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Issue ESAIM: Proc.
Volume 7, 1999
Third International Workshop on Vortex Flows and Related Numerical Methods
Page(s) 270 - 279
DOI http://dx.doi.org/10.1051/proc:1999025

ESAIM: Proc., 1999, Vol. 7, pp. 270-279
DOI: 10.1051/proc:1999025

The different equations of motion of the central line of a slender vortex filament and their use to study perturbed vortices

D. Margerit and J-P. Brancher

LEMTA (CNRS UMR 7563) 2 avenue de la forêt de Haye BP 160 54504 Vandoeuvre les Nancy, France


Abstract
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.



© EDP Sciences, ESAIM 1999


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