Geodesic
The different equations of motion of the central line of a slender vortex filament and their use to study perturbed vortices
D. Margerit1 ; J-P. Brancher1
1 LEMTA (CNRS UMR 7563) 2 avenue de la forêt de Haye BP 160 54504 Vandoeuvre les Nancy, France
ESAIM. Proceedings, Tome 7 (1999), pp. 270-279.

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A comparison between the equation of motion of the central line of a slender vortex filament deduced from a matched asymptotic expansion(A. Callegari and L. Ting) and the expansion of the equation of motion of the ad-hoc cut-off methods(S. Crow) with the cut-off length as the small asymptotic parameter is performed. It justifies the cut-off methods and gives the link between the cut-off lengths and the thickness of a viscous or inviscid vortex with an axial velocity component. The asymptotic equation of motion for an open filament is then simplified in case of a perturbed straight filament and different regimes are displayed. They depend of relatives values of the amplitude of the perturbation and the small thickness of the filament.
DOI : 10.1051/proc:1999025

D. Margerit 1 ; J-P. Brancher 1

1 LEMTA (CNRS UMR 7563) 2 avenue de la forêt de Haye BP 160 54504 Vandoeuvre les Nancy, France 
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     title = {The different equations of motion of the central line of a slender vortex filament and their use to study perturbed vortices},
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D. Margerit; J-P. Brancher. The different equations of motion of the central line of a slender vortex filament and their use to study perturbed vortices. ESAIM. Proceedings, Tome 7 (1999), pp. 270-279. doi : 10.1051/proc:1999025. http://geodesic.mathdoc.fr/articles/10.1051/proc:1999025/

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