Optimal Length Scale for a Turbulent Dynamo

We demonstrate that there is an optimal forcing length scale for low Prandtl number dynamo flows that can significantly reduce the required energy injection rate. The investigation is based on simulations of the induction equation in a periodic box of size 2 pi L. The flows considered are the laminar and turbulent ABC flows forced at different forcing wave numbers k(f), where the turbulent case is simulated using a subgrid turbulence model. At the smallest allowed forcing wave number k(f) = k(min) = 1/L the laminar critical magnetic Reynolds number Rm(c)(lam) is more than an order of magnitude smaller than the turbulent critical magnetic Reynolds number Rm(c)(turb) due to the hindering effect of turbulent fluctuations. We show that this hindering effect is almost suppressed when the forcing wave number k(f) is increased above an optimum wave number kfL similar or equal to 4 for which Rm(c)(turb) is minimum. At this optimal wave number, Rm(c)(turb) is smaller by more than a factor of 10 than the case forced in k(f) = 1. This leads to a reduction of the energy injection rate by 3 orders of magnitude when compared to the case where the system is forced at the largest scales and thus provides a new strategy for the design of a fully turbulent experimental dynamo.