  Two vortex rings can form a localized configuration whereby they continually
pass through one another in an alternating fashion. This phenomenon is called
leapfrogging. Using parameters suitable for superfluid helium-4, we describe a
recurrence phenomenon that is similar to leapfrogging, which occurs for two
coaxial straight vortex filaments with the same Kelvin wave mode. For
small-amplitude Kelvin waves we demonstrate that our full Biot-Savart
simulations closely follow predictions obtained from a simpified model that
provides an analytical approximation developed for nearly parallel vortices.
Our results are also relevant to thin-cored helical vortices in classical
fluids.
