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Wave motions on vortex cores

Published online by Cambridge University Press:  20 April 2006

T. Maxworthy ,
E. J. Hopfinger  and
L. G. Redekopp
T. Maxworthy
Affiliation:
Institut de Mécanique (Laboratoire Associé au CNRS), Université de Grenoble, B.P. n° 68, 38402 St Martin d'Hères Cedex, France Permanent address: Departments of Mechanical and Aerospace Engineering, University of Southern California, Los Angeles, CA 90039-1453, U.S.A.
E. J. Hopfinger
Affiliation:
Institut de Mécanique (Laboratoire Associé au CNRS), Université de Grenoble, B.P. n° 68, 38402 St Martin d'Hères Cedex, France
L. G. Redekopp
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, CA 90089-1454, U.S.A.
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Abstract

The observation of large-amplitude ‘kink’ waves on the vortex cores produced by an oscillating grid in a rotating fluid (Hopfinger, Browand & Gagne 1982) has motivated the study of such waves under more controlled circumstances. We have experimentally observed the properties of helical waves, rotating, plane standing waves and evolving, isolated kink-waves. Their characteristics have been related to theories based on the localized induction equation of Arms & Hama (1965), the ‘cut-off’ theory of Crow (1970) as extended by Moore & Saffman (1972), and an extension of Pocklington's (1895) dispersion relationship for ‘hollow-core’ vortices. It is shown that the latter dispersion relation and the Moore & Saffman theory are good approximations to our experimental results. Using these, we present new results on solitary kink-wave properties of concentrated vortex flows, and in particular show that envelope solitons are possible only for a restricted range of carrier wavenumbers. A second class of waves was also observed: the axisymmetric solitary waves of Benjamin (1967). These were found to become unstable to spiral disturbances when their amplitude exceeded a certain magnitude, as has been found in the study of the related vortex-breakdown phenomenon. All of these observations are used to interpret the experiments presented by HBG and to discuss qualitatively the dynamics of rotating turbulence. In the Appendix we propose a possible mechanism by which concentrated vortices can be formed in a rotating turbulent fluid.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 151 , February 1985 , pp. 141 - 165
Copyright
© 1985 Cambridge University Press

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