Kelvin wave and soliton propagation in classical viscous vortex filaments

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.