Skip to main content

Visualization of Coherent Structures in Transient 2D Flows

  • Chapter
Topology-Based Methods in Visualization II

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

Summary

The depiction of a time-dependent flow in a way that effectively sup ports the structural analysis of its salient patterns is still a challenging problem for flow visualization research. While a variety of powerful approaches have been investigated for over a decade now, none of them so far has been able to yield repre sentations that effectively combine good visual quality and a physical interpretation that is both intuitive and reliable. Yet, with the huge amount of flow data generated by numerical computations of growing size and complexity, scientists and engineers are faced with a daunting analysis task in which the ability to identify, extract, and display the most meaningful information contained in the data is becoming absolutely indispensable.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Eberly, R. Gardner, B. Morse, and S. Pizer. Ridges for image analysis. Journal of Mathematical Imaging and Vision, 4:355–371, 1994.

    Article  Google Scholar 

  2. M.A. Green, C.W. Rowley, and G. Haller. Detection of lagrangian coherent structures in 3d turbulence. J. Fluid Mech., to appear, 2006.

    Google Scholar 

  3. G. Haller. Finding finite-time invariant manifolds in two-dimensional velocity fields. Chaos, 10(1):99–108, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  4. G. Haller and G. Yuan. Lagrangian coherent structures and mixing in two-dimensional turbulence. Physica D, 147:352–370, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  5. G. Haller. Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence. Physics of Fluids, 13(11), 2001.

    Article  MathSciNet  Google Scholar 

  6. G. Haller. Distinguished material surfaces and coherent structures in three-dimensional flows. Physica D, 149:248–277, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  7. G. Haller. Lagrangian coherent structures from approximate velocity data. Physics of Fluids, 14(6):1851–1861, june 2002.

    Article  MathSciNet  Google Scholar 

  8. T. Inanc, S.C. Shadden, and J.E. Marsden. Optimal trajectory generation in ocean flows. In Proceedi ngs of the Ameri can Control Conference, pages 674–679, 2005.

    Google Scholar 

  9. B. Laramee, J.J. van Wijk, B. Jobard, and H. Hauser. ISA and IBFVS: Image space based visualization of flow on surfaces. IEEE Transactions on Visualization and Computer Graphics, 10(6):637–648, nov 2004.

    Article  Google Scholar 

  10. F. Lekien, S.C. Shadden, and J.E. Marsden. Lagrangian coherent structures in n-dimensional systems. Physica D, submitted, 2006.

    Google Scholar 

  11. G.-S. Li, X. Tricoche, and C.D. Hansen. GPUFLIC: Interactive and dense visualization of unsteady flows. In Data Analysis 2006: Proceedings of Joint IEEE VGTC and EG Symposium on Visualization (EuroVis) 2006, pages 29–34, may 2006.

    Google Scholar 

  12. M. Mathur, G. Haller, T. Peacock, J.E. Ruppert-Felsot, and H.L. Swinney. Uncovering the lagrangian skeleton of turbulence. Phys. Rev. Lett., submitted, 2006.

    Google Scholar 

  13. S.C. Shadden, F. Lekien, and J.E. Marsden. Definition and properties of lagrangian coherent structures from finit-time lyapunov exponents in two-dimensional aperiodic flows. Physica D, 212:271–304, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  14. S.C. Shadden, J.O. Dabiri, and J.E. Marsden. Lagrangian analysis of fluid transport in empirical vortex ring flows. Physics of Fluids, 18:047105, 2006.

    Article  MathSciNet  Google Scholar 

  15. H.W. Shen and D.L. Kao. A new line integral convolution algorithm for visu alizing unsteady flows. IEEE Transactions on Visualization and Computer Graphics, 4(2), 1998.

    Google Scholar 

  16. H. Theisel and H.-P. Seidel. Feature flow fields. In Proceedings of Joint Eurographics — IEEE TCVG Symposium on Visualization (VisSym '03), pages 141–148, 2003.

    Google Scholar 

  17. H. Theisel, T. Weinkauf, H.-C. Hege, and H.-P. Seidel. Topological methods for 2d time-dependent vector fields based on streamlines and path lines. IEEE Transations on Visualization and Computer Graphics, 11(4):383–394, 2005.

    Article  Google Scholar 

  18. X. Tricoche, T. Wischgoll, G. Scheuermannn, and H. Hagen. Topology tracking for the visualization of time-dependent two-dimensional flows. Computer and Graphics, 26:249–257, 2002.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Garth, C., Li, GS., Tricoche, X., Hansen, C.D., Hagen, H. (2009). Visualization of Coherent Structures in Transient 2D Flows. 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_1

Download citation

Publish with us

Policies and ethics