A NOTE ON THE LEAPFROGGING BETWEEN 2 COAXIAL VORTEX RINGS AT LOW REYNOLDS-NUMBERS

In the early 1970s, Maxworthy [J. Fluid. Mech. 51, 15 (1972)] and Oshi ma et al. [J. Phys. Soc. Jpn. 38, 1159 (1975)] attempted to produce le apfrogging between two coaxial vortex rings at low Reynolds numbers in their laboratories. However, the rings failed to undergo the classica l leapfrogging behavior and merged to form a single ring. In a recent numerical study, Shariff et al. (NASA Tech. Memo. 102257, 1989) attrib uted the failure partly to the effect of core distortion. They pointed out that vortex cores at low Reynolds numbers are thicker and therefo re more susceptible to distortion during the leapfrogging. In this Bri ef Communication, it is shown through a systematic investigation that the initial generating condition also plays an important role in deter mining 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 w hen the Reynolds number is low. This finding may help to explain the r esults of Maxworthy and Oshima et al. (C) 1997 American Institute of P hysics.