, Matthew O; Rypina, Irina I; Rowley, Clarence W

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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 examples of increasing complexity: The first is the double gyre, the second is the Bickley Jet, and the third is data from numerically simulated drifters in the Sulu Sea.
Publication Date: Aug-2015
Citation: Williams, Matthew O, Rypina, Irina I, Rowley, Clarence W. "Identifying finite-time coherent sets from limited quantities of Lagrangian data" Chaos: An Interdisciplinary Journal of Nonlinear Science,25, 8, 087408-1 - 087408-13, doi:10.1063/1.4927424
DOI: doi:10.1063/1.4927424
ISSN: 1054-1500
EISSN: 1089-7682
Pages: 087408-1 - 087408-13
Type of Material: Journal Article
Journal/Proceeding Title: Chaos: An Interdisciplinary Journal of Nonlinear Science
Version: This is the publisher’s version of the article (version of record). All rights reserved to the publisher. Please refer to the publisher's site for terms of use.

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