Experiments on long-wavelength instability and reconnection of a vortex pair

We present results from an experimental study of the long-wavelength Crow instability of a counter-rotating vortex pair. Employing a vortex generator in a water tank, comprising rotating horizontal computer-controlled flaps, we follow the vortices, marked by laser-induced fluorescence, using dual simultaneous light-sheets to determine the growth rate of the Crow instability as a function of the perturbation wavelength. In order to make a meaningful comparison to theory [S. C. Crow, AIAA J. 8, 2172 (1970); S. E. Widnall, Annu. Rev. Fluid Mech. 4, 141 (1975)], one requires, as input to the theory, the distribution of circumferential velocity and thereby the equivalent core size of the vortices. These distributions are measured using particle image velocimetry. The resulting agreement of the growth rates, between theory and experiment, appears to be very good. Of relevance to this study, we compute a stability diagram using the exact expression for the self-induced rotation speed of perturbation waves on the vortices. Measurement of the nondimensional reconnection time, when the vortex pair evolves into a series of rings at later times, is compared to existing numerical simulations, and we find evidence to suggest it varies with the inverse curvature of the vortices where they approach each other. The major axes of the resulting elliptical vortex rings switch with their minor axes, as the rings descend in the fluid, leading to a surprising phenomenon where the rings reconnect for the second time. By considering the conservation of impulse, and a linear relationship between the major axis length and the vortex spacing, we find that the relative descent speed of the rings increases with Reynolds number. It is coincidentally only at our chosen value that the descent speed of the subsequent rings appears to be close to the initial speed of the vortex pairs. Finally, the paper presents clear visualizations of the Crow instability phenomenon. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3531720]