Hostname: page-component-84b7d79bbc-x5cpj Total loading time: 0 Render date: 2024-07-28T20:33:32.369Z Has data issue: false hasContentIssue false
  • English
  • Français

A steady vortex ring close to Hill's spherical vortex

Published online by Cambridge University Press:  24 October 2008

J. Norbury
J. Norbury
Affiliation:
Department of Mathematics, University College, London
Get access Rights & Permissions [Opens in a new window]

Abstract

The existence of a steady vortex ring close to Hill's spherical vortex is established, and an approximate description of its boundary is given. The vorticity in the ring is proportional to the distance from the axis of symmetry. The core propagates steadily in an unbounded fluid at rest at infinity. The boundary of the vortex ring is close to an interior stream surface of Hill's vortex.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 2 , September 1972 , pp. 253 - 284
Copyright
Copyright © Cambridge Philosophical Society 1972

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

REFERENCES

(1)Hill, M. J.On a spherical vortex. Phil. Trans. Roy. Soc. A 185 (1894).Google Scholar
(2)Maruhn, K.Proc. 9th International Congress Appl. Mech. (Brussells, 1957), 1, 173.Google Scholar
(3)Fraenkel, L. E.On steady vortex rings of small cross-section in an ideal fluid. Proc. Roy. Soc. (London) Ser. A 316 (1970), 29.Google Scholar
(4)Fraenkel, L. E. Examples of steady vortex rings of small cross-section. To appear in J. Fluid Mech.Google Scholar
(5)Mikhlin, S. G.Linear Integral Equations (Hindustan, 1960).Google Scholar
(6)Kellogg, O. D.Potential theory (Springer, 1963).Google Scholar
(7)Smirnov, V. I.Higher Mathematics. V (Pergamon, 1964).Google Scholar
(8)Taylor, A. B.Introduction to Functional Analysis (Wiley, 1958).Google Scholar
(9)Hardy, G. H.Orders of Infinity (Cambridge University Press, 1924).Google Scholar
(10)Courant, and Hilbert, Methods of Math. Physics. II (Interscience, 1962).Google Scholar
(11)Norbury, J. A family of steady vortex rings, numerical and asymptotic results. To be submitted to J. Fluid Mech.Google Scholar
(12)Fraenkel, L. E. On the method of matched asymptotic expansions. Proc. Cambridge Philos. Soc. 65, 209.CrossRefGoogle Scholar
(13)Erdélyi, et al. Tables of integral transforms. II (McGraw-Hill, 1953).Google Scholar