Abstract
A classical problem in fluid dynamics concerns the interaction of multiple vortex rings sharing a common axis of symmetry in an incompressible, inviscid three-dimensional fluid. In 1858, Helmholtz observed that a pair of similar thin, coaxial vortex rings may pass through each other repeatedly due to the induced flow of the rings acting on each other. This celebrated configuration, known as leapfrogging, has not yet been rigorously established. We provide a mathematical justification for this phenomenon by constructing a smooth solution of the 3D Euler equations exhibiting this motion pattern.
| Original language | English |
|---|---|
| Pages (from-to) | 3843-3957 |
| Number of pages | 115 |
| Journal | Communications on Pure and Applied Mathematics |
| Volume | 77 |
| Issue number | 10 |
| Early online date | 6 May 2024 |
| DOIs | |
| Publication status | Published - 31 Oct 2024 |
Funding
J. D\u00E1vila has been supported by a Royal Society Wolfson Fellowship, UK and Fondecyt Grant 1170224, Chile. M. del Pino has been supported by a Royal Society Research Professorship, UK. M. Musso has been supported by EPSRC research Grant EP/T008458/1.
| Funders | Funder number |
|---|---|
| Royal Society | |
| Fondo Nacional de Desarrollo Científico y Tecnológico | 1170224 |
| Fondo Nacional de Desarrollo Científico y Tecnológico | |
| Engineering and Physical Sciences Research Council | EP/T008458/1 |
| Engineering and Physical Sciences Research Council |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics