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Nested contour dynamics models for axisymmetric vortex rings and vortex wakes

Published online by Cambridge University Press:  01 May 2014

Clara O’Farrell  and
John O. Dabiri
Clara O’Farrell
Affiliation:
Control and Dynamical Systems, California Institute of Technology, Pasadena CA 91125, USA
John O. Dabiri*
Affiliation:
Graduate Aeronautical Laboratories and Bioengineering, California Institute of Technology, Pasadena CA 91125, USA
*
†Email address for correspondence: [email protected]
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Abstract

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.

JFM classification

Biological Fluid Dynamics: Propulsion Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 748 , 10 June 2014 , pp. 521 - 548
Copyright
© 2014 Cambridge University Press 

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