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A family of steady vortex rings

Published online by Cambridge University Press:  29 March 2006

J. Norbury
J. Norbury
Affiliation:
Department of Mathematics, University College London
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Abstract

Axisymmetric vortex rings which propagate steadily through an unbounded ideal fluid at rest at infinity are considered. The vorticity in the ring is proportional to the distance from the axis of symmetry. Recent theoretical work suggests the existence of a one-parameter family, [npar ]2 ≥ α ≥ 0 (the parameter α is taken as the non-dimensional mean core radius), of these vortex rings extending from Hill's spherical vortex, which has the parameter value α = [npar ]2, to vortex rings of small cross-section, where α → 0. This paper gives a numerical description of vortex rings in this family. As well as the core boundary, propagation velocity and flux, various other properties of the vortex ring are given, including the circulation, fluid impulse and kinetic energy. This numerical description is then compared with asymptotic descriptions which can be found near both ends of the family, that is, when α → [npar ]2 and α → 0.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 57 , Issue 3 , 20 February 1973 , pp. 417 - 431
Copyright
© 1973 Cambridge University Press

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References

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Norbury, J. 1972 A steady vortex ring close to Hill. s spherical vortex. Proc. Comb. Phil. Soc. 72, 253Google Scholar
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