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Identification of individual coherent sets associated with flow trajectories using coherent structure coloring

Schlueter-Kuck, Kristy L. and Dabiri, John O. (2017) Identification of individual coherent sets associated with flow trajectories using coherent structure coloring. Chaos, 27 (9). Art. No. 091101. ISSN 1054-1500. https://resolver.caltech.edu/CaltechAUTHORS:20190422-164852375

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Abstract

We present a method for identifying the coherent structures associated with individual Lagrangian flow trajectories even where only sparse particle trajectory data are available. The method, based on techniques in spectral graph theory, uses the Coherent Structure Coloring vector and associated eigenvectors to analyze the distance in higher-dimensional eigenspace between a selected reference trajectory and other tracer trajectories in the flow. By analyzing this distance metric in a hierarchical clustering, the coherent structure of which the reference particle is a member can be identified. This algorithm is proven successful in identifying coherent structures of varying complexities in canonical unsteady flows. Additionally, the method is able to assess the relative coherence of the associated structure in comparison to the surrounding flow. Although the method is demonstrated here in the context of fluid flow kinematics, the generality of the approach allows for its potential application to other unsupervised clustering problems in dynamical systems such as neuronal activity, gene expression, or social networks. In recent years, there has been a proliferation of techniques that aim to characterize fluid flow kinematics on the basis of Lagrangian trajectories of collections of tracer particles. Most of these techniques depend on the presence of tracer particles that are initially closely spaced, in order to compute local gradients of their trajectories. In many applications, the requirement of close tracer spacing cannot be satisfied, especially when the tracers are naturally occurring and their distribution is dictated by the underlying flow. Moreover, current methods often focus on determination of the boundaries of coherent sets, whereas in practice it is often valuable to identify the complete set of trajectories that are coherent with an individual trajectory of interest. We extend the concept of Coherent Structure Coloring, an approach based on spectral graph theory, to achieve identification of the coherent set associated with individual Lagrangian trajectories. The method does not require a priori determination of the number of coherent structures in the flow, nor does it require heuristics regarding the eigenvalue spectrum corresponding to the generalized eigenvalue problem. Importantly, although the method is demonstrated here in the context of fluid flow kinematics, the generality of the approach allows for its potential application to other unsupervised clustering problems in dynamical systems such as neuronal activity, gene expression, or social networks.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1063/1.4993862DOIArticle
https://arxiv.org/abs/1708.05757arXivDiscussion Paper
ORCID:
AuthorORCID
Schlueter-Kuck, Kristy L.0000-0002-6335-168X
Dabiri, John O.0000-0002-6722-9008
Additional Information:© 2017 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). (Received 1 July 2017; accepted 18 August 2017; published online 5 September 2017) This work was supported by the U.S. National Science Foundation and by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program. A MATLAB implementation of the CSC algorithm is available for free download at http://dabirilab.com/software.
Group:GALCIT
Funders:
Funding AgencyGrant Number
NSFUNSPECIFIED
National Defense Science and Engineering Graduate (NDSEG) FellowshipUNSPECIFIED
Issue or Number:9
Record Number:CaltechAUTHORS:20190422-164852375
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190422-164852375
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:94884
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:23 Apr 2019 14:42
Last Modified:03 Oct 2019 21:08

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