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 ($\sim 160$).

arXiv comment12 pages, 10 figures, Version accepted in MNRAS

References in corpus (33)

• Astrophysical magnetic fields and nonlinear dynamo theory
• The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulence
• Simulations of nonhelical hydromagnetic turbulence
• Mach Number Dependence of Turbulent Magnetic Field Amplification: Solenoidal versus Compressive Flows
• Dynamic nonlinearity in large scale dynamos with shear
• Direct simulations of a supernova-driven galactic dynamo
• Numerical demonstration of fluctuation dynamo at low magnetic Prandtl numbers
• A Unified treatment of small and large- scale dynamos in helical turbulence
• The onset of a small-scale turbulent dynamo at low magnetic Prandtl numbers
• The supernova-regulated ISM. I. The multi-phase structure
• Kinematic alpha effect in isotropic turbulence simulations
• Scale dependence of alpha effect and turbulent diffusivity
• Mach number dependence of the onset of dynamo action
• Critical Magnetic Prandtl Number for Small-Scale Dynamo
• 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
• Characteristic Lengths of Magnetic Field in Magnetohydrodynamic Turbulence
• Magnetic helicity in stellar dynamos: new numerical experiments
• Galactic spiral patterns and dynamo action I: A new twist on magnetic arms
• Large-scale dynamos at low magnetic Prandtl numbers
• Nonlinear small-scale dynamos at low magnetic Prandtl numbers
• Magnetic-field generation in helical turbulence
• The Small-Scale Dynamo at Low Magnetic Prandtl Numbers
• Dynamo coefficients from local simulations of the turbulent ISM
• The small-scale dynamo: Breaking universality at high Mach numbers
• On Large-Scale Dynamo Action at High Magnetic Reynolds Number
• Magnetic dynamo action at low magnetic Prandtl numbers
• Fluctuation dynamo at finite correlation times and the Kazantsev spectrum
• Galactic Spiral Patterns and Dynamo Action II: Asymptotic Solutions
• The kinetic helicity needed to drive large-scale dynamos
• Magnetic dynamo action in helical turbulence
• Anomalous Scalings and Dynamics of Magnetic Helicity

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