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Collision of Almost Parallel Vortex Filaments
Author(s) -
Banica Valeria,
Faou Erwan,
Miot Evelyne
Publication year - 2017
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21637
Subject(s) - vortex , physics , polygon (computer graphics) , classical mechanics , collision , work (physics) , circulation (fluid dynamics) , mechanics , symmetry (geometry) , point (geometry) , tourbillon , geometry , mathematics , quantum mechanics , telecommunications , computer security , frame (networking) , computer science
We investigate the occurrence of collisions in the evolution of vortex filaments through a system introduced by Klein, Majda, and Damodaran and Zakharov . 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 one of the self‐similar solutions of the model, described by the authors in an earlier work. In the second part of this paper we extend this construction to the case of an arbitrary number of filaments, with polygonal symmetry, that are perturbations of a configuration of parallel vortex filaments forming a polygon, with or without its center, rotating with constant angular velocity.© 2016 Wiley Periodicals, Inc.