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arXiv · 2105.01635

Time evolution of vortex rings with large radius and very concentrated vorticity

Guido Cavallaro·Carlo Marchioro
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Abstract

We study the time evolution of an incompressible fluid with axial symmetry without swirl when the vorticity is sharply concentrated on $N$ annuli of radii $\approx$ $r_0$ and thickness $\epsilon$. We prove that when $r_0= |\log \epsilon|^\alpha, \,\, \alpha>2$, the vorticity field of the fluid converges as $\epsilon \to 0$ to the point vortex model, at least for a small but positive time. This result generalizes a previous paper that assumed a power law for the relation between $r_0$ and $\epsilon$.

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Guido Cavallaro, Carlo Marchioro. 2021-05-04. Time evolution of vortex rings with large radius and very concentrated vorticity. https://doi.org/10.1063/5.0022358

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