Collisions of Vortex Filament Pairs
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- 作者：Valeria Banica (1)
Erwan Faou (2)
Evelyne Miot (3) - 关键词：Fluid mechanics ; Pairs of vortex filaments ; Collisions ; Self ; similar solutions ; Schr?dinger equation ; Numerical simulations ; 35Q35 ; 35Q55 ; 35B44 ; 65M22
- 刊名：Journal of Nonlinear Science
- 出版年：2014
- 出版时间：December 2014
- 年：2014
- 卷：24
- 期：6
- 页码：1263-1284
- 全文大小：829 KB
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Erwan Faou (2)
Evelyne Miot (3)
1. Laboratoire de Mathématiques et de Modélisation d’évry (UMR 8071), Université d’évry, 23 Bd. de France, 91037, Evry, France
2. Département de mathématiques et applications (UMR 8553), ENS, 45 rue d’Ulm, 75005, Paris, France
3. Centre de Mathématiques Laurent Schwartz (UMR 7640), école Polytechnique, 91128, Palaiseau, France - ISSN：1432-1467
文摘
We consider the problem of collisions of vortex filaments for a model introduced by Klein et al. (J Fluid Mech 288:201-48, 1995) and Zakharov (Sov Phys Usp 31(7):672-74, 1988, Lect. Notes Phys 536:369-85, 1999) to describe the interaction of almost parallel vortex filaments in three-dimensional fluids. Since the results of Crow (AIAA J 8:2172-179, 1970) 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.