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Examples of steady vortex rings of small cross-section in an ideal fluid

Published online by Cambridge University Press:  29 March 2006

L. E. Fraenkel
L. E. Fraenkel
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Cambridge
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Abstract

The existence theory for steady vortex rings of small cross-section is used to derive asymptotic formulae that describe the shape and overall properties of such rings. A certain two-parameter family of rings is studied in detail, to a first approximation; for members of this family, the ratio ω/r (of vorticity to cylindrical radius) falls from a positive maximum at a central point of the core cross-section to a value at the core boundary that can be substantially smaller or even negative. The case of uniform ω/r is considered to a higher order of approximation, and the formulae given for this case appear to be useful for quite substantial cross-sections.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 51 , Issue 1 , 11 January 1972 , pp. 119 - 135
Copyright
© 1972 Cambridge University Press

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