A Unified Energy Feature of Vortex Rings for Identifying the Pinch-Off Mechanism

Abstract

Owing to the limiting effect of energy, vortex rings cannot grow indefinitely and thus pinch off. In this paper, experiments on the vortex rings generated using a piston-cylinder apparatus are conducted so as to investigate the pinch-off mechanisms and identify the limiting effect of energy. Both theoretical and experimental results show that the generated vortex rings share a unified energy feature, regardless of whether they are pinched-off or not. Moreover, the unified energy feature is quantitatively described by a dimensionless energy number γ, defined as γ=(E/I2Γωmax) and exhibiting a critical value γring = 0.14 ± 0.01 for the generated vortex rings. This unified energy feature reflects the limiting effect of energy and specifies the target of vortex ring formation. Furthermore, based on the tendency of γ during vortex ring formation, criteria for determining the two timescales, i.e., pinch-off time and separation time, which correspond to the onset and end of pinch-off process, respectively, are suggested.