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Published June 2014 | Published
Journal Article Open

Nested contour dynamics models for axisymmetric vortex rings and vortex wakes


Inviscid models for vortex rings and dipoles are constructed using nested patches of vorticity. These models constitute more realistic approximations to experimental vortex rings and dipoles than the single-contour models of Norbury and Pierrehumbert, and nested contour dynamics algorithms allow their simulation with low computational cost. In two dimensions, nested-contour models for the analytical Lamb dipole are constructed. In the axisymmetric case, a family of models for vortex rings generated by a piston–cylinder apparatus at different stroke ratios is constructed from experimental data. The perturbation response of this family is considered by the introduction of a small region of vorticity at the rear of the vortex, which mimics the addition of circulation to a growing vortex ring by a feeding shear layer. Model vortex rings are found to either accept the additional circulation or shed vorticity into a tail, depending on the perturbation size. A change in the behaviour of the model vortex rings is identified at a stroke ratio of three, when it is found that the maximum relative perturbation size vortex rings can accept becomes approximately constant. We hypothesise that this change in response is related to pinch-off, and that pinch-off might be understood and predicted based on the perturbation responses of model vortex rings. In particular, we suggest that a perturbation response-based framework can be useful in understanding vortex formation in biological flows.

Additional Information

© 2014 Cambridge University Press. Received 26 May 2013; revised 9 March 20l4; accepted 5 April 2014; first published online 1 May 2014. This work was funded by an NSF Graduate Research Fellowship to C.O'F. and by Office of Naval Research awards N000140810918 and N000141010137 to J.O.D. The authors gratefully acknowledge the contributions of Professor Tony Leonard, through many helpful discussions on the axisymmetric contour dynamics formulation.

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Published - O'Farrell_2014p521.pdf

Published - O=0027Farrell_2014p521.pdf


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