An analytical study of the MHD clamshell instability on a sphere
dc.contributor.author | Wang, C | |
dc.contributor.author | Gilbert, AD | |
dc.contributor.author | Mason, J | |
dc.date.accessioned | 2022-12-15T14:22:21Z | |
dc.date.issued | 2022-12-15 | |
dc.date.updated | 2022-12-15T14:06:24Z | |
dc.description.abstract | This paper studies the instability of two-dimensional magnetohydrodynamic (MHD) systems on a sphere using analytical methods. The underlying flow consists of a zonal differential rotation and a toroidal magnetic field is present. Semicircle rules that prescribe the possible domain of the wave velocity in the complex plane for general flow and field profiles are derived. The paper then sets out an analytical study of the `clamshell instability', which features field lines on the two hemispheres tilting in opposite directions (Cally 2001, Sol. Phys. vol. 199, pp. 231--249). An asymptotic solution for the instability problem is derived for the limit of weak shear of the zonal flow, via the method of matched asymptotic expansions. It is shown that when the zonal flow is solid body rotation, there exists a neutral mode that tilts the magnetic field lines, referred to as the `tilting mode'. A weak shear of the zonal flow excites the critical layer of the tilting mode, which reverses the tilting direction to form the clamshell pattern and induces the instability. The asymptotic solution provides insights into properties of the instability for a range of flow and field profiles. A remarkable feature is that the magnetic field affects the instability only through its local behaviour in the critical layer. | en_GB |
dc.description.sponsorship | Engineering and Physical Sciences Research Council (EPSRC) | en_GB |
dc.identifier.citation | Vol. 953, article A38 | en_GB |
dc.identifier.doi | https://doi.org/10.1017/jfm.2022.973 | |
dc.identifier.grantnumber | EP/T023139/1 | en_GB |
dc.identifier.uri | http://hdl.handle.net/10871/132039 | |
dc.identifier | ORCID: 0000-0002-3577-7245 (Wang, Chen) | |
dc.language.iso | en | en_GB |
dc.publisher | Cambridge University Press | en_GB |
dc.rights | © The Author(s), 2022. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited. | en_GB |
dc.subject | magnetic fluids | en_GB |
dc.subject | critical layers | en_GB |
dc.title | An analytical study of the MHD clamshell instability on a sphere | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2022-12-15T14:22:21Z | |
dc.identifier.issn | 1469-7645 | |
dc.description | This is the final version. Available on open access from Cambridge University Press via the DOI in this record | en_GB |
dc.description | Data access statement: No data were created or analysed in this study. | en_GB |
dc.identifier.journal | Journal of Fluid Mechanics | en_GB |
dc.relation.ispartof | Journal of Fluid Mechanics | |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0 | en_GB |
dcterms.dateAccepted | 2022-11-14 | |
dcterms.dateSubmitted | 2022-06-06 | |
rioxxterms.version | VoR | en_GB |
rioxxterms.licenseref.startdate | 2022-12-15 | |
rioxxterms.type | Journal Article/Review | en_GB |
refterms.dateFCD | 2022-12-15T14:06:26Z | |
refterms.versionFCD | AM | |
refterms.dateFOA | 2022-12-15T14:22:25Z | |
refterms.panel | B | en_GB |
refterms.dateFirstOnline | 2022-12-15 |
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Except where otherwise noted, this item's licence is described as © The Author(s), 2022. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.