As shown by Crow in 1970, the evolution of two almost parallel vortex filaments with opposite circulation exhibits a long-wave instability. Ultimately, the symmetric mode increases its amplitude reconnecting both filaments and ending into the formation of an almost periodic structure of vortex rings. This is a universal process, which appears in a wide range of scales: from the vortex trails behind an airplane to a microscopic scale of superfluids and Bose–Einstein condensates. In this paper, I will focus on the vortex reconnection for the latter case by employing Gross–Pitaevskii theory. Essentially, I focus on the well-known laws of interaction and motion of vortex filaments. By means of numerical simulations, as well as theoretically, I show that a self-similar finite-time dynamics manifests near the reconnection time. A self-similar profile is selected showing excellent agreement with numerical simulations.
Comme le montre Crow en 1970, l'évolution de deux filaments de vortex presque parallèles à circulation opposée présente une instabilité à grand longueur d'onde. Le mode symétrique augmente d'amplitude en reconnectant les deux filaments et se termine par la formation d'une structure presque périodique d'anneaux de vortex. Il s'agit d'un processus universel qui apparaît à différentes échelles : des allées de vortex derrière un avion à l'échelle microscopique des superfluides et des condensats de Bose–Einstein. Dans cet article, je me concentre sur la reconnection de vortex pour le dernier cas en utilisant la théorie de Gross–Pitaevskii. Je me concentre essentiellement sur les lois bien connues de l'interaction et du mouvement des filaments de vortex. À l'aide de simulations numériques ainsi que théoriquement, je montre qu'une dynamique en temps fini auto-similaire se manifeste près du temps de reconnection. Un profil auto-similaire est sélectionné, montrant un excellent accord avec les simulations numériques.
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Mots-clés : Reconnection de vortex, Filaments de vorticité, Équation de Gross–Pitaevskii, Solutions auto-similaires
Sergio Rica 1, 2, 3
@article{CRMECA_2019__347_4_365_0,
author = {Sergio Rica},
title = {Self-similar vortex reconnection},
journal = {Comptes Rendus. M\'ecanique},
pages = {365--375},
publisher = {Elsevier},
volume = {347},
number = {4},
year = {2019},
doi = {10.1016/j.crme.2019.03.011},
language = {en},
}
Sergio Rica. Self-similar vortex reconnection. Comptes Rendus. Mécanique, Patterns and dynamics: homage to Pierre Coullet / Formes et dynamique: hommage à Pierre Coullet, Volume 347 (2019) no. 4, pp. 365-375. doi : 10.1016/j.crme.2019.03.011. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.03.011/
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