vortex rings. Firstly, at the very first instants, the velocity profile at the exhaust exhibits extrema near the edge causing a large vorticity flux into the vortex ring. Secondly, as the ring grows in size at the edge of the exhaust, negative vorticity is generated on the outer wall of the generator which considerably reduces the circulation accumulated by the primary ring. Thirdly, as the boundary layer inside the pipe, or nozzle, thickens, the velocity profile approaches the one of a Poiseuille flow and the centerline velocity at the exhaust is measured to be larger than the prescribed piston speed. Last but not least, in the event the piston-generated vortex ring is pushed through the exhaust, it may interact or even merge with the primary vortex, hence modifying its characteristic, such as circulation, and potentially forcing the transition of the vortex ring to turbulence. Vortex ring structures are easily observable in nature. For instance, a mushroom cloud formed by a nuclear explosion or a volcano irruption, has a vortex ring-like structure. Vortex rings are also seen in many different biological flows; blood is discharged into the left ventricle of the human heart in the form of a vortex ring and jellyfishes or squids were shown to propel themselves in water by periodically discharging vortex rings in the surrounding. Finally, for more industrial applications, the synthetic jet which consists in periodically-formed vortex rings, was proved to be an appealing technology for flow control, heat and mass transfer and thrust generation Vortex formation number Prior to Gharib et al. (1998), few studies had focused on the formation of vortex rings generated with long stroke-to-diameter ratios , where is the length of the column of fluid discharged through the exhaust and is the diameter of the exhaust. For short stroke ratios, only one isolated vortex ring is generated and no fluid is left behind in the formation process. For long stroke ratios, however, the vortex ring is followed by some energetic fluid, referred as the trailing jet. On top of showing experimental evidence of the phenomenon, an explanation of the phenomenon was provided in terms of energy maximisation invoking a variational principle first reported by Kelvin and later proven by Benjamin (1976), or Friedman & Turkington (1981). Ultimately, Gharib et al. (1998) observed the transition between these two states to occur at a non-dimensional time , or equivalently a stroke ratio , of