Time evolution of concentrated vortex rings
| Autor: | Paolo Buttà, Carlo Marchioro |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Physics
Applied Mathematics 010102 general mathematics Mathematical analysis Time evolution Order (ring theory) FOS: Physical sciences Disjoint sets Mathematical Physics (math-ph) Vorticity Condensed Matter Physics 01 natural sciences Concentration approximation incompressible Euler flow vortex rings Vortex ring 010101 applied mathematics Physics::Fluid Dynamics Computational Mathematics Condensed Matter::Superconductivity Compressibility Limit (mathematics) 0101 mathematics Intensity (heat transfer) Mathematical Physics 76B47 37N10 |
| DOI: | 10.48550/arxiv.1904.04785 |
| Popis: | We study the time evolution of an incompressible fluid with axisymmetry without swirl when the vorticity is sharply concentrated. In particular, we consider $N$ disjoint vortex rings of size $\varepsilon$ and intensity of the order of $|\log\varepsilon|^{-1}$. We show that in the limit $\varepsilon\to 0$, when the density of vorticity becomes very large, the movement of each vortex ring converges to a simple translation, at least for a small but positive time. Comment: 24 pages. This updated version provides a new Appendix B, containing the corrected proof of Lemma 3.1. For the sake of clarity, this proof has already been included in arXiv:2102.07807 (where the results of this article have been extended) |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|