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arXiv · 1402.6165

Leapfrogging vortex rings in the Landau-Lifshitz equation

Antti J. Niemi·Paul Sutcliffe
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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.

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cond-mat.mes-hallhep-thnlin.CDphysics.flu-dyn

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Antti J. Niemi, Paul Sutcliffe. 2014-02-25. Leapfrogging vortex rings in the Landau-Lifshitz equation. https://doi.org/10.1088/0951-7715%2F27%2F9%2F2095

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