Hardy, CM orcid.org/0000-0002-4550-4822, Livermore, PW orcid.org/0000-0001-7591-6716, Niesen, J orcid.org/0000-0002-6693-3810 et al. (2 more authors) (2018) Determination of the instantaneous geostrophic flow within the three-dimensional magnetostrophic regime. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474 (2218). ARTN 20180. ISSN 1364-5021
Abstract
In his seminal work, Taylor (1963 Proc. R. Soc. Lond. A 274, 274–283. (doi:10.1098/rspa.1963.0130).) argued that the geophysically relevant limit for dynamo action within the outer core is one of negligibly small inertia and viscosity in the magnetohydrodynamic equations. Within this limit, he showed the existence of a necessary condition, now well known as Taylor's constraint, which requires that the cylindrically averaged Lorentz torque must everywhere vanish; magnetic fields that satisfy this condition are termed Taylor states. Taylor further showed that the requirement of this constraint being continuously satisfied through time prescribes the evolution of the geostrophic flow, the cylindrically averaged azimuthal flow. We show that Taylor's original prescription for the geostrophic flow, as satisfying a given second-order ordinary differential equation, is only valid for a small subset of Taylor states. An incomplete treatment of the boundary conditions renders his equation generally incorrect. Here, by taking proper account of the boundaries, we describe a generalization of Taylor's method that enables correct evaluation of the instantaneous geostrophic flow for any three-dimensional Taylor state. We present the first full-sphere examples of geostrophic flows driven by non-axisymmetric Taylor states. Although in axisymmetry the geostrophic flow admits a mild logarithmic singularity on the rotation axis, in the fully three-dimensional case we show that this is absent and indeed the geostrophic flow appears to be everywhere regular.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | (c) 2018 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/ by/4.0/, which permits unrestricted use, provided the original author and source are credited. |
Keywords: | Taylor's constraint; dynamos; Earth's core |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) The University of Leeds > Faculty of Environment (Leeds) > School of Earth and Environment (Leeds) > Inst of Geophysics and Tectonics (IGT) (Leeds) |
Funding Information: | Funder Grant number NERC (Natural Environment Research Council) NE/G014043/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 04 Sep 2018 09:32 |
Last Modified: | 16 Mar 2020 15:50 |
Status: | Published |
Publisher: | The Royal Society |
Identification Number: | 10.1098/rspa.2018.0412 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:135243 |