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

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

Abstract

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Panton, R.L.: Incompressible Flow. Wiley & Sons (2005)Google Scholar
  2. 2.
    Tobak, M., Peake, D.: Topology of three-dimensional separated flows. Ann. Review of Fluid Mechanics 14 (1982) 61–85MathSciNetCrossRefGoogle Scholar
  3. 3.
    Haller, G.: Lagrangian coherent structures from approximate velocity data. Physics of Fluids 14(6) (2002) 1851–1861MathSciNetCrossRefGoogle Scholar
  4. 4.
    Helman, J., Hesselink, L.: Representation and display of vector field topology in fluid flow data sets. Computer 22(8) (1989) 27–36CrossRefGoogle Scholar
  5. 5.
    Helman, J., Hesselink, L.: Visualizing vector field topology in fluid flows. IEEE Comput. Graph. Appl. 11(3) (1991) 36–46CrossRefGoogle Scholar
  6. 6.
    Laramee, R., Hauser, H., Zhao, L., Post, F.: Topology-based flow visualization, the state of the art. In Hauser, H., Hagen, H., Theisel, H., eds.: Topology-based Methods in Visualization, Springer, Berlin (2007) 1–19CrossRefGoogle Scholar
  7. 7.
    Hunt, J.: Vorticity and vortex dynamics in complex turbulent flows. CSME Trans. 11(1) (1987) 21–35Google Scholar
  8. 8.
    Jeong, J., Hussain, F.: On the identification of a vortex. Journal of Fluid Mechanics 285 (1995) 69–94MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Sadarjoen, I., Post, F.: Detection, quantification, and tracking of vortices using streamline geometry. Comput. Graph. 24(3) (2000) 333–341CrossRefGoogle Scholar
  10. 10.
    Peikert, R., Roth, M.: The parallel vectors operator - a vector field visualization primitive. In: IEEE Visualization ’00. (2000) 263–270Google Scholar
  11. 11.
    Theisel, H., Weinkauf, T., Hege, H.C., Seidel, H.P.: Topological methods for 2D time-dependent vector fields based on stream lines and pathlines. IEEE Trans. Vis. Comput. Graph. 11(4) (2005) 383–394CrossRefGoogle Scholar
  12. 12.
    Weinkauf, T., Sahner, J., Theisel, H., Hege, H.C.: Cores of swirling particle motion in unsteady flows. IEEE Trans. Vis. Comput. Graph. 13(6) (2007) 1759–1766CrossRefGoogle Scholar
  13. 13.
    Fuchs, R., Peikert, R., Sadlo, F., Alsallakh, B., Gröller, E.: Delocalized unsteady vortex region detectors. In O. Deussen, D. Keim, D.S., ed.: VMV ’08. (October 2008) 81–90Google Scholar
  14. 14.
    Shi, K., Theisel, H., Weinkauf, T., Hege, H.C., Seidel, H.P.: Finite-time transport structures of flow fields. In: IEEE Pacific Visualization ’08. (2008) 63–70Google Scholar
  15. 15.
    Haller, G.: Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Physica D 149 (2001) 248–277MATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    Sadlo, F., Peikert, R.: Efficient visualization of lagrangian coherent structures by filtered AMR ridge extraction. IEEE Trans. Vis. Comput. Graph. 13(6) (2007) 1456–1463CrossRefGoogle Scholar
  17. 17.
    Garth, C., Gerhardt, F., Tricoche, X., Hagen, H.: Efficient computation and visualization of coherent structures in fluid flow applications. IEEE Trans. Vis. Comput. Graph. 13(6) (2007) 1464–1471CrossRefGoogle Scholar
  18. 18.
    Haller, G.: Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence. Physics of Fluids 13 (2001) 3365–3385MathSciNetCrossRefGoogle Scholar
  19. 19.
    Soille, P.: Morphological image analysis. Springer Berlin (1999)Google Scholar
  20. 20.
    Rom-Kedar, V., Leonard, A., Wiggins, S.: An analytical study of transport, mixing and chaos in an unsteady vortical flow. Journal of Fluid Mechanics 214 (1990) 347–394MATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    Noack, B., Mezić, I., Tadmor, G., Banaszuk, A.: Optimal mixing in recirculation zones. Physics of Fluids 16(4) (2004) 867–888MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2011

Authors and Affiliations

  • Jens Kasten
    • 1
  • 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

Personalised recommendations