Vortex ring pinchoff in the presence of simultaneously initiated uniform background co-flow

Vortex rings were formed with a piston-cylinder mechanism in the presence of uniform background co-flow supplied through a shroud surrounding the cylinder. The jet and co-flow were started simultaneously. Ratios of the co-flow to jet velocity (Rv) in the range 0–1 were considered. The formation number (F) as a function of Rv was determined using the procedure of Gharib et al. [J. Fluid Mech. 360, 121 (1998)] and a generalized definition of formation time. The results show a sharp decrease in F as Rv increases from 0.5–0.75, suggesting possible performance limitations for pulsed-jet propulsion.