Cooperative elliptic instability of a vortex pair
摘要：
In this paper, we investigate the three-dimensional instability of a counter-rotating vortex pair to short waves, which are of the order of the vortex core size, and less than the inter-vortex spacing. Our experiments involve detailed visualizations and velocimetry to reveal the spatial structure of the instability for a vortex pair, which is generated underwater by two rotating plates. We discover, in this work, a symmetry-breaking phase relationship between the two vortices, which we show to be consistent with a kinematic matching condition for the disturbances evolving on each vortex. In this sense, the instabilities in each vortex evolve in a coupled, or 'cooperative', manner. Further results demonstrate that this instability is a manifestation of an elliptic instability of the vortex cores, which is here identified clearly for the first time in a real open flow. We establish a relationship between elliptic instability and other theoretical instability studies involving Kelvin modes. In particular, we note that the perturbation shape near the vortex centres is unaffected by the finite size of the cores. We find that the long-term evolution of the flow involves the inception of secondary transverse vortex pairs, which develop near the leading stagnation point of the pair. The interaction of these short-wavelength structures with the long-wavelength Crow instability is studied, and we observe significant modifications in the longevity of large vortical structures.
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关键词：
Experimental/ flow instability flow visualisation vortices/ elliptic instability vortex pair three-dimensional instability counter-rotating vortex pair vortex core size inter-vortex spacing visualization velocimetry spatial structure rotating plates symmetry-breaking phase relationship kinematic matching condition open flow Kelvin modes vortex centres long-term evolution secondary transverse vortex pairs long-wavelength Crow instability vortical structures/ A4720 Hydrodynamic stability and instability A4730 Rotational flow, vortices, buoyancy and other flows involving body forces
DOI：
10.1063/1.4934350
被引量：
年份：
1998
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