Closure tests for mean field magnetohydrodynamics using a self-consistent reduced model |
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| Authors: | V V Pipin M R E Proctor |
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| Institution: | Institute for Solar-Terrestrial Physics, Siberian Division of Russian Academy of Sciences, 664033 Irkutsk, Russia;Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA |
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| Abstract: | The mean electromotive force and α effect are computed for a forced turbulent flow using a simple non-linear dynamical model. The results are used to check the applicability of two basic analytic ansätze of mean-field magnetohydrodynamics – the second-order correlation approximation (SOCA) and the τ approximation. In the numerical simulations the effective Reynolds number Re is 2–20, while the magnetic Prandtl number P m varies from 0.1 to 107. We present evidence that the τ approximation may be appropriate in dynamical regimes where there is a small-scale dynamo. Catastrophic quenching of the α effect is found for high P m. Our results indicate that for high P m SOCA gives a very large value of the α coefficient compared with the 'exact' solution. The discrepancy depends on the properties of the random force that drives the flow, with a larger difference occurring for δ-correlated force compared with that for a steady random force. |
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| Keywords: | turbulence Sun: activity Sun: magnetic fields |
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