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Inverse cascades and alpha-effect at low magnetic Prandtl number

P. D. Mininni
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Abstract

Dynamo action in a fully helical Beltrami (ABC) flow is studied using both direct numerical simulations and subgrid modeling. Sufficient scale separation is given in order to allow for large-scale magnetic energy build-up. Growth of magnetic energy obtains down to a magnetic Prandtl number PM=RM/RV close to 0.005, where RV and RM are the kinetic and magnetic Reynolds numbers. The critical magnetic Reynolds number for dynamo action RMc seems to saturate at values close to 20. Detailed studies of the dependence of the amplitude of the saturated magnetic energy with PM are presented. In order to decrease PM, numerical experiments are conducted with either RV or RM kept constant. In the former case, the ratio of magnetic to kinetic energy saturates to a value slightly below unity as PM decreases. Examination of energy spectra and structures in real space both reveal that quenching of the velocity by the large-scale magnetic field takes place, with an inverse cascade of magnetic helicity and a force-free field at large scale in the saturated regime.

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P. D. Mininni. 2007-02-13. Inverse cascades and alpha-effect at low magnetic Prandtl number. https://doi.org/10.1103/physreve.76.026316

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