Applied Scientific Research

, Volume 51, Issue 1–2, pp 55–59 | Cite as

Spiral vortices between concentric cylinders

  • J. Sánchez
  • D. Crespo
  • F. Marquès
Chapter I: Dynamical Systems And Transition

Abstract

Spiral vortices appearing in Couette-Taylor flows are studied by means of numerical simulation. Transition curves from Couette to spiral vortices for different radius ratios and wavenumbers have been calculated in order to test our technique. Critical Reynolds numbers, angular velocities and slopes of the spirals at the onset of the instability agree with previous results [1]. Non-linear solutions obtained by a pseudospectral collocation method are studied, and they show a weak net axial flow. In order to counteract this effect, which is absent in the usual experimental set-up, an axial pressure gradient has been included. This procedure has proved to be sufficient to make the axial flow negligible. The onset of a quasiperiodic flow for larger Reynolds numbers, corresponding to a secondary bifurcation is also presented.

Key words

Couette-Taylor system spiral vortices Hopf bifurcation quasiperiodic flow 

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References

  1. 1.
    W.F. Langford, R. Tagg, E. J. Kostelich, H.L. Swinney, and M. Golubitsky 1988 ‘Primary instabilities and bicriticality in flow between counter-rotating cylinders.’Phys. Fluids vol.31, 776Google Scholar
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    C.D. Andereck, S.S. Liu, H.L. Swinney. 1986 ‘Flow regimes in a circular Couette system with independently rotating cylinders.’J. Fluid Mechanics vol.164, 155Google Scholar
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    F. Marquès. 1990 ‘On boundary condition for velocity flows: Application to Couette flow.’Phys. Fluids A 2, 729Google Scholar
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    C. Canuto, M. Yousuff Hussaini, A. Quarteroni, and T.A. Zang. 1988 ‘Spectral Methods in Fluid Dynamics’ Springer-Verlag.Google Scholar
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    F.Marquès, I. Mercader, M. Net and J Massaguer. 1992 ‘Thermal convection in vertical cylinders. A method based on potentials of velocity.’Computer Meths Appl Mech Engng. (submitted).Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • J. Sánchez
    • 1
  • D. Crespo
    • 1
  • F. Marquès
    • 1
  1. 1.Dept. Física AplicadaUniversitat Politécnica de CatalunyaSpain

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