Inverse cascades and α 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 RM 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.