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

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, themore » second is the Bickley Jet, and the third is data from numerically simulated drifters in the Sulu Sea.« less
Authors:
 [1] ;  [2] ;  [3]
  1. Program in Applied and Computational Mathematics, Princeton University, New Jersey 08544 (United States)
  2. Department of Physical Oceanography, Woods Hole Oceanographic Institute, Massachusetts 02543 (United States)
  3. Department of Mechanical and Aerospace Engineering, Princeton University, New Jersey 08544 (United States)
Publication Date:
OSTI Identifier:
22482317
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 25; Journal Issue: 8; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; LAGRANGIAN FUNCTION; OPTIMIZATION; POTENTIALS; SIMULATION; SPACE; STOCHASTIC PROCESSES; TRAJECTORIES