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Circulation and formation number of laminar vortex rings

Rosenfeld, Moshe and Rambod, Edmond and Gharib, Morteza (1998) Circulation and formation number of laminar vortex rings. Journal of Fluid Mechanics, 376 . pp. 297-318. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:ROSjfm98

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Abstract

The formation time scale of axisymmetric vortex rings is studied numerically for relatively long discharge times. Experimental findings on the existence and universality of a formation time scale, referred to as the `formation number', are confirmed. The formation number is indicative of the time at which a vortex ring acquires its maximal circulation. For vortex rings generated by impulsive motion of a piston, the formation number was found to be approximately four, in very good agreement with experimental results. Numerical extensions of the experimental study to other cases, including cases with thick shear layers, show that the scaled circulation of the pinched-off vortex is relatively insensitive to the details of the formation process, such as the velocity programme, velocity profile, vortex generator geometry and the Reynolds number. This finding might also indicate that the properly scaled circulation of steady vortex rings varies very little. The formation number does depend on the velocity profile. Non-impulsive velocity programmes slightly increase the formation number, while non-uniform velocity profiles may decrease it significantly. In the case of a parabolic velocity profile of the discharged flow, for example, the formation number decreases by a factor as large as four. These findings indicate that a major source of the experimentally found small variations in the formation number is the different evolution of the velocity profile of the discharged flow.


Item Type:Article
Additional Information:"Reprinted with the permission of Cambridge University Press." (Received 27 January 1997 and in revised form 24 July 1998).
Record Number:CaltechAUTHORS:ROSjfm98
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:ROSjfm98
Alternative URL:http://journals.cambridge.org/bin/bladerunner?30REQEVENT=&REQAUTH=0&500000REQSUB=&REQSTR1=S0022112098003115
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:427
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:17 Jun 2005
Last Modified:26 Dec 2012 08:40

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