Collisions of vortex filament pairs

Abstract : We consider the problem of collisions of vortex filaments for a model introduced by Klein, Majda and Damodaran, and Zakharov to describe the interaction of almost parallel vortex filaments in three-dimensional fluids. Since the results of Crow examples of collisions are searched as perturbations of antiparallel translating pairs of filaments, with initial perturbations related to the unstable mode of the linearized problem; most results are numerical calculations. In this article we first consider a related model for the evolution of pairs of filaments and we display another type of initial perturbation leading to collision in finite time. Moreover we give numerical evidence that it also leads to collision through the initial model. We finally study the self-similar solutions of the model.
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https://hal.inria.fr/hal-00948563
Contributor : Erwan Faou <>
Submitted on : Tuesday, February 18, 2014 - 2:40:29 PM
Last modification on : Thursday, February 7, 2019 - 5:34:29 PM
Long-term archiving on : Sunday, May 18, 2014 - 11:51:14 AM

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  • HAL Id : hal-00948563, version 1
  • ARXIV : 1402.4418

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Valeria Banica, Erwan Faou, Evelyne Miot. Collisions of vortex filament pairs. Journal of Nonlinear Science, Springer Verlag, 2014, 24 (6), pp.22. ⟨hal-00948563⟩

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