The Fascination of Vortex Rings

We present inviscid and viscous models for the formation and propagation of single, and co-axial pairs of, vortex rings. Inviscid flows are based on both thin rings, and thick rings treated by a contour dynamics approach, whilst viscous flows are determined from numerical solutions of the Navier–Stokes equations. A kaleidoscope of different flow behaviours for these axisymmetric flows is presented.