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The magnetic non-hydrostatic shallow-water model
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dc.contributor.author | Dritschel, David Gerard | |
dc.contributor.author | Tobias, Steven M. | |
dc.date.accessioned | 2023-10-26T16:30:06Z | |
dc.date.available | 2023-10-26T16:30:06Z | |
dc.date.issued | 2023-10-25 | |
dc.identifier | 293710236 | |
dc.identifier | c9e7c9ad-26f1-4086-bda9-e604faa1d16a | |
dc.identifier | 85175326998 | |
dc.identifier.citation | Dritschel , D G & Tobias , S M 2023 , ' The magnetic non-hydrostatic shallow-water model ' , Journal of Fluid Mechanics , vol. 973 , A17 . https://doi.org/10.1017/jfm.2023.746 | en |
dc.identifier.issn | 0022-1120 | |
dc.identifier.other | ORCID: /0000-0001-6489-3395/work/145516350 | |
dc.identifier.uri | https://hdl.handle.net/10023/28579 | |
dc.description | Funding: DGD would like to thank the Leverhulme Trust for support received during a Research Fellowship. SMT was supported by funding from the European Research Council (ERC) under the EU's Horizon 2020 research and innovation programme (grant agreement D5S-DLV-786780). | en |
dc.description.abstract | We consider the dynamics of a set of reduced equations describing the evolution of a magnetised, rotating stably stratified fluid layer, atop a stagnant dense, perfectly conducting layer. We consider two closely related models. In the first, the layer has, above it, relatively light fluid where the magnetic pressure is much larger than the gas pressure, and the magnetic field is largely force-free. In the second model, the magnetic field is constrained to lie within the dynamical layer by the implementation of a model diffusion operator for the magnetic field. The model derivation proceeds by assuming that the horizontal velocity and the horizontal magnetic field are independent of the vertical coordinate, whilst the vertical components in the layer have a linear dependence on height. The full system comprises evolution equations for the magnetic field, horizontal velocity and height field together with a linear elliptic equation for the vertically integrated non-hydrostatic pressure. In the magneto-hydrostatic limit, these equations simplify to equations of shallow-water type. Numerical solutions for both models are provided for the fiducial case of a Gaussian vortex interacting with a magnetic field. The solutions are shown to differ negligibly. We investigate how the interaction of the vortex changes in response to the magnetic Reynolds number Rm, the Rossby deformation radius LD, and a Coriolis buoyancy frequency ratio f/N measuring the significance of non-hydrostatic effects. The magneto-hydrostatic limit corresponds to f/N→0. | |
dc.format.extent | 27 | |
dc.format.extent | 2390782 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of Fluid Mechanics | en |
dc.subject | Shallow water flows | en |
dc.subject | Magnetic fluids | en |
dc.subject | Contour dynamics | en |
dc.subject | QC Physics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QC | en |
dc.title | The magnetic non-hydrostatic shallow-water model | en |
dc.type | Journal article | en |
dc.contributor.sponsor | The Leverhulme Trust | en |
dc.contributor.institution | University of St Andrews. Marine Alliance for Science & Technology Scotland | en |
dc.contributor.institution | University of St Andrews. Applied Mathematics | en |
dc.identifier.doi | https://doi.org/10.1017/jfm.2023.746 | |
dc.description.status | Peer reviewed | en |
dc.identifier.grantnumber | RF-2020-190 | en |
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