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Streamline Topology of Axisymmetric Flows

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Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 52))

Abstract

When a fluid velocity field v(x, t) is given, the streamlines at the time instant t 0 are found as trajectories of the system of ordinary differential equations

$$\dot{x}= v(x, t_{0})$$

. In general, this is a nonlinear system, and qualitative (topological) information on the streamlines may be obtained using tools from the theory of nonlinear dynamics.

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References

  1. P. G. Bakker. On the topology of three-dimensional separations, a guide for classification. In D. Roose, editor, Continuation and Bifurcations: Numerical Techniques and Applications, pages 297–318. Klüwer, Dordrecht, 1990.

    Chapter  Google Scholar 

  2. P. G. Bakker. Bifurcations in Flow Patterns. Klüver Academic Publishers, Dordrecht, 1991.

    Book  MATH  Google Scholar 

  3. M. Brøns. Topological fluid dynamics of interfacial flows. Physics of Fluids, 6(8):2730–2737, 1994.

    Article  MathSciNet  ADS  Google Scholar 

  4. M. Brøns. Topological fluid mechanics with applications to free surfaces and ax-isymmetric flows. Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), 76 suppl. 5:73–74, 1996.

    Google Scholar 

  5. S.-N. Chow, C. Li, and D. Wang. Normal Forms and Bifurcation of Planar Vector Fields. Cambridge University Press, 1994.

    Google Scholar 

  6. U. Dallmann. Three-dimensional vortex structures and vorticity topology. Fluid Dynamics Research, 3:183–189, 1988.

    Article  ADS  Google Scholar 

  7. M. P. Escudier. Observations of the flow produced in a cylindrical container by a rotating endwall. Experiments in Fluids, 2:189–196, 1984.

    Article  ADS  Google Scholar 

  8. H. Goldstein. Classical Mechanics. Addison-Wesley, Reading Mass., 1950.

    Google Scholar 

  9. J. Guckenheimer and P. Holmes. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer Verlag, New York, 1983.

    MATH  Google Scholar 

  10. J. M. Lopez. Axisymmetric vortex breakdown part 1. Confined swirling flow. Journal of Fluid Mechanics, 221:533–552, 1990.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. H. J. Lugt. Local properties at a viscous free surface. Physics of Fluids, 30:3647–3652, 1987.

    Article  ADS  MATH  Google Scholar 

  12. H. J. Lugt. Oblique vortices on a solid wall and on an interface between two immiscible fluids. Physics of Fluids A, 1:1424–1426, 1989.

    Article  ADS  Google Scholar 

  13. A. E. Perry and M. S. Chong. A description of eddying motions and flow patterns using critical-point concepts. Annual Review of Fluid Mechanics, 19:125–155, 1987.

    Article  ADS  Google Scholar 

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© 1999 Springer Science+Business Media Dordrecht

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Brøns, M. (1999). Streamline Topology of Axisymmetric Flows. In: Sørensen, J.N., Hopfinger, E.J., Aubry, N. (eds) IUTAM Symposium on Simulation and Identification of Organized Structures in Flows. Fluid Mechanics and Its Applications, vol 52. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4601-2_19

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  • DOI: https://doi.org/10.1007/978-94-011-4601-2_19

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5944-2

  • Online ISBN: 978-94-011-4601-2

  • eBook Packages: Springer Book Archive

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