Numerical experiments on vortex ring formation (Q2710454)

Vortex ring formation by long-duration nonconservative force, simulating experimental vortex ring generation with large stroke ratio, is studied numerically. For sufficiently long-duration forces, the authors investigate the extent to which the properties of the leading vortex ring are invariant under the force distribution. The results confirm the existence of a universal formation number defined by \textit{M. Gharib}, \textit{E. Rambod} and \textit{K. Shariff} [ibid. 360, 121-140 (1998; Zbl 0922.76021)], beyond which the leading vortex ring is separated from a trailing jet. It is found that, if the rate of generation of the integrals of motion is constant during the forcing period, and if the shear layer is sufficiently thin (and the Reynolds number sufficiently high), the leading vortex ring pinches off the normalized energy and circulation of about 0.3 and 2.0, respectively, consistent with the theoretical predictions of \textit{K. Mohseni} and \textit{M. Gharib} [Phys. Fluids 10, 2436 ff (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. It is also demonstrated 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. The normalized energy and circulation of the leading vortex rings are shown to be consistent well with the same properties of vortices in Norbury family with the same mean core radius.