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On the Onset of Nonsteadiness in the Flows with Vortex Breakdown in a Cylindrical Container

  • N. Tsitverblit
  • E. Kit
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Abstract

In the experiment by Escudier (1984), the appearance of vortex breakdown in a cylindrical container has been accompanied by the onset of axisymmetric oscillations, when the Reynolds number was increased within a wide range of the aspect ratios. In this work, we emphasize that this axisymmetric instability can arise from the region of the negative Rayleigh discriminant near the cylindrical wall rather than is associated with the presence of vortex breakdown in the approaching steady solution. In view of indications of the presence of three-dimensional instability, the result appears to be corroborative of the hypothesis promulgated by Leibovich (1984) and Leibovich & Kribus (1990) about the primary role of nonaxisymmetric instability in the flows with vortex breakdown.

Keywords

Reynolds Number Secondary Flow Recirculation Zone Steady Solution Azimuthal Velocity 
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References

  1. [1]
    Escudier, M. P. (1984) Observations of the flow produced in a cylindrical container by a rotating endwall. Experiments in Fluids 2, 189–196.ADSCrossRefGoogle Scholar
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    Leibovich, S. (1984) Vortex stability and breakdown: survey and extension. AIAA J. 22, 1192–1206.ADSCrossRefGoogle Scholar
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    Leibovich, S. & Kribus, A. (1990) Large-amplitude wave trains and solitary waves in vortices.J. Fluid Mech. 216, 459–504.ADSMATHCrossRefGoogle Scholar
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    Tsitverblit, N. (1993) Vortex breakdown in a cylindrical container in the light of continuation of a steady solution. Fluid Dynamics Research 11, 19–35.ADSCrossRefGoogle Scholar
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    Tsitverblit, N. & Kit, E. (1992) Axisymmetric vortex breakdown in an annulus. Eleventh Australian Fluid Mechanics Conference. 1, 143–146.Google Scholar
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    Chandrasekhar, S. (1961) Hydrodynamic and hydromagnetic stability. Dover Publication, Inc. New York.MATHGoogle Scholar

Copyright information

© Springer-Verlag, Berlin Heidelberg 1994

Authors and Affiliations

  • N. Tsitverblit
    • 1
  • E. Kit
    • 1
  1. 1.Tel-Aviv UniversityTel-AvivIsrael

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