Transport Properties Of Viscous Vortex Rings

This study involves the transport or stirring properties of viscous vortex rings. In order to take into account the Reynolds - number dependence, the method of entrainment diagrams is applied. The system for path lines of fluid particles is developed with the help of obtained analytical solution for a vortex ring. The idea of such approach is based on the property of this dynamical system to include complicated Reynolds - number dependence despite the fact that the linear solution of Navier-Stokes equations is used. Unsteady particle trajectories are examined as a bifurcation of an autonomous system with the initial Reynolds number as a parameter. It is shown that for small ratio of external and internal radiuses of the ring, three regimes of particle motion exist and the pattern bifurcates at a two Reynolds numbers of 140 and 640