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A note on liquid vortex sloshing and Kelvin's equilibria

Published online by Cambridge University Press:  26 April 2006

Georgios H. Vatistas
Georgios H. Vatistas
Affiliation:
Mechanical Engineering Department, Concordia University, Montreal, Canada
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Abstract

Observations of liquid vortex sloshing and Kelvin's equilibrium states were made inside a cylindrical container using a spinning disk near its base. Both steady and periodic free-surface sloshing phenomena were found to take place. During periodic sloshing, the air core sustained shape transformations, assuming an elliptical cross-section at the end, and then collapsed forming a pair of vortices. Kelvin's equilibrium states emerged at lower liquid levels. These were stable within an interval of rotational speeds. The bandwidth of stationary states decreased as the wavenumber (N) increased. For N greater than six, the states appeared critically stable. Between equilibria, unstable transitional regions were found to exist. As the liquid level was decreased, the core shape spectrum shifted towards smaller frequencies.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 217 , August 1990 , pp. 241 - 248
Copyright
© 1990 Cambridge University Press

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References

Escudier, M. 1987 Confined vortices in flow machinery. Ann. Rev. Fluid Mech. 19, 27–52.Google Scholar
Feynman, R. P. 1954 Atomic theory of two-fluid model of liquid helium. Phys. Rev. 94, 262–277.Google Scholar
Helfrich, R. K. & Send, U. 1988 Finite-amplitude evolution of two-layer geostrophic vortices. J. Fluid Mech. 197, 331–348.Google Scholar
Holter, J. N. & Glasscock, R. W. 1952 Vibrations of evaporating liquid drops. J. Acoust. Soc. Am. 24, 682–686.Google Scholar
Kelvin, Lord 1880 On the vibrations of a columnar vortex. Phil. Mag. 5(10), 155–168. Also in Lamb, H. 1932 Hydrodynamics. Sixth ed. Cambridge University Press, 783 pp.Google Scholar
Knauss, J. (ed.) 1987 Swirling Flow Problems at Intakes. A. A. Balkema. 165 pp.
Kozlov, V. F. & Makarov, V. G. 1985 Simulation of the instability of axisymmetric vortices using the contour dynamics method. Fluid Dyn. 20, 28–34.Google Scholar
Markus, S. 1988 The Mechanics of Vibrations of Cylindrical Shells. Studies in Applied Mechanics vol. 17. Elsevier. 159 pp.
Maxworthy, T. 1972 A vorticity source for large dust devils and other comments on naturally occurring columnar vortices. J. Atmos. Sci. 30, 1717–1722.Google Scholar
Maxworthy, T., Hopfinger, E. J. & Redekopp, L. G. 1985 Wave motions on vortex cores. J. Fluid Mech. 151, 141–165.Google Scholar
Vatistas, G. H. 1989 Analysis of fine particle concentrations in a combined vortex. J. Hydraul. Res. 27, 417–427.Google Scholar
Ward, N. B. 1972 The exploration of certain features of tornado dynamics using a laboratory model. J. Atmos. Sci 29, 1194–1204.Google Scholar
Yarmchuk, E. J., Gordon, J. V. & Packard, R. E. 1979 Observation on stationary vortex arrays in rotating superfluid helium. Phys. Rev. Lett. 43, 214–217.Google Scholar