The instability of the thin vortex ring of constant vorticity

A theoretical study indicating that vortex rings at moderate Reynolds numbers are unstable to azimuthal bending waves is presented. Only the case of a thin vortex ring with a core of constant vorticity in an inviscid flow is examined. The disturbance flow and the mean flow of the vortex ring are derived as asymptotic solutions near the core; the stability analysis is developed completely for a certain class of bending waves that are unstable on a line filament in the presence of strain. The vortex ring is found to be always unstable for at least two wavenumbers for which waves on a line filament of the same vorticity distribution would not rotate. Published experimental results are cited to support these conclusions.