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The evolution of an elliptic vortex ring

Published online by Cambridge University Press:  20 April 2006

M. R. Dhanak  and
B. DE Bernardinis
M. R. Dhanak
Affiliation:
Department of Mathematics, Imperial College, London
B. DE Bernardinis
Affiliation:
Department of Mathematics, Imperial College, London
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Abstract

The evolution of a vortex ring in an ideal fluid under self-induction from a flat and elliptic configuration is followed numerically using the cut-off approximation (Crow 1970) for the velocity at the vortex. Calculations are presented for four different axes ratios of the initial ellipse. A particular choice is made for the core size and vorticity distribution in the core of the vortex ring. When the initial axes ratio is close to 1, the vortex ring oscillates periodically. The periodicity is lost as more eccentric cases are considered. For initial axes ratio 0·2, the calculations suggest a break-up of the ring through the core at one portion of the ring touching that at another, initially distant, portion of the ring.

Results from quantitative experiments, conducted at moderate Reynolds number with the vortex rings produced by puffing air through elliptic orifices, are compared with the calculations. The agreement is fairly good and it is found that a vortex ring produced from an orifice of axes ratio 0·2 breaks up into two smaller rings. The relevance of the results to the vortex trail of an aircraft is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 109 , August 1981 , pp. 189 - 216
Copyright
© 1981 Cambridge University Press

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