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Vortex Breakdown as a Catastrophe

  • Conference paper
IUTAM Symposium on Dynamics of Slender Vortices

Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 44))

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Abstract

By studying swirling viscous jets, we develop a new explanation of vortex breakdown, show how solution non-uniqueness appears through cusp and fold catastrophes as the Reynolds number Re increases, and obtain analytical solutions for Re → ∞. Although inviscid theories also involve fold catastrophe, they have a strong limitation: the dependence of the head H and circulation Гd on stream function ψ is undetermined inside a recirculatory zone. Analytical continuation and stagnation zone models used to resolve this indeterminacy appear inadequate for swirling jets: H(ψ) and Гd(ψ), which we obtain here by the inviscid limit, differ from those based on the inviscid theories. We therefore suggest a new model consistent with the limiting transition. Also, we analyze turbulent vortex breakdown with a conical wake which has been recently observed at large Re.

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Houston, Houston, TX, 77204-4792, USA

    Vladimir Shtern & Fazle Hussain

Authors
  1. Vladimir Shtern
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  2. Fazle Hussain
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Editors and Affiliations

  1. Aerodynamisches Institut, Rheinisch-Westfälische Technische Hochschule Aachen, Germany

    E. Krause

  2. Institut für Thermo- und Fluiddynamik, Ruhr-Universität Bochum, Germany

    K. Gersten

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© 1998 Springer Science+Business Media Dordrecht

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Shtern, V., Hussain, F. (1998). Vortex Breakdown as a Catastrophe. In: Krause, E., Gersten, K. (eds) IUTAM Symposium on Dynamics of Slender Vortices. Fluid Mechanics and Its Applications, vol 44. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5042-2_25

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  • DOI: https://doi.org/10.1007/978-94-011-5042-2_25

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6117-9

  • Online ISBN: 978-94-011-5042-2

  • eBook Packages: Springer Book Archive

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