Inverse cascades and alpha effect at a low magnetic Prandtl number.
Dynamo action in a fully helical Arn'old-Beltrami-Childress 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 buildup. Growth of magnetic energy obtains down to a magnetic Prandtl number P(M) = R(M)/R(V) close to 0.005, where R(V) and R(M) are the kinetic and magnetic Reynolds numbers. The critical magnetic Reynolds number for dynamo action R(M)(c) seems to saturate at values close to 20. Detailed studies of the dependence of the amplitude of the saturated magnetic energy with P(M) are presented. When P(M) is decreased, numerical experiments are conducted with either R(V) or R(M) kept constant. In the former case, the ratio of magnetic to kinetic energy saturates to a value slightly below unity as P(M) decreases. Examination of energy spectra and structures in real space reveals that quenching of the velocity by a 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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