Hori, K, Tobias, SM and Jones, CA orcid.org/0000-0002-1105-3920 (2020) Solitary magnetostrophic Rossby waves in spherical shells. Journal of Fluid Mechanics, 904 (R3). ISSN 0022-1120
Abstract
Finite-amplitude hydromagnetic Rossby waves in the magnetostrophic regime are studied. We consider the slow mode, which travels in the opposite direction to the hydrodynamic or fast mode, in the presence of a toroidal magnetic field and zonal flow by means of quasi-geostrophic models for thick spherical shells. The weakly nonlinear long waves are derived asymptotically using a reductive perturbation method. The problem at the first order is found to obey a second-order ordinary differential equation, leading to a hypergeometric equation for a Malkus field and a confluent Heun equation for an electrical wire field, and is non-singular when the wave speed approaches the mean flow. Investigating its neutral non-singular eigensolutions for different basic states, we find the evolution is described by the Korteweg–de Vries equation. This implies that the nonlinear slow wave forms solitons and solitary waves. These may take the form of a coherent eddy, such as a single anticyclone. We speculate on the relation of the anticyclone to the asymmetric gyre seen in the Earth's fluid core, and in state-of-the-art dynamo direct numerical simulations.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s), 2020. 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 in any medium, provided the original work is properly cited. |
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) The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) |
Funding Information: | Funder Grant number STFC (Science and Technology Facilities Council) ST/S00047X/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 08 Sep 2020 11:15 |
Last Modified: | 25 Jun 2023 22:24 |
Status: | Published |
Publisher: | Cambridge University Press |
Identification Number: | 10.1017/jfm.2020.743 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:165110 |
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