Interaction of large- and small-scale dynamos in isotropic turbulent flows from GPU-accelerated simulations

Abstract

Magnetohydrodynamical (MHD) dynamos emerge in many different astrophysical situations where turbulence is present, but the interaction between large-scale (LSD) and small-scale dynamos (SSD) is not fully understood. We performed a systematic study of turbulent dynamos driven by isotropic forcing in isothermal MHD with magnetic Prandtl number of unity, focusing on the exponential growth stage. Both helical and non-helical forcing was employed to separate the effects of LSD and SSD in a periodic domain. Reynolds numbers (Rm) up to $\approx 250$ were examined and multiple resolutions used for convergence checks. We ran our simulations with the Astaroth code, designed to accelerate 3D stencil computations on graphics processing units (GPUs) and to employ multiple GPUs with peer-to-peer communication. We observed a speedup of $\approx 35$ in single-node performance compared to the widely used multi-CPU MHD solver Pencil Code. We estimated the growth rates both from the averaged magnetic fields and their power spectra. At low Rm, LSD growth dominates, but at high Rm SSD appears to dominate in both helically and non-helically forced cases. Pure SSD growth rates follow a logarithmic scaling as a function of Rm. Probability density functions of the magnetic field from the growth stage exhibit SSD behaviour in helically forced cases even at intermediate Rm. We estimated mean-field turbulence transport coefficients using closures like the second-order correlation approximation (SOCA). They yield growth rates similar to the directly measured ones and provide evidence of $\alpha$ quenching. Our results are consistent with the SSD inhibiting the growth of the LSD at moderate Rm, while the dynamo growth is enhanced at higher Rm.

arXiv comment22 pages, 23 figures, 2 tables, Accepted for publication in the Astrophysical Journal

References in corpus (25)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Array Programming with NumPy
• 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
• FARGO3D: A new GPU-oriented MHD code
• Magnetic field generation in fully convective rotating spheres
• Mean-field concept and direct numerical simulations of rotating magnetoconvection and the geodynamo
• Dynamo theories
• Current status of turbulent dynamo theory: From large-scale to small-scale dynamos
• Numerical demonstration of fluctuation dynamo at low magnetic Prandtl numbers
• Large-scale dynamos in turbulent convection with shear
• Kinematic alpha effect in isotropic turbulence simulations
• The supernova-regulated ISM. II. The mean magnetic field
• Computational aspects of astrophysical MHD and turbulence
• Nonlinear magnetic diffusivity and alpha tensors in helical turbulence
• Large-scale dynamos at low magnetic Prandtl numbers
• Mean--field electrodynamics: Critical analysis of various analytical approaches to the mean electromotive force
• A unified large/small-scale dynamo in helical turbulence
• Electromotive force due to magnetohydrodynamic fluctuations in sheared rotating turbulence
• Varying the forcing scale in low Prandtl number dynamos
• Growth rate of small-scale dynamo at low magnetic Prandtl numbers
• Methods for compressible fluid simulation on GPUs using high-order finite differences
• On the existence of shear-current effects in magnetized burgulence
• Quantifying the effect of turbulent magnetic diffusion on the growth rate of the magneto-rotational instability

Cited by in corpus (5)

• Evolution of primordial magnetic fields during large-scale structure formation
• Numerical evidence for a small-scale dynamo approaching solar magnetic Prandtl numbers
• Scalable communication for high-order stencil computations using CUDA-aware MPI
• Compressible test-field method and its application to shear dynamos
• Small-scale and large-scale dynamos in global convection simulations of solar-like stars