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The number of waves on unstable vortex rings

Published online by Cambridge University Press:  12 April 2006

P. G. Saffman
P. G. Saffman
Affiliation:
Applied Mathematics, California Institute of Technology, Pasadena
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Abstract

An explanation is proposed for the dependence on Reynolds number and other parameters of the number of waves which appear on vortex rings formed by pushing fluid out of a tube. It is shown that the number of waves can be sensitive to the vorticity distribution in the core of the ring. The process of ring formation is discussed and it is concluded that peaked vorticity distributions, limited by viscosity, will occur. Quantitative estimates of the number of waves are made. Agreement with observation is satisfactory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 84 , Issue 4 , 27 February 1978 , pp. 625 - 639
Copyright
© 1978 Cambridge University Press

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