Optimal lengthscale for a turbulent dynamo

TL;DR

The paper identifies an optimal forcing length scale in turbulent dynamo flows that minimizes energy requirements, with simulations showing a significant reduction in critical magnetic Reynolds number at this scale, offering new experimental design strategies.

Contribution

It reveals the existence of an optimal forcing wavenumber that reduces the energy needed for dynamo action, supported by simulation results.

Findings

Critical magnetic Reynolds number decreases with increasing forcing wavenumber up to an optimal point.

At the optimal wavenumber, the critical magnetic Reynolds number is over ten times smaller.

Energy injection rate can be reduced by three orders of magnitude at the optimal scale.

Abstract

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 turbulent ABC flows forced at different forcing wavenumbers $k_f$ simulated using a subgrid turbulent model. The critical magnetic Reynolds number $Rm_c^T$ decreases as the forcing wavenumber $k_f$ increases from the smallest allowed $k_{min}=1/L$. At large $k_f$ on the other hand, $Rm_c^T$ increases with the forcing wavenumber as $Rm_c^T \propto \sqrt{ k_f}$ in agreement with mean-field scaling prediction. At $k_f L\simeq 4$ an optimal wavenumber is reached where $Rm_c^T$ obtains its minimum value. At this optimal wavenumber $Rm_c^T$ is smaller by more than a factor of ten than the case forced in $k_f=1$. This leads to a reduction of the energy injection rate by three orders of magnitude when compared to the case that the system is forced in the largest scales and thus provides a new strategy for the design of a fully turbulent experimental dynamo.