Mohseni, Kamran and Ran, Hongyu and Colonius, Tim (2001) Numerical experiments on vortex ring formation. Journal of Fluid Mechanics, 430 . pp. 267-282. ISSN 0022-1120 http://resolver.caltech.edu/CaltechAUTHORS:MOHjfm01
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Numerical simulations are used to study the formation of vortex rings that are generated by applying a non-conservative force of long duration, simulating experimental vortex ring generation with large stroke ratio. For sufficiently long-duration forces, we investigate the extent to which properties of the leading vortex ring are invariant to the force distribution. The results confirm the existence of a universal ‘formation number’ defined by Gharib, Rambod & Shariff (1998), beyond which the leading vortex ring is separated from a trailing jet. We find that the formation process is governed by two non-dimensional parameters that are formed with three integrals of the motion (energy, circulation, and impulse) and the translation velocity of the leading vortex ring. Limiting values of the normalized energy and circulation of the leading vortex ring are found to be around 0.3 and 2.0, respectively, in agreement with the predictions of Mohseni & Gharib (1998). It is shown that under this normalization smaller variations in the circulation of the leading vortex ring are obtained than by scaling the circulation with parameters associated with the forcing. We show that by varying the spatial extent of the forcing or the forcing amplitude during the formation process, thicker rings with larger normalized circulation can be generated. Finally, the normalized energy and circulation of the leading vortex rings compare well with the same properties for vortices in the Norbury family with the same mean core radius.
|Additional Information:||© Cambridge University Press 2001. Reprinted with permission. (Received 17 December 1999 and in revised form 14 June 2000) Published online 22 June 2001. The authors would like to acknowledge many helpful discussions with Professor Mory Gharib. We are also grateful to the National Science Foundation (Grant CTS-9501349) for supporting the development of the numerical simulation code used for this study.|
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|Deposited On:||14 Mar 2007|
|Last Modified:||26 Dec 2012 09:33|
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