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Rigid Sets and Coherent Sets in Realistic Ocean Flows

by F. Feppon and P. F. J. Lermusiaux

(Report number 2021-11)

Abstract
This paper focuses on the extractions of Lagrangian Coherent Sets from realistic velocity fields obtained from ocean data and simulations, each of which can be highly resolved and non volume-preserving. Two classes of methods have emerged for such purpose: those relying on the flow map diffeomorphism associated with the velocity field, and those based on spectral decompositions of the Koopman or Perron-Frobenius operators. The two classes of methods are reviewed, synthesized, augmented, and compared numerically on three velocity fields. First, we propose a new "diffeomorphism-based" criterion to extract "rigid sets", defined as sets over which the flow map acts approximately as a rigid transformation. Second, we develop a matrix-free methodology that provides a simple and efficient framework to compute "coherent sets" with operator methods. Both new methods and their resulting rigid sets and coherent sets are illustrated and compared using three numerically simulated flow examples, including a realistic, submesocale to large-scale dynamic ocean current field in the Palau Island region of the western Pacific Ocean.

Keywords: LCS, Rigid sets, Koopman operator, Arnoldi Iterations, Ocean Modeling, Lagrangian transport, Realistic data

@Techreport{FL21_953,
  author = {F. Feppon and P. F. J. Lermusiaux},
  title = {Rigid Sets and Coherent Sets in Realistic Ocean Flows},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2021-11},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2021/2021-11.pdf },
  year = {2021}
}

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