Publication details for Paul SutcliffeNiemi, A.J. & Sutcliffe, P.M. (2014). Leapfrogging vortex rings in the Landau–Lifshitz equation. Nonlinearity 27(9): 2095-2109.
- Publication type: Journal Article
- ISSN/ISBN: 0951-7715, 1361-6544
- DOI: 10.1088/0951-7715/27/9/2095
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
Vortex rings are ubiquitous in fluids, with smoke rings being a familiar example. The interaction of multiple vortex rings produces complex dynamical behaviour, such as the leapfrogging motion first analysed by Helmholtz more than a century and a half ago. Here we report on numerical investigations of vortex ring dynamics in a different setting from fluids, namely, as solutions of the Landau-Lifshitz equation that models the evolution of the local magnetization in a ferromagnetic medium. We present the results of the first study on the dynamics of interacting magnetic vortex rings and provide a novel link between fluids and magnetism, by showing that a range of phenomena familiar in fluids are reproduced in ferromagnets. This includes the leapfrogging motion of a pair of vortex rings and evidence for the chaotic dynamics of a trio of rings.