Collision of almost parallel vortex filaments

TL;DR

This paper rigorously demonstrates finite-time collision of almost parallel vortex filaments with opposite circulation and extends the analysis to multiple symmetric filaments, revealing collision mechanisms in vortex dynamics.

Contribution

It provides a rigorous proof of vortex filament collision and extends the construction to multiple symmetric filaments with perturbations.

Findings

Existence of colliding vortex filaments with opposite circulation.

Extension to multiple symmetric filaments with polygonal configurations.

Collision mechanism based on self-similar solutions.

Abstract

We investigate the occurrence of collisions in the evolution of vortex filaments through a system introduced by Klein, Majda and Damodaran [KMD95] and Zakharov [Z88,Z99]. We first establish rigorously the existence of a pair of almost parallel vortex filaments, with opposite circulation, colliding at some point in finite time. The collision mechanism is based on the one of the self-similar solutions of the model, described in [BFM14]. In the second part of this paper we extend this construction to the case of an arbitrary number of filaments, with polygonial symmetry, that are perturbations of a configuration of parallel vortex filaments forming a polygon, with or without its center, rotating with constant angular velocity.