Numerical experiments on vortex ring formation

• Published in: Journal of fluid mechanics Vol. 430; pp. 267 - 282
• Main Authors: MOHSENI, KAMRAN, RAN, HONGYU, COLONIUS, TIM
• Format: Journal Article
• Language: English
• Published: Cambridge Cambridge University Press 10.03.2001
• Subjects: Circulation; Computational fluid dynamics; Computer simulation; Constraining; Exact sciences and technology; Fluid dynamics; Fluid mechanics; Fundamental areas of phenomenology (including applications); Invariants; Mathematical models; Physics; Rotational flow and vorticity; Translations; Vortex dynamics; Vortex rings; Compressible fluid; Digital simulation; Vorticity; Ring vortex; Velocity distribution; Vortex flow; Linear momentum; Axial symmetry; Navier-Stokes equations
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112000003025

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.