SELF-INDUCED MOTION AND STABILITY OF CONCENTRATED VORTEX FILAMENTS.
The self-induced motion and stability of vortex filaments is investigated both theoretically and experimentally. Through an application of the method of matched asymptotic expansions, a general solution is obtained for the self-induced motion of a vortex filament containing an arbitrary distribution of swirl and possibly axial velocities. This solution has been applied to several vortex-flow stability problems: the stability of a vortex line containing an axial jet, the mutual inductance instability of a vortex pair and the instability of helical vortex filaments and vortex rings. Only the results for the vortex ring are discussed in detail. Experimental studies of a vortex ring using a Laser Doppler Velocimeter were performed to determine the circulation and vorticity distribution within the vortex rings. Comparison of the observed vortex-ring motion and instability with theoretical predictions are presented.
