Leapfrogging Kelvin waves

TL;DR

This paper investigates a leapfrogging-like recurrence phenomenon in vortex filaments with Kelvin waves, using simulations and analytical models, relevant to superfluid helium-4 and classical fluids.

Contribution

It introduces a new recurrence phenomenon in vortex filaments with Kelvin waves and validates simplified models with full Biot-Savart simulations.

Findings

Full simulations match analytical predictions for small-amplitude Kelvin waves.

Recurrence phenomenon observed in vortex filaments similar to leapfrogging.

Results applicable to superfluid helium-4 and classical fluid vortices.

Abstract

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.