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Durham University

Research & business

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Publication details for Paul Sutcliffe

Niemi, A.J. & Sutcliffe, P.M. (2014). Leapfrogging vortex rings in the Landau–Lifshitz equation. Nonlinearity 27(9): 2095-2109.

Author(s) from Durham

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.