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A universal time scale for vortex ring formation

Gharib, Morteza and Rambod, Edmond and Shariff, Karim (1998) A universal time scale for vortex ring formation. Journal of Fluid Mechanics, 360 . pp. 121-140. ISSN 0022-1120.

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The formation of vortex rings generated through impulsively started jets is studied experimentally. Utilizing a piston/cylinder arrangement in a water tank, the velocity and vorticity fields of vortex rings are obtained using digital particle image velocimetry (DPIV) for a wide range of piston stroke to diameter (L/D) ratios. The results indicate that the flow field generated by large L/D consists of a leading vortex ring followed by a trailing jet. The vorticity field of the leading vortex ring formed is disconnected from that of the trailing jet. On the other hand, flow fields generated by small stroke ratios show only a single vortex ring. The transition between these two distinct states is observed to occur at a stroke ratio of approximately 4, which, in this paper, is referred to as the ‘formation number’. In all cases, the maximum circulation that a vortex ring can attain during its formation is reached at this non-dimensional time or formation number. The universality of this number was tested by generating vortex rings with different jet exit diameters and boundaries, as well as with various non-impulsive piston velocities. It is shown that the ‘formation number’ lies in the range of 3.6–4.5 for a broad range of flow conditions. An explanation is provided for the existence of the formation number based on the Kelvin–Benjamin variational principle for steady axis-touching vortex rings. It is shown that based on the measured impulse, circulation and energy of the observed vortex rings, the Kelvin–Benjamin principle correctly predicts the range of observed formation numbers.

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Additional Information:"Reprinted with the permission of Cambridge University Press." (Received 20 December 1996 and in revised form 10 November 1997) This work has been conducted through a grant from ONR (URI N00014-91-J-1610) and a grant from NIH (PHS-1-7R01-HL43287-03). We would like to thank Professor C. Pozrikidis and S.-H. Lam for numerous discussions regarding Hill's vortices and the vortex formation process. We are also indebted to Professor P. Saffman for pointing out that the pedigree of the energy maximization principle extends to Kelvin. Professors H. Johari and M. Rosenfeld, and Drs M. Hammache, F. Noca, and D. Dabiri; and R. Henderson and D. Jeon have, in various capacities, contributed to the progress and completion of this work.
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Deposited On:18 Jun 2005
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