Large-to small-scale dynamo in domains of large aspect ratio: kinematic regime

Shumaylova, V., Teed, R. J. and Proctor, M. R.E. (2017) Large-to small-scale dynamo in domains of large aspect ratio: kinematic regime. Monthly Notices of the Royal Astronomical Society, 466(3), pp. 3513-3518. (doi: 10.1093/mnras/stw3379)

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The Sun’s magnetic field exhibits coherence in space and time on much larger scales than the turbulent convection that ultimately powers the dynamo. In this work, we look for numerical evidence of a large-scale magnetic field as the magnetic Reynolds number, Rm, is increased. The investigation is based on the simulations of the induction equation in elongated periodic boxes. The imposed flows considered are the standard ABC flow (named after Arnold, Beltrami & Childress) with wavenumber ku = 1 (small-scale) and a modulated ABC flow with wavenumbers ku = m, 1, 1 ± m, where m is the wavenumber corresponding to the long-wavelength perturbation on the scale of the box. The critical magnetic Reynolds number Rcrit m decreases as the permitted scale separation in the system increases, such that Rcrit m ∝ [Lx /Lz] −1/2. The results show that the α-effect derived from the mean-field theory ansatz is valid for a small range of Rm after which small scale dynamo instability occurs and the mean-field approximation is no longer valid. The transition from large- to small-scale dynamo is smooth and takes place in two stages: a fast transition into a predominantly small-scale magnetic energy state and a slower transition into even smaller scales. In the range of Rm considered, the most energetic Fourier component corresponding to the structure in the long x-direction has twice the length-scale of the forcing scale. The long-wavelength perturbation imposed on the ABC flow in the modulated case is not preserved in the eigenmodes of the magnetic field.

Item Type:Articles
Additional Information:Part of this work was supported by the Isaac Newton Studentship at the University of Cambridge and the Science and Technology Facilities Council, grant ST/L000636/1
Glasgow Author(s) Enlighten ID:Teed, Dr Robert
Authors: Shumaylova, V., Teed, R. J., and Proctor, M. R.E.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Monthly Notices of the Royal Astronomical Society
Publisher:Oxford University Press
ISSN (Online):1365-2966
Published Online:31 December 2016
First Published:First published in Monthly Notices of the Royal Astronomical Society 166(3):3513-3518
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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