Generation and development of a viscous vortex ring

The vorticity transport and definition of vorticity equations are derived for an axisymmetric incompressible viscous vortex ring. The coupled system is solved numerically by the Peaceman-Rachford method and the method of successive over-relaxation. Instantaneous streaklines, velocity vector fields, vorticity contours, and streamline patterns offer a detailed picture of vortex ring generation. Results compare well with experimental observations of the behavior of viscous vortex rings. The radius, trajectory, and velocity of the ring are calculated and employed to predict the propagation velocity of the vortex ring using the vortex models of Helmholtz and Hill.