Optimal lengthscale for a turbulent dynamo

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 $R{m}_c^T$ decreases as the forcing wavenumber $k_f$ increases from the smallest allowed $k_{min}=1/L$. At large $k_f$ on the other hand, $R{m}_c^T$ increases with the forcing wavenumber as $R{m}_c^T\propto \sqrt{k_f}$ in agreement with mean-field scaling prediction. At $k_{f}L\simeq 4$ an optimal wavenumber is reached where $R{m}_c^T$ obtains its minimum value. At this optimal wavenumber $R{m}_c^T$ 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.

References in corpus (5)

• Generation of magnetic field by dynamo action in a turbulent flow of liquid sodium
• Numerical demonstration of fluctuation dynamo at low magnetic Prandtl numbers
• Statistical equilibria of large scales in dissipative hydrodynamic turbulence
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Cited by in corpus (6)

• Systematic parameter study of dynamo bifurcations in geodynamo simulations
• Large-scale dynamics of magnetic helicity
• Effects of magnetic and kinetic helicities on the growth of magnetic fields in laminar and turbulent flows by helical-Fourier decomposition
• Transition to turbulent dynamo saturation
• The onset of turbulent rotating dynamos at the low $Pm$ limit
• Effect of electromagnetic boundary conditions on the onset of small-scale dynamos driven by convection