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On a generalization of Kaden's problem

Published online by Cambridge University Press:  20 April 2006

D. I. Pullin  and
W. R. C. Phillips
D. I. Pullin
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville, Victoria 3052, Australia
W. R. C. Phillips
Affiliation:
Department of Mechanical and Production Engineering, University of Singapore, Kent Ridge, Singapore 0511
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Abstract

Kaden's problem of the roll-up of an initially planar semi-infinite vortex sheet with a parabolic distribution of circulation is extended to include vortex sheets exhibiting a general power law circulation distribution, resulting in the presence of a power law, and in one case a logarithmic-like, velocity-field singularity. Both semi-infinite and infinite initially plane sheets with this property are considered and the form of their roll-up in the similarity plane, into single and double-branched spirals respectively, is obtained numerically. Estimates of the Betz constant obtained from the solutions are found to be significantly different from values predicted by the Betz approximation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 104 , March 1981 , pp. 45 - 53
Copyright
© 1981 Cambridge University Press

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