Vortex ring pairs: numerical simulation and experiment

Abstract

In this paper we discuss the possibility that concentric vortex rings, with-associated circulation of opposite sign, can propagate steadily as a coherent pair. Inviscid flow considerations suggest that such a configuration, which we define as a vortex ring pair, may be possible. Numerical solutions of the Navier-Stokes equations for incompressible, laminar flow show that, although diffusion results in a continual redistribution of vorticity, a quasi-steadily propagating vortex ring pair could be attained in practice. Experiments are reported to test this idea by generating counterrotating vortex ring pairs by impulsive fluid motion through an annular orifice. Depending on the normalized impulse and the orifice radius ratio, the vortex rings are observed either (i) to propagate together until diffusive effects or vortex ring instability destroys the coherent motion, or (ii) the inner ring propagates to some maximum axial distance where it reverses its direction and returns to the orifice wall, leaving the outer ring free to continue its forward motion unabated. Numerical simulation shows that the stable flow of the vortex ring trajectories can be reasonably well reproduced. The boundary separating motion (i) from (ii) and the normalized inner ring penetration distance are found over the range of impulse and radius ratio covered by the experiments. Other observed features of vortex ring motion including self-similar trajectories of the spiral core centres during vortex sheet roll-up and ring instability are also presented.