Circulation conservation and vortex breakup in magnetohydrodynamics at low magnetic Prandtl number
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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.
Dritschel , D G , Diamond , P H & Tobias , S M 2018 , ' Circulation conservation and vortex breakup in magnetohydrodynamics at low magnetic Prandtl number ' Journal of Fluid Mechanics , vol. 857 , pp. 38-60 . https://doi.org/10.1017/jfm.2018.719
Journal of Fluid Mechanics
© 2018, Cambridge University Press. This work has been made available online in accordance with the publisher’s policies. This is the author created accepted version manuscript following peer review and as such may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1017/jfm.2018.719
DescriptionFunding: UK Engineering and Physical Sciences Research Council (EP/H001794/1).
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