Effect of Slipping Motion on the Hasimoto Soliton on a Vortex Filament in Self-Induced Motion: An Exact Solution

TL;DR

This paper investigates how slipping motion due to viscosity affects the propagation of Hasimoto solitons on vortex filaments, providing an exact solution and identifying a critical slipping speed related to torsion.

Contribution

It presents an exact analytical solution describing the impact of slipping motion on Hasimoto solitons and identifies the critical slipping speed for soliton existence.

Findings

Strong slipping motion prevents Hasimoto soliton formation.

Critical slipping speed equals the torsion of the filament.

Exact solution characterizes the slipping effect on vortex filaments.

Abstract

A vortex filament immersed in a non-ideal fluid, thanks to viscous diffusion, experiences a slipping motion with respect to the fluid. In recognition of this, in this paper, the effect of this slipping motion on the Hasimoto soliton propagating on a vortex filament is investigated, and an exact solution is given to describe this process. A strong slipping motion is shown to prevent the existence of the Hasimoto soliton. The critical slipping speed (above which the Hasimoto soliton fails to exist) is shown to be equal to the torsion.