Marquez Artavia, X, Jones, CA orcid.org/0000-0002-1105-3920 and Tobias, SM (2017) Rotating magnetic shallow water waves and instabilities in a sphere. Geophysical & Astrophysical Fluid Dynamics, 111 (4). pp. 282-322. ISSN 0309-1929
Abstract
Waves in a thin layer on a rotating sphere are studied. The effect of a toroidal magnetic field is considered, using the shallow water ideal MHD equations. The work is motivated by suggestions that there is a stably stratified layer below the Earth’s core mantle boundary, and the existence of stable layers in stellar tachoclines. With an azimuthal background field known as the Malkus field, Bφ = B0sinθ, θ being the co-latitude, a non-diffusive instability is found with azimuthal wavenumber m = 1. A necessary condition for instability is that the Alfvėn speed exceeds Ω0R0 where Ω0 is the rotation rate and R0 the sphere radius. Magneto-inertial gravity waves propagating westward and eastward occur, and become equatorially trapped when the field is strong. Magneto-Kelvin waves propagate eastward at low field strength, but a new westward propagating Kelvin wave is found when the field is strong. Fast magnetic Rossby waves travel westward, whilst the slow magnetic Rossby waves generally travel eastward, except for some m = 1 modes at large field strength. An exceptional very slow westward m = 1 magnetic Rossby wave mode occurs at all field strengths. The current-driven instability occurs for m = 1 when the slow and fast magnetic Rossby waves interact. With strong field the magnetic Rossby waves become trapped at the pole. An asymptotic analysis giving the wave speed and wave form in terms of elementary functions is possible both in polar trapped and equatorially trapped cases.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 Informa UK Limited, trading as Taylor & Francis Group. This is an Accepted Manuscript of an article published by Taylor & Francis in Geophysical & Astrophysical Fluid Dynamics on 27th March 2017, available online: http://www.tandfonline.com/10.1080/03091929.2017.1301937. |
Keywords: | MHD waves; shallow water model; azimuthal field; rotating MHD fluids |
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: | 02 Mar 2017 10:55 |
Last Modified: | 09 May 2019 13:22 |
Published Version: | https://doi.org/10.1080/03091929.2017.1301937 |
Status: | Published |
Publisher: | Taylor & Francis |
Identification Number: | 10.1080/03091929.2017.1301937 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:113053 |