Numerical study of dynamo action at low magnetic Prandtl numbers

We present a three-pronged numerical approach to the dynamo problem at low magnetic Prandtl numbers P-M. The difficulty of resolving a large range of scales is circumvented by combining direct numerical simulations, a Lagrangian-averaged model and large-eddy simulations. The flow is generated by the Taylor-Green forcing; it combines a well defined structure at large scales and turbulent fluctuations at small scales. Our main findings are (i) dynamos are observed from P-M=1 down to P-M=10(-2), (ii) the critical magnetic Reynolds number increases sharply with P-M(-1) as turbulence sets in and then it saturates, and (iii) in the linear growth phase, unstable magnetic modes move to smaller scales as P-M is decreased. Then the dynamo grows at large scales and modifies the turbulent velocity fluctuations.