SELF-INDUCED MOTION AND STABILITY OF CONCENTRATED VORTEX FILAMENTS
THE SELF-INDUCED MOTION AND STABILITY OF VORTEX FILAMENTS WAS INVESTIGATED BOTH THEORETICALLY AND EXPERIMENTALLY.THOUGH 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.(A)
