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Ridge Concepts for the Visualization of Lagrangian Coherent Structures

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Topological Methods in Data Analysis and Visualization II

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

Abstract

The popularity of vector field topology in the visualization community is due mainly to the topological skeleton which captures the essential information on a vector field in a set of lines or surfaces separating regions of different flow behavior. Unfortunately, vector field topology has no straightforward extension to unsteady flow, and the concept probably most closely related to the topological skeleton are the so-called Lagrangian coherent structures (LCS). LCS are material lines or material surfaces that separate regions of different flow behavior. Ideally, such structures are material lines (or surfaces) in an exact sense and at the same time maximally attracting or repelling, but practical realizations such as height ridges of the finite-time Lyapunov exponent (FTLE) fulfill these two requirements only in an approximate sense. In this paper, we quantify the deviation from exact material lines/surfaces for several FTLE-based concepts, and we propose a numerically simpler variants of FTLE ridges that has equal or better error characteristics than classical FTLE height ridges.

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Acknowledgements

We thank Youcef Ait-Bouziad and Filip Sadlo for the simulation of the flow about a cuboid, and Andritz Hydro for the Francis turbine dataset. This work was partially funded by the Swiss National Science Foundation under grant 200021_127022. The project SemSeg acknowledges the financial support of the Future and Emerging Technologies (FET) program within the Seventh Framework Program for Research of the European Commission, under FET-Open grant number 226042.

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Authors and Affiliations

  1. ETH Zurich, Rämistrasse 101, 8092, Zurich, Switzerland

    Benjamin Schindler, Ronald Peikert & Raphael Fuchs

  2. University of Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Holger Theisel

Authors
  1. Benjamin Schindler
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  2. Ronald Peikert
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  3. Raphael Fuchs
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  4. Holger Theisel
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Corresponding author

Correspondence to Benjamin Schindler .

Editor information

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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Schindler, B., Peikert, R., Fuchs, R., Theisel, H. (2012). Ridge Concepts for the Visualization 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_15

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