Movement of solid filaments in axisymmetric fluid flow

David Meyer

doi:10.5802/jep.293

Movement of solid filaments in axisymmetric fluid flow
[Mouvement de filaments solides dans un écoulement fluide axisymétrique]

David Meyer ¹

¹ Instituto de Ciencias Matemáticas, Calle Nicolás Cabrera 13-15, 28049 Madrid, Spain

Journal de l’École polytechnique — Mathématiques, Tome 12 (2025), pp. 351-419.

Résumé
Abstract

Nous considérons le mouvement de minces filaments toroïdaux immergés dans un fluide à trois dimensions dont la dynamique est décrite par les équations d’Euler incompressibles. Les filaments sont régis par la mécanique newtonienne et interagissent avec le fluide par le biais de la pression exercée à leur bord. Nous supposons que les filaments sont quasiment rigides, dans le sens où le seul mouvement non rigide qu’ils peuvent subir est un changement de longueur, et aussi que le fluide est irrotationnel, avec une circulation non nulle autour de chaque filament. Nous démontrons que ce type d’interaction fluide-structure peut être décrit par un système d’EDO sur les positions des axes des filaments et qu’à la limite où la masse des filaments se réduit à zéro, ce système converge vers un système d’EDO similaire à la dynamique des anneaux tourbillonnaires.

We consider the movement of slender toroidal filaments immersed in a 3D fluid described by the incompressible Euler equations. The filaments are described by Newtonian mechanics and interact with the fluid through the pressure exerted at the boundary. We assume that the filaments are almost rigid in the sense that the only non-rigid movement they can undergo is a change of length and that the fluid is irrotational, but can have a nonzero circulation around the filaments. We show that this kind of system can be described through an ODE in the positions of the bodies and that in the limit, where the bodies shrink to massless filaments, the system converges to an ODE system similar to the dynamics of the corresponding vortex filaments.

Reçu le : 2023-12-12
Accepté le : 2025-02-21
Publié le : 2025-03-07

DOI : 10.5802/jep.293

Classification : 35Q31, 35Q70, 76B47
Keywords: Fluid-Solid system, axisymmetric fluid flow, vortex rings, leapfrogging, vanishing body limit
Mots-clés : Système fluide-structure, écoulement fluide axisymétrique, anneaux tourbillonnaires, phénomène de « leapfrogging », limite des filaments de masse nulle

Affiliations des auteurs :

David Meyer ¹

¹ Instituto de Ciencias Matemáticas, Calle Nicolás Cabrera 13-15, 28049 Madrid, Spain

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Movement of solid filaments in axisymmetric~fluid flow},
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David Meyer. Movement of solid filaments in axisymmetric fluid flow. Journal de l’École polytechnique — Mathématiques, Tome 12 (2025), pp. 351-419. doi : 10.5802/jep.293. https://jep.centre-mersenne.org/articles/10.5802/jep.293/

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