Energy and velocity of a forming vortex ring

It is known that vortex rings formed by large stroke ratios (in a piston/cy linder arrangement) pinch off from their generating jets at a fairly consta nt universal time scale. In this paper we show that the hypothesis that at the pinch off the translational velocity of the ring equals the jet flow ve locity near the ring is equivalent to the recently proposed idea based on a variational principle by Kelvin and Benjamin that the pinch off occurs whe n the apparatus is no longer able to deliver energy at a rate required for steady vortex ring existence. A formula for the propagation velocity of a t hick vortex ring is also proposed and compared with available experimental data and empirical relations. (C) 2000 American Institute of Physics. [S107 0-6631(00)00703-0].