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Small-scale dynamos are expected to operate in all astrophysical fluids thatare turbulent and electrically conducting, for example the interstellar medium,stellar interiors, and accretion disks, where they may also be affected by orcompeting with large-scale dynamos. However, the possibility of small-scaledynamos being excited at small and intermediate ratios of viscosity to magneticdiffusivity (the magnetic Prandtl number) has been debated, and the possibilityof them depending on the large-scale forcing wavenumber has been raised. Herewe show, using four values of the forcing wavenumber, that the small-scaledynamo does not depend on the scale-separation between the size of thesimulation domain and the integral scale of the turbulence, i.e., the forcingscale. Moreover, the spectral bottleneck in turbulence, which has been impliedas being responsible for raising the excitation conditions of small-scaledynamos, is found to be invariant under changing the forcing wavenumber.However, when forcing at the lowest few wavenumbers, the effective forcingwavenumber that enters in the definition of the magnetic Reynolds number isfound to be about twice the minimum wavenumber of the domain. Our work isrelevant to future studies of small-scale dynamos, of which severalapplications are being discussed.

Varying the forcing scale in low Prandtl number dynamos