Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-19T11:04:06.895Z Has data issue: false hasContentIssue false

Axisymmetric vortex breakdown. Part 3 Onset of periodic flow and chaotic advection

Published online by Cambridge University Press:  26 April 2006

J. M. Lopez
Affiliation:
Aeronautical Research Laboratory, 506 Lorimer Street, Fishermens Bend, Victoria 3207, Australia
A. D. Perry
Affiliation:
Aeronautical Research Laboratory, 506 Lorimer Street, Fishermens Bend, Victoria 3207, Australia Present address: Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125, USA.

Abstract

When the fluid inside a completely filled cylinder is set in motion by the rotation of one endwall, steady and unsteady axisymmetric vortex breakdown is possible. Nonlinear dynamical systems theory is used to describe the changing kinematics of the flow as the speed of the rotating endwall is increased. Two distinct modes of oscillation have been found in the unsteady regime and the chaotic advection caused by the oscillations has been investigated. The results of this study are used to describe the filling and emptying processes of the vortex breakdown bubbles observed in flow visualization experiments.

Type
Research Article
Copyright
© 1992 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Benjamin, T. B. 1962 Theory of the vortex breakdown phenomenon. J. Fluid Mech. 14, 593629.Google Scholar
Brown, G. L. & Lopez, J. M. 1990 Axisymmetric vortex breakdown. Part 2. Physical mechanisms. J. Fluid Mech. 221, 553576.Google Scholar
Daube, O. & Sorensen, J. N. 1989 Simulation numérique de l’écoulement périodique axisymétrique dans une cavité cylindrique. C. R. Acad. Sci. Paris 308, 463469.Google Scholar
Davey, A. 1961 Boundary-layer flow at a saddle point of attachment. J. Fluid Mech. 10, 593610.Google Scholar
Escudier, M. P. 1984 Observations of the flow produced in a cylindrical container by a rotating endwall. Expts. Fluids 2, 189196.Google Scholar
Faler, J. H. & Leibovich, S. 1977 Disrupted states of vortex flow and vortex breakdown. Phys. Fluids 20, 13851400.Google Scholar
Guckenheimer, J. & Holmes, P. 1986 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer.
Hama, F. R. 1962 Streaklines in a perturbed shear flow. Phys. Fluids 5, 644650.Google Scholar
Holmes, P. 1984 Some remarks on chaotic particle paths in time-periodic, three dimensional swirling flows. Contemp. Maths 28, 393403.Google Scholar
Hunt, J. C. R., Abell, C. J., Peterka, J. A. & Woo, H. 1978 Kinematical studies of the flows around free or surface-mounted obstables; applying topology to flow visualization. J. Fluid Mech. 86, 179200.Google Scholar
Lichtenberg, A. J. & Lieberman, M. A. 1983 Regular and Stochastic Motion. Springer.
Lopez, J. M. 1988 Vortex breakdown of a confined swirling flow. In Computational Fluid Dynamics. Proc Intl Symp. Comp. Fluid Dyn., Sydney, Australia, August 1987 (ed. G. de Vahl Davis & C. Fletcher), pp. 501501. North-Holland.
Lopez, J. M. 1989 Axisymmetric vortex breakdown in an enclosed cylinder flow. In 11th Intl Conf. on Numerical Methods in Fluid Dynamics (ed. D. L. Dwoyer, M. Y. Hussaini & R. G. Voigt). Lecture Notes in Physics, vol. 323, pp. 388388. Springer.
Lopez, J. M. 1990 Axisymmetric vortex breakdown. Part 1. Confined swirling flow. J. Fluid Mech. 221, 533552.Google Scholar
Lugt, H. J. & Abboud, M. 1987 Axisymmetric vortex breakdown with and without temperature effects in a container with a rotating lid. J. Fluid Mech. 179, 179200.Google Scholar
Neitzel, G. P. 1988 Streak-line motion during steady and unsteady axisymmetric vortex breakdown. Phys. Fluids 31, 958960.Google Scholar
Ottino, J. M. 1989 The Kinematics of Mixing: Stretching, Chaos, and Transport. Cambridge University Press.
Percival, I. C. 1979 Variational principles for invariant tori and cantori. Am. Inst. Phys. Conf. Proc. 57, 302310.Google Scholar
Perry, A. E. & Fairlie, B. D. 1974 Critical points in flow patterns. Adv. Geophys. 18B, 229315.Google Scholar
Rom-Kedar, V., Leonard, A. & Wiggins, S. 1990 An analytical study of transport, mixing and chaos in an unsteady vortical flow. J. Fluid Mech. 214, 347394.Google Scholar
Rom-Kedar, V. & Wiggins, S. 1990 Transport in two-dimensional maps. Arch. Rat. Mech. Anal. 109, 239298.Google Scholar
Ronnenberg, B. 1977 Ein selbstjustierendes 3-Komponenten Laserdoppleraremometer nach dem Vergleichsstrahlverfahren, angewandt für Untersuchungen in einer stationären zylindersymmetrischen Drehströmung mit einen Rückstromgebiet. Max-Planck-Inst. Bericht 20.Google Scholar
Stuart, J. T., Pankhurst, R. C. & Bryer, D. W. 1963 Particle paths, filament lines and streamlines. NPL Aero Rep. 1057.Google Scholar
Vogel, H. U. 1968 Experimentelle Ergebnisse über die laminare Strömung in einen zylindrischen Gehäuse mit darin rotierender Scheibe. Max-Planck-Inst. Bericht 6.Google Scholar
Wiggins, S. 1988 Global Bifurcations and Chaos: Analytical Methods. Springer.
Wiggins, S. 1990 Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer.