Kelvin wave and soliton propagation in classical viscous vortex filaments

TL;DR

This paper uses numerical simulations to study Kelvin waves and solitons in viscous vortex filaments, confirming theoretical predictions and demonstrating the potential for experimental observation of vortex solitons.

Contribution

It provides numerical evidence of Kelvin wave dispersion relations and vortex solitons, and proposes an experimental setup for their generation.

Findings

Kelvin wave dispersion matches Lord Kelvin's predictions.

Existence of vortex solitons confirmed numerically.

Proposed feasible experiment for vortex soliton generation.

Abstract

Vortex filaments are highly rotating localized structures of fluids that admits several types of excitation. Here, we study them by using numerical simulations of the three-dimensional incompressible Navier-Stokes equations. We first address the propagation of Kelvin waves, helicoidal excitations propagating along the filament, and measure their dispersion relation which turns out to be in good agreement with the original Lord Kelvin predictions. Then, inspired by the connection between vortex line dynamics and an integrable system, we show numerically the existence of solitons propagating along vortex filaments and study the collision of two of such structures. Finally, we show numerically the experimental feasibility of studying vortex solitons in the lab, by proposing an experiment for their generation.