Collision of Almost Parallel Vortex Filaments |
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Authors: | Valeria Banica Erwan Faou Evelyne Miot |
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Institution: | 1. Laboratoire de Mathématiques et de Modélisation d'évry (UMR 8071), Université d'évry, évry, France;2. INRIA‐Rennes Bretagne Atlantique and IRMAR (UMR 6625), Université de Rennes I, Rennes, France;3. Centre de Mathématiques Laurent Schwartz (UMR 7640), école Polytechnique, Palaiseau, France |
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Abstract: | 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. |
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