The Velocity of Viscous Vortex Rings

The motion of vortex rings of small cross section is considered. A formula is derived for the velocity of a ring in an ideal fluid with an arbitrary distribution of vorticity in the core. The effects of viscosity are then examined. A definition of the velocity of an unsteady diffusing ring is given and it is shown that the method used to calculate the ring speed in an ideal fluid can be extended to give the velocity of a vortex ring subject to viscous diffusion.