Vanishing viscosity limit for concentrated vortex rings

Abstract

We study the time evolution of a viscous incompressible fluid with axial symmetry without swirl, when the initial vorticity is very concentrated in $N$ disjoint rings. We show that in a suitable joint limit, in which both the thickness of the rings and the viscosity tend to zero, the vorticity remains concentrated in $N$ disjointed rings, each one of them performing a simple translation along the symmetry axis with constant speed.

arXiv comment29 pages, LaTex. This article is an extension of the results in arXiv:1904.04785 and arXiv:2102.07807 and therefore draws from these articles

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• Interaction of vortices in viscous planar flows
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• Time evolution of concentrated vortex rings
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Cited by in corpus (2)

• Vanishing viscosity limit for axisymmetric vortex rings
• Long time evolution of concentrated vortex rings with large radius