Comptes Rendus
no. 2
Exact geometric theory for flexible, fluid-conducting tubes
[Théorie géométriquement exacte des tuyaux souples avec écoulement interne]
François Gay-Balmaz1  ; Vakhtang Putkaradze2
1 LMD – École normale supérieure de Paris – CNRS, 75005 Paris, France
2 Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada
Comptes Rendus. Mécanique, Volume 342 (2014) no. 2, pp. 79-84.

L'instabilité des tuyaux souples avec écoulement interne, ou « instabilité du tuyau d'arrosage », est un phénomène commun, étudié de longue date, et qui a d'importantes applications. Cependant, les travaux antérieurs ne tiennent pas compte d'un effet crucial : la dynamique de la section transversale du tube. Nous montrons comment l'inclure dans la dynamique en utilisant un principe de Hamilton avec contrainte, couplant la dynamique d'une tige géométriquement exacte et celle de l'écoulement interne. Nous prouvons que cela affecte l'instabilité et calculons une classe de solutions exactes de type ondes progressives.

Instability of flexible tubes conducting fluid, or “garden hose instability”, is a phenomenon both familiar from everyday life and important for applications, which has been actively studied. However, previous works did not consider one of the most crucial physical effects — the dynamical change of the cross-section. We show how to consistently address this issue by coupling the geometrically exact rod dynamics with the fluid motion via the use of a constrained Hamilton's variational principle. We find strong effect of this dynamics on stability, and derive a variety of exact nonlinear solutions of traveling-wave type.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2014.01.001
Keywords: Fluid–structure interactions, Flexible tubes, Garden hose instability, Geometrically exact models, Variational principles
Mot clés : Interaction fluide–structure, Tuyaux souples, Instabilité du tuyau d'arrosage, Modèles géométriquement exacts, Principes variationels
François Gay-Balmaz 1 ; Vakhtang Putkaradze 2

1 LMD – École normale supérieure de Paris – CNRS, 75005 Paris, France
2 Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada 
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François Gay-Balmaz; Vakhtang Putkaradze. Exact geometric theory for flexible, fluid-conducting tubes. Comptes Rendus. Mécanique, Volume 342 (2014) no. 2, pp. 79-84. doi : 10.1016/j.crme.2014.01.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.01.001/

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