A note on the leapfrogging between two coaxial vortex rings at low Reynolds numbers

In the early 1970s, Maxworthy J. Fluid. Mech. 51, 15 (1972) and Oshima et al. J. Phys. Soc. Jpn. 38, 1159 (1975) attempted to produce leapfrogging between two coaxial vortex rings at low Reynolds numbers in their laboratories. However, the rings failed to undergo the classical leapfrogging behavior and merged to form a single ring. In a recent numerical study, Shariff et al. (NASA Tech. Memo. 102257, 1989) attributed the failure partly to the effect of core distortion. They pointed out that vortex cores at low Reynolds numbers are thicker and therefore more susceptible to distortion during the leapfrogging. In this Brief Communication, it is shown through a systematic investigation that the initial generating condition also plays an important role in determining the success or failure of leapfrogging. The common belief that leapfrogging can be achieved simply by generating two vortex rings in quick succession may not be true for all flow conditions, especially when the Reynolds number is low. This finding may help to explain the results of Maxworthy and Oshima et al.