Dritschel, DG, Diamond, PH and Tobias, SM (2018) Circulation conservation and vortex breakup in magnetohydrodynamics at low magnetic Prandtl number. Journal of Fluid Mechanics, 857. pp. 38-60. ISSN 0022-1120
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 ). 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 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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018, Cambridge University Press. This article has been published in a revised form in Journal of Fluid Mechanics https://doi.org/10.1017/jfm.2018.719. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. |
Keywords: | contour dynamics; MHD and electrohydrodynamics; vortex dynamics |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 22 Aug 2018 10:24 |
Last Modified: | 17 Jul 2019 07:16 |
Status: | Published |
Publisher: | Cambridge University Press |
Identification Number: | 10.1017/jfm.2018.719 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:134805 |