MOTION OF AN ELLIPTIC VORTEX UNDER APPLIED PERIODIC STRAIN

The effect of subjecting a uniform elliptical vortex to a periodically varying plane straining field is considered. For plane steady straini ng fields, it is known that a Rankine-type vortex core of uniform vort icity and elliptical shape can exist in a state in which it (a) is ste ady and stationary, (b) rotates about its axis or nutates about a fixe d axis, or (c) elongates indefinitely, smearing the core into a thin l ayer. In state (a), for sufficiently weak straining fields, a vortex o f small enough aspect ratio of the ellipse persists under such a plane strain, being robust to small two-dimensional disturbances present in the flow field. It is shown that if, however, a small periodically va rying component is added to the basic straining field, then at frequen cies corresponding to the natural frequency of vibration of the vortex and their harmonics, a resonance phenomenon takes place which destabi lizes the apparently stable stationary vortex in finite time, causing it to flip from state (a) into states (b) or (c), in which action of i nstabilities associated with a higher, nonelliptical, mode of deformat ion of the vortex boundary by disturbances in the flow field would lea d to disintegration of the vortex structure. In fact it is found that the vortex also flips to states (b) and (c) for a range of non-natural frequencies of oscillation of the straining field. The effect of the periodic plane straining on the three-dimensional Crow instability is also discussed.