Chen, L, Herreman, W, Li, K et al. (3 more authors) (2018) The optimal kinematic dynamo driven by steady flows in a sphere. Journal of Fluid Mechanics, 839. pp. 1-32. ISSN 0022-1120
Abstract
We present a variational optimisation method that can identify the most efficient kinematic dynamo in a sphere, where efficiency is based on the value of a magnetic Reynolds number that uses enstrophy to characterize the inductive effects of the fluid flow. In this large scale optimisation, we restrict the flow to be steady and incompressible, and the boundary of the sphere to be no-slip and electrically insulating. We impose these boundary conditions using a Galerkin method in terms of specifically designed vector field bases. We solve iteratively for the flow field and the accompanying magnetic eigenfunction in order to find the minimal critical magnetic Reynolds number Rm c,min for the onset of a dynamo. Although nonlinear, this iteration procedure converges to a single solution and there is no evidence that this is not a global optimum. We find Rm c,min=64.45 is at least three times lower than that of any published example of a spherical kinematic dynamo generated by steady flows, and our optimal dynamo clearly operates above the theoretical lower bounds for dynamo action. The corresponding optimal flow has a spatially localized helical structure in the centre of the sphere, and the dominant components are invariant under rotation by π.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018, Cambridge University Press. This article has been published in a revised form in Journal of Fluid Mechanics https://doi.org/10.1017/jfm.2017.924. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | dynamo theory; variational methods |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Environment (Leeds) > School of Earth and Environment (Leeds) > Inst of Geophysics and Tectonics (IGT) (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 12 Jan 2018 12:22 |
Last Modified: | 25 Jul 2018 00:41 |
Status: | Published |
Publisher: | Cambridge University Press |
Identification Number: | 10.1017/jfm.2017.924 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:126104 |