COOPERATIVE ELLIPTIC INSTABILITY OF A VORTEX PAIR

In this paper, we investigate the three-dimensional instability of a c ounter-rotating vortex pair to short waves, which are of the order of the vortex core size, and less than the inter-vortex spacing. Our expe riments involve detailed visualizations and velocimetry to reveal the spatial structure of the instability for a vortex pair, which is gener ated underwater by two rotating plates. We discover, in this work, a s ymmetry-breaking phase relationship between the two vortices, which we show to be consistent with a kinematic matching condition for the dis turbances evolving on each vortex. In this sense, the instabilities in each vortex evolve in a coupled, or 'cooperative', manner. Further re sults demonstrate that this instability is a manifestation of an ellip tic instability of the vortex cores, which is here identified clearly for the first time in a real open flow. We establish a relationship be tween elliptic instability and other theoretical instability studies i nvolving Kelvin modes. In particular, we note that the perturbation sh ape near the vortex centres is unaffected by the finite size of the co res. We find that the long-term evolution of the flow involves the inc eption of secondary transverse vortex pairs, which develop near the le ading stagnation point of the pair. The interaction of these short-wav elength structures with the long-wavelength Crow instability is studie d, and we observe significant modifications in the longevity of large vortical structures.