Leapfrogging vortex rings in the Landau–Lifshitz equation

Niemi, A.J.; Sutcliffe, P.M.

Abstract

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.

Citation

Niemi, A., & Sutcliffe, P. (2014). Leapfrogging vortex rings in the Landau–Lifshitz equation. Nonlinearity, 27(9), https://doi.org/10.1088/0951-7715/27/9/2095

• Journal Article Type: Article
• Publication Date: Sep 1, 2014
• Deposit Date: May 19, 2014
• Publicly Available Date: Jul 23, 2014
• Journal: Nonlinearity
• Print ISSN: 0951-7715
• Electronic ISSN: 1361-6544
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 27
• Issue: 9
• DOI: https://doi.org/10.1088/0951-7715/27/9/2095