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Circulation conservation and vortex breakup in magnetohydrodynamics at low magnetic Prandtl number

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Abstract

In this paper we examine the role of weak magnetic fields in breaking Kelvin’s circulation theorem and in vortex breakup in two-dimensional magnetohydrodynamics for the physically important case of a fluid with low magnetic Prandtl number (low Pm ). We consider three canonical inviscid solutions for the purely hydrodynamical problem, namely a Gaussian vortex, a circular vortex patch and an elliptical vortex patch. We examine how magnetic fields lead to an initial loss of circulation Γ and attempt to derive scaling laws for the loss of circulation as a function of field strength and diffusion as measured by two non-dimensional parameters. We show that for all cases the loss of circulation depends on the integrated effects of the Lorentz force, with the patch cases leading to significantly greater circulation loss. For the case of the elliptical vortex, the loss of circulation depends on the total area swept out by the rotating vortex, and so this leads to more efficient circulation loss than for a circular vortex.
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Details

Original languageEnglish
Pages (from-to)38-60
JournalJournal of Fluid Mechanics
Volume857
Early online date15 Oct 2018
DOIs
StatePublished - 25 Dec 2018

    Research areas

  • Contour dynamics, MHD and electrohydrodynamics, Vortex dynamics

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