Critical-layer instability of shallow water magnetohydrodynamic shear flows
dc.contributor.author | Wang, C | |
dc.contributor.author | Gilbert, A | |
dc.contributor.author | Mason, J | |
dc.date.accessioned | 2022-05-16T08:19:31Z | |
dc.date.issued | 2022-06-13 | |
dc.date.updated | 2022-05-11T23:07:44Z | |
dc.description.abstract | In this paper, the instability of shallow water shear flow with a sheared parallel magnetic field is studied. Waves propagating in such magnetic shear flows encounter critical levels where the phase velocity relative to the basic flow c − U(y) matches the Alfven wave velocities ±B(y)/√µρ, based on the local magnetic field B(y), the magnetic permeability µ and the mass density of the fluid ρ. It is shown that when the two critical levels are close to each other, the critical layer can generate an instability. The instability problem is solved, combining asymptotic solutions at large wavenumbers and numerical solutions, and the mechanism of instability explained using the conservation of momentum. For the shallow water MHD system, the paper gives the general form of the local differential equation governing such coalescing critical layers for any generic field and flow profiles, and determines precisely how the magnetic field modifies the purely hydrodynamic stability criterion based on the potential vorticity gradient in the critical layer. The curvature of the magnetic field profile, or equivalently the electric current gradient, J′ = −B′′/µ in the critical layer is found to play a complementary role in the instability. | en_GB |
dc.description.sponsorship | Engineering and Physical Sciences Research Council (EPSRC) | en_GB |
dc.description.sponsorship | Leverhulme Trust | en_GB |
dc.identifier.citation | Vol. 943, article A24 | en_GB |
dc.identifier.doi | 10.1017/jfm.2022.424 | |
dc.identifier.grantnumber | EP/T023139/1 | en_GB |
dc.identifier.uri | http://hdl.handle.net/10871/129635 | |
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. | |
dc.title | Critical-layer instability of shallow water magnetohydrodynamic shear flows | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2022-05-16T08:19:31Z | |
dc.identifier.issn | 0022-1120 | |
dc.description | This is the final version. Available on open access from Cambridge University Press via the DOI in this record | en_GB |
dc.identifier.eissn | 1469-7645 | |
dc.identifier.journal | Journal of Fluid Mechanics | en_GB |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0 | en_GB |
dcterms.dateAccepted | 2022-05-06 | |
rioxxterms.version | VoR | en_GB |
rioxxterms.licenseref.startdate | 2022-05-06 | |
rioxxterms.type | Journal Article/Review | en_GB |
refterms.dateFCD | 2022-05-11T23:07:46Z | |
refterms.versionFCD | AM | |
refterms.dateFOA | 2022-06-30T14:42:06Z | |
refterms.panel | B | en_GB |
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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.