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.