Traces of large-scale dynamo action in the kinematic stage

Abstract

Using direct numerical simulations (DNS) we verify that in the kinematic regime, a turbulent helical dynamo grows in such a way that the magnetic energy spectrum remains to high precision shape-invariant, i.e., at each wavenumber $k$ the spectrum grows with the same growth rate. Signatures of large-scale dynamo action can be identified through the excess of magnetic energy at small $k$, of one of the two oppositely polarized constituents. Also a suitably defined planar average of the magnetic field can be chosen such that its rms value isolates the strength of the mean field. However, these different means of analysis suggest that the strength of the large-scale field diminishes with increasing magnetic Reynolds number ${\mathrm{Re}}_{\mathrm{M}}$ like ${\mathrm{Re}}_{\mathrm{M}}^{-1/2}$ for intermediate values and like ${\mathrm{Re}}_{\mathrm{M}}^{-3/4}$ for larger ones. Both an analysis from the Kazantsev model including helicity and the DNS show that this arises due to the magnetic energy spectrum still peaking at resistive scales, even when helicity is present. As expected, the amplitude of the large-scale field increases with increasing fractional helicity, enabling us to determine the onset of large scale dynamo action and distinguishing it from that of the small-scale dynamo. Our DNS show that, contrary to earlier results for smaller scale separation (only 1.5 instead of now 4), the small-scale dynamo can still be excited at magnetic Prandtl numbers of 0.1 and only moderate values of the magnetic Reynolds numbers ($\sim 160$).

12 pages, 10 figures, Version accepted in MNRAS

References in corpus (14)

• Simulations of nonhelical hydromagnetic turbulence
• Direct simulations of a supernova-driven galactic dynamo
• Numerical demonstration of fluctuation dynamo at low magnetic Prandtl numbers
• Kinematic alpha effect in isotropic turbulence simulations
• The supernova-regulated ISM. I. The multi-phase structure
• Scale dependence of alpha effect and turbulent diffusivity
• Mach number dependence of the onset of dynamo action
• Minimal tau approximation and simulations of the alpha effect
• The supernova-regulated ISM. II. The mean magnetic field
• Fluctuation dynamos and their Faraday rotation signatures
• Magnetic-field generation in helical turbulence
• Dynamo coefficients from local simulations of the turbulent ISM
• On Large-Scale Dynamo Action at High Magnetic Reynolds Number
• Fluctuation dynamo at finite correlation times and the Kazantsev spectrum

Cited by in corpus (12)

• Galactic Dynamos
• Amplification of large-scale magnetic field in nonhelical magnetohydrodynamics
• Transition from small-scale to large-scale dynamo in a supernova-driven, multiphase medium
• On the Inverse Transfer of (Non-)Helical Magnetic Energy in a Decaying Magnetohydrodynamic Turbulence
• The fate of alpha dynamos at large $Rm$
• Dissipative magnetic structures and scales in small-scale dynamos
• Batchelor, Saffman, and Kazantsev spectra in galactic small-scale dynamos
• Chiral anomaly and dynamos from inhomogeneous chemical potential fluctuations
• Magnetic helicity and fluxes in an inhomogeneous alpha squared dynamo
• Magnetic field amplification during a turbulent collapse
• Galactic magnetic fields II. Applying the model to nearby galaxies
• Synthesizing Observations and Theory to Understand Galactic Magnetic Fields: Progress and Challenges