On the Extraction of Long-living Features in Unsteady Fluid Flows

  • Jens KastenEmail author
  • Ingrid Hotz
  • Bernd R. Noack
  • Hans-Christian Hege
Part of the Mathematics and Visualization book series (MATHVISUAL)


This paper proposes aGalilean invariant generalization of critical points ofvector field topology for 2D time-dependent flows. The approach is based upon a Lagrangian consideration of fluid particle motion. It extracts long-living features, likesaddles and centers, and filters out short-living local structures. This is well suited for analysis ofturbulent flow, where standard snapshot topology yields an unmanageable large number of topological structures that are barely related to the few main long-living features employed in conceptual fluid mechanics models. Results are shown for periodic and chaoticvortex motion.


Vortex Core Lagrangian Coherent Structure Vortex Region Galilean Transformation Acceleration Magnitude 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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The project is part of the SFB 557 “Control of complex turbulent shear flows” and is partially supported by the DFG Emmy Noether program. The authors wish to thank George Haller, Gilead Tadmor, and Igor Mezić for fruitful discussions. All visualizations have been created using Amira - a system for advanced visual data analysis ( The authors further want to thank the reviewers for their suggestions, which helped to improve the paper significantly.


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Copyright information

© Springer Berlin Heidelberg 2011

Authors and Affiliations

  • Jens Kasten
    • 1
    Email author
  • Ingrid Hotz
    • 1
  • Bernd R. Noack
    • 2
  • Hans-Christian Hege
    • 1
  1. 1.Zuse Institute Berlin (ZIB)BerlinGermany
  2. 2.Berlin Institute of Technology MB1BerlinGermany

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