On the Elusive Concept of Lagrangian Coherent Structures

  • Jens Kasten
  • Ingrid Hotz
  • Hans-Christian Hege
Part of the Mathematics and Visualization book series (MATHVISUAL)


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.


Lyapunov Exponent Coherent Structure Material Line Lagrangian Coherent Structure Local Separation 
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 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 (


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Zuse Institute Berlin (ZIB)BerlinGermany

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