Abstract
The topology of vector fields offers a well known way to show a “condensed” view of the stream line behavior of a vector field. The global structure of a field can be shown without time-consuming user interaction. With regard to large data visualization, one encounters a major drawback: the necessity to analyze a whole data set, even when interested in only a small region. We show that one can localize the topology concept by including the boundary in the topology analysis. The idea is demonstrated for a turbulent swirling jet simulation example. Our concept works for all planar, piecewise analytic vector fields on bounded domains.
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
Billant, P., Chomaz, J., and Huerre, P. (1999). Experimental Study of Vortex Breakdown in Swirling Jets. Journal of Fluid Mechanics, 376:183–219.
Faler, J. H. and Leibovich, S. (1977). Disrupted States of Vortex Flow and Vortex Breakdown. Physics of Fluids, 96:1385–1400.
Globus, A., Levit, C, and Lasinski, T. (1991). A Tool for Visualizing the Topology of Three-Dimensional Vector Fields. In Nielson, G. M., Rosenblum, L. J., editors, IEEE Visualization ’91, IEEE Computer Society Press, Los Alamitos, CA, pages 33–40..
Helman, J. L. and Hesselink, L. (1990). Surface Representations of Two- and Three-Dimensional Fluid Flow Topology. In Nielson, G. M. and Shriver, B., editors, Visualization in scientific computing, IEEE Computer Society Press, Los Alamitos, CA, pages 6–13.
Lambourne, N. C. and Bryer, D. W. (1961). The Bursting of Leading Edge Vortices: Some Observations and Discussion of the Phenomenon. Aeronautical Research Council R. & M., 3282:1–36.
Leibovich, S. (1984). Vortex Stability and Breakdown: Survey and Extension. AIAA Journal, 22:1192–1206.
Lopez, J. M. (1990). Axisymmetric Vortex Breakdown, part 1. confined Swirling Flow. Journal of Fluid Mechanics, 221:533–552.
Lopez, J. M. (1994). On the Bifurcation Structure of Axisymmetric Vortex Breakdown in a Constricted Pipe. Physics of Fluids, 6:3683–3693.
Sarpkaya, T. (1971). On Stationary and Travelling Vortex Breakdown. Journal of Fluid Mechanics, 45:545–559.
Scheuermann, G. (1999). Topological Vector Field Visualization with Clifford Algebra, dissertation, Computer Science Department, University of Kaiserslautern, Kaiserslautern, Germany.
Scheuermann, G., Hagen, H., and Krüger, H. (1998). An Interesting Class of Polynomial Vector Fields. In Dæhlen, M., Lyche, T., and Schumaker, L. L., editors, Mathematical Methods for Curves and Surfaces II, pages 429–436, Nashville.
Tricoche, X., Scheuermann, G., and Hagen, H. (2000). A topology simplification method for 2d vector fields. In Ertl., T., Hamann, B. and Varshney, A., editors, IEEE Visualization 2000, IEEE Computer Society Press, Los Alamitos, CA, pages 359–366.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Scheuermann, G., Hamann, B., Joy, K.I., Kollmann, W. (2003). Localizing Vector Field Topology. In: Post, F.H., Nielson, G.M., Bonneau, GP. (eds) Data Visualization. The Springer International Series in Engineering and Computer Science, vol 713. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1177-9_2
Download citation
DOI: https://doi.org/10.1007/978-1-4615-1177-9_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-5430-7
Online ISBN: 978-1-4615-1177-9
eBook Packages: Springer Book Archive