Collision of almost parallel vortex filaments
Analysis of PDEs
2015-07-03 v1
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.
Keywords
Cite
@article{arxiv.1507.00549,
title = {Collision of almost parallel vortex filaments},
author = {Valeria Banica and Erwan Faou and Evelyne Miot},
journal= {arXiv preprint arXiv:1507.00549},
year = {2015}
}