Abstract
The topology of three-dimensional separated flow structures is examined for Navier-Stokes flows. A classification strategy is developed so that viscous flow patterns with complicated topology can be analyzed in a systematic way. The method relies on the qualitative theory of differential equations and on bifurcation theory. Some examples illustrate the method.
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
Andronov, A.A., et.al. (1973) Qualitative theory of second order dynamical systems. Wiley, New York.
Bakker, P.G., (1988) Bifurcations in flow patterns. PhD thesis, Delft University of Technology.
Dallmann, U., (1983) Topological structures of three-dimensional vortex flow separation, AIAA-paper 1735.
Guckenheimer, J., Holmes, P.J. (1983) Nonlinear oscillations, dynamical systems and bifurcation of vector fields. Springer, New York, Berlin.
Hornung, H.G., (1983) The vortex-skeleton model for three-dimensional steady flows. AGARD Conference Proc. 342.
Kooij, R.E., Bakker, P.G., (1989) Three-dimensional viscous flow structures from bifurcation of a degenerate singularity with three zero eigenvalues, Report LR-572, Delft University of Technology.
Legendre, R., (1965) Lignes de courant d’un ecoulement continu, La Recherche Aerospatiale, 105.
Perry, A.E., Chong, M.S., (1986) A series-expansion study of the Navier-Stokes equations with three-dimensional separation points, J. Fluid Mech., vol. 173.
Shirer, H.N., Wells, R., (1983) Mathematical structures of the singularities at the transitions between steady states in hydrodynamic systems, Lecture notes in physics, vol. 185, Springer, New York.
Takens, F., (1974) Singularities of vector fields, Publ. Math. IHES, 43, 47–100.
Wang, K.C. (1983) On the disputes about open separation, AIAA-paper 83–0296.
Winkel, M.E.M. de, Bakker, P.G., (1988) On the topology of three-dimensional viscous flow structures near a plane wall. A classification of hyperbolic and non-hyperbolic singularities on the wall, Report LR-541, Delft University of Technology.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Kluwer Academic Publishers
About this chapter
Cite this chapter
Bakker, P.G. (1990). On the Topology of Three-Dimensional Separations, A Guide For Classification. In: Roose, D., Dier, B.D., Spence, A. (eds) Continuation and Bifurcations: Numerical Techniques and Applications. NATO ASI Series, vol 313. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0659-4_20
Download citation
DOI: https://doi.org/10.1007/978-94-009-0659-4_20
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6781-2
Online ISBN: 978-94-009-0659-4
eBook Packages: Springer Book Archive