Summary
This paper takes a look at the visualization side of vector field anal ysis based on Lagrangian coherent structures. The Lagrangian coherent structures are extracted as height ridges of finite-time Lyapunov exponent fields. The result ing visualizations are compared to those from traditional instantaneous vector field topology of steady and unsteady vector fields: they often provide more and better interpretable information. The examination is applied to 3D vector fields from a dynamical system and practical CFD simulations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Asimov, D.: Notes on the Topology of Vector Fields and Flows. Tech. Report RNR-93-003, NASA Ames Research Center (1993)
David Eberly: Ridges in Image and Data Analysis. Computational Imaging and Vision. Kluwer Academic Publishers (1996)
Furst, J.D., Pizer, S.M.: Marching Ridges. 2001 IASTED International Confer ence on Signal and Image Processing (2001)
George Haller: Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Physica D 149 248–277 (2001)
George Haller: Lagrangian coherent structures from approximate velocity data. Phys. Fluids A14 1851–1861 (2002)
George Haller: An objective definition of a vortex. J. Fluid Mech. 525 1–26 (2005)
James Helman, Lambertus Hesselink: Representation and Display of Vector Field Topology in Fluid Flow Data Sets. IEEE Computer 22(8) 27–36 (1989)
Michel Henon: Sur la topologie des lignes de courant dans un cas particulier. Comptes Rendus Acad. Sci. Paris 262 312–314 (1966)
De-Bin Huang, Xiao-Hua Zhao, Hui-Hui Dai: Invariant tori and chaotic streamlines in the ABC flow. Phys. Lett. A 237(3) 136–140 (1998)
Gordon Kindlmann, Xavier Tricoche, Carl-Fredrik Westin: Anisotropy Creases Delineate White Matter Structure in Diffusion Tensor MRI. In: MICCAI'06, Lecture Notes in Computer Science 3749 (2006)
Yuval Levy, David Degani, Arnan Seginer: Graphical Visualization of Vortical Flows by Means of Helicity. AIAA 28(8) 1347–1352 (1990)
Lindeberg, T.: Edge detection and ridge detection with automatic scale selection. International Journal of Computer Vision 30(2) 77–116 (1996)
Peter Majer: A Statistical Approach to Feature Detection and Scale Selection in Images. Ph.D. thesis, University of Goettingen (2000)
Kuangyu Shi, Holger Theisel, Tino Weinkauf, Helwig Hauser, Hans-Christian Hege, Hans-Peter Seidel: Path Line Oriented Topology for Periodic 2D Time-Dependent Vector Fields. Proc. Eurographics/IEEE VGTC Symposium on Visualization (EuroVis '06) 139–146 (2006)
Holger Theisel, Tino Weinkauf, Hans-Christian Hege, Hans-Peter Seidel: Saddle Connectors — An Approach to Visualizing the Topological Skeleton of Complex 3D Vector Fields. Proc. IEEE Visualization 225–232 (2003)
Holger Theisel, Tino Weinkauf, Hans-Christian Hege, Hans-Peter Seidel: Stream Line and Path Line Oriented Topology for 2D Time-Dependent Vector Fields. Proc. IEEE Visualization 321–328 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Sadlo, F., Peikert, R. (2009). Visualizing Lagrangian Coherent Structures and Comparison to Vector Field Topology. In: Hege, HC., Polthier, K., Scheuermann, G. (eds) Topology-Based Methods in Visualization II. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88606-8_2
Download citation
DOI: https://doi.org/10.1007/978-3-540-88606-8_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-88605-1
Online ISBN: 978-3-540-88606-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)