Vanishing viscosity limit for concentrated vortex rings
Analysis of PDEs
2022-12-22 v1 Mathematical Physics
math.MP
Abstract
We study the time evolution of a viscous incompressible fluid with axial symmetry without swirl, when the initial vorticity is very concentrated in 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 disjointed rings, each one of them performing a simple translation along the symmetry axis with constant speed.
Keywords
Cite
@article{arxiv.2209.02666,
title = {Vanishing viscosity limit for concentrated vortex rings},
author = {Paolo Buttà and Guido Cavallaro and Carlo Marchioro},
journal= {arXiv preprint arXiv:2209.02666},
year = {2022}
}
Comments
29 pages, LaTex. This article is an extension of the results in arXiv:1904.04785 and arXiv:2102.07807 and therefore draws from these articles