Hostname: page-component-6bf8c574d5-mggfc Total loading time: 0 Render date: 2025-02-23T18:55:07.359Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

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

Bliss, D. B. 1970 The dynamics of curved rotational vortex lines. M.S. thesis, Massachusetts Institute of Technology.
Bliss, D. B. 1973 The dynamics of flows with high concentrations of vorticity. Ph.D. thesis, Massachusetts Institute of Technology.
Crow, S. C. 1970 Stability theory for a pair of trailing vortices A.I.A.A. J. 8, 2172.Google Scholar
Moore, D. W. & Saffman, P. G. 1972 The motion of a vortex filament with axial flow Phil. Trans. 272, 403–429.Google Scholar
Plobeck, L. V. 1974 Stability calculations for rotating gas flows. M.S. thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology.
Saffman, P. G. 1971 The velocity of viscous vortex rings Studies in Appl. Math. 49, 370–380.Google Scholar
Sullivan, J. P., Widnall, S. E. & Ezekiel, S. 1973 A study of vortex rings using a laser Doppler velocimeter A.I.A.A. J. 11, 1384–1398.Google Scholar
Thompson, J. J. 1883 A Treatise on the Motion of Vortex Rings. Macmillan.
Widnall, S. E., Bliss, D. B. & Zalay, A. 1971 Theoretical and experimental study of the stability of a vortex pair. In Aircraft Wake Turbulence and Its Detection, p. 305. Plenum.
Widnall, S. E. & Sullivan, J. P. 1973 On the stability of vortex rings. Proc. Roy. Soc A 332, 335–353.Google Scholar