On the formation and propagation of vortex rings and pairs of vortex rings

Abstract

Axisymmetric high-Reynolds-number laminar flows are simulated numerically. In particular, we consider the formation and propagation of single vortex rings from a circular orifice in a plane boundary, and pairs of vortex rings from a circular annulus in a plane boundary. During formation, single rings grow within an essentially potential flow, as in the similarity theory of Pullin (1979). When released they are shown to propagate in an almost inviscid manner, as described by Saffman (1970). Pairs of vortex rings, formed at a circular annulus, have been studied by Weidman & Riley (1993), both experimentally and computationally. They conclude from their observations that the behaviour of the rings depends primarily upon two parameters, namely the impulse applied to the fluid, during ring formation, and the gap width of the annulus. The results we present in this paper confirm the dependence of the flow on these parameters.