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On the Elusive Concept of Lagrangian Coherent Structures

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Book cover Topological Methods in Data Analysis and Visualization II

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

Many of the recently developed methods for analysis and visualization of time-dependent flows are related to concepts, which can be subsumed under the term Lagrangian coherent structures (LCS). Thereby, no universal definition of LCS exists and different interpretations are used. Mostly, LCS are considered to be features linked to pathlines leading to the ideal conception of features building material lines. Such time-dependent features are extracted by averaging local properties of particles along their trajectories, e.g., separation, acceleration or unsteadiness. A popular realization of LCS is the finite-time Lyapunov exponent (FTLE) with its different implementations. The goal of this paper is to stimulate a discussion on the generality of the underlying assumptions and concepts. Using a few well-known datasets, the interpretation and usability of Lagrangian analysis methods are discussed.

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Acknowledgements

The project is supported by the DFG. The authors wish to thank Bernd Noack for fruitful discussions, Pierre Comte and Michael Schlegel for providing the jet dataset, and Gerd Mutschke for providing the cylinder dataset. All visualizations have been created using Amira – a system for advanced visual data analysis (http://amira.zib.de).

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Authors and Affiliations

  1. Zuse Institute Berlin (ZIB), Takustraße 7, 14195, Berlin, Germany

    Jens Kasten, Ingrid Hotz & Hans-Christian Hege

Authors
  1. Jens Kasten
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  2. Ingrid Hotz
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  3. Hans-Christian Hege
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Corresponding author

Correspondence to Jens Kasten .

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Editors and Affiliations

  1. Inst. Computational Science, CAB G 65.1, ETH Zürich, Universitätsstraße 6, Zürich, 8092, Switzerland

    Ronald Peikert

  2. , Dept. of Informatics, University of Bergen, Bergen, Norway

    Helwig Hauser

  3. , School of Computing, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT, United Kingdom

    Hamish Carr

  4. , Computational Science, ETH Zürich, Universitätsstraße 6, Zürich, 8092, Switzerland

    Raphael Fuchs

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Kasten, J., Hotz, I., Hege, HC. (2012). On the Elusive Concept of Lagrangian Coherent Structures. In: Peikert, R., Hauser, H., Carr, H., Fuchs, R. (eds) Topological Methods in Data Analysis and Visualization II. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23175-9_14

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