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Pinch-off of non-axisymmetric vortex rings

O'Farrell, Clara and Dabiri, John O. (2014) Pinch-off of non-axisymmetric vortex rings. Journal of Fluid Mechanics, 740 . pp. 61-96. ISSN 0022-1120.

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The formation and pinch-off of non-axisymmetric vortex rings is considered experimentally. Vortex rings are generated using a non-circular piston–cylinder arrangement, and the resulting velocity fields are measured using digital particle image velocimetry. Three different nozzle geometries are considered: an elliptical nozzle with an aspect ratio of two, an elliptical nozzle with an aspect ratio of four and an oval nozzle constructed from tangent circular arcs. The formation of vortices from the three nozzles is analysed by means of the vorticity and circulation, as well as by investigation of the Lagrangian coherent structures in the flow. The results indicate that, in all three nozzles, the maximum circulation the vortex can attain is determined by the equivalent diameter of the nozzle: the diameter of a circular nozzle of identical cross-sectional area. In addition, the time at which the vortex rings pinch off is found to be constant along the nozzle contours, and independent of relative variations in the local curvature. A formation number for this class of vortex rings is defined based on the equivalent diameter of the nozzle, and the formation number for vortex rings of the three geometries considered is found to lie in the range of 3–4. The implications of the relative shape and local curvature independence of the formation number on the study and modelling of naturally occurring vortex rings such as those that appear in biological flows is discussed.

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Additional Information:© 2014 Cambridge University Press. Received 15 April 2013; revised 29 September 2013; accepted 29 November 2013; first published online 10 January 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 R.W. Whittlesey, who was responsible for the design of the AR4 nozzle, and who assisted in the design and construction of the experimental setup.
Funding AgencyGrant Number
NSF Graduate Research FellowshipUNSPECIFIED
Office of Naval Research (ONR)N000140810918
Office of Naval Research (ONR)N000141010137
Subject Keywords:biological fluid dynamics, vortex flows, wakes/jets
Record Number:CaltechAUTHORS:20140421-105244403
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Official Citation:Clara O’Farrell and John O. Dabiri (2014). Pinch-off of non-axisymmetric vortex rings . Journal of Fluid Mechanics, 740, pp 61-96 doi:10.1017/jfm.2013.639
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:45073
Deposited By: Tony Diaz
Deposited On:21 Apr 2014 20:41
Last Modified:21 Apr 2014 21:54

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