Calkins, M, Julien, K, Tobias, SM et al. (1 more author) (2015) A Multiscale Dynamo Model Driven by Quasi-geostrophic Convection. Journal of Fluid Mechanics, 780. pp. 143-166. ISSN 0022-1120
Abstract
A convection-driven multiscale dynamo model is developed in the limit of low Rossby number for the plane layer geometry in which the gravity and rotation vectors are aligned. The small-scale fluctuating dynamics are described by a magnetically-modified quasi-geostrophic equation set, and the large-scale mean dynamics are governed by a diagnostic thermal wind balance. The model utilizes three timescales that respectively characterize the convective timescale, the large-scale magnetic evolution timescale, and the large-scale thermal evolution timescale. Distinct equations are derived for the cases of order one and low magnetic Prandtl number. It is shown that the low magnetic Prandtl number model is characterized by a magnetic to kinetic energy ratio that is asymptotically large, with ohmic dissipation dominating viscous dissipation on the large-scales. For the order one magnetic Prandtl number model the magnetic and kinetic energies are equipartitioned and both ohmic and viscous dissipation are weak on the large-scales; large-scale ohmic dissipation occurs in thin magnetic boundary layers adjacent to the horizontal boundaries. For both magnetic Prandtl number cases the Elsasser number is small since the Lorentz force does not enter the leading order force balance. The new models can be considered fully nonlinear, generalized versions of the dynamo model originally developed by Childress and Soward [Phys. Rev. Lett., 29, p.837, 1972], and provide a new theoretical framework for understanding the dynamics of convection-driven dynamos in regimes that are only just becoming accessible to direct numerical simulations.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015 Cambridge University Press. This is an author-produced version of a paper published in Journal of Fluid Mechanics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | dynamo theory; geodynamo; geophysical and geological flows |
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: | 14 Sep 2015 11:56 |
Last Modified: | 19 Jan 2018 19:26 |
Published Version: | http://dx.doi.org/10.1017/jfm.2015.464 |
Status: | Published |
Publisher: | Cambridge University Press |
Identification Number: | 10.1017/jfm.2015.464 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:88779 |