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The instability of short waves on a vortex ring

Published online by Cambridge University Press:  29 March 2006

Sheila E. Widnall ,
Donald B. Bliss  and
Chon-Yin Tsai
Sheila E. Widnall
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge
Donald B. Bliss
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge
Chon-Yin Tsai
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge
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Abstract

A simple model for the experimentally observed instability of the vortex ring to azimuthal bending waves of wavelength comparable with the core size is presented. Short-wave instabilities are discussed for both the vortex ring and the vortex pair. Instability for both the ring and the pair is predicted to occur whenever the self-induced rotation of waves on the filament passes through zero. Although this does not occur for the first radial bending mode of a vortex filament, it is shown to be possible for bending modes with a more complex radial structure with at least one node at some radius within the core. The previous work of Widnall & Sullivan (1973) is discussed and their experimental results are compared with the predictions of the analysis presented here.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 66 , Issue 1 , 21 October 1974 , pp. 35 - 47
Copyright
© 1974 Cambridge University Press

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References

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