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/ris considered to a higher order of approximation, and the formulae given for this case appear to be useful for quite substantial cross-sections.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
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