Angular momentum transport and large eddy simulations in magnetorotational turbulence: the small Pm limit

Abstract

Angular momentum transport in accretion discs is often believed to be due to magnetohydrodynamic turbulence mediated by the magnetorotational instability. Despite an abundant literature on the MRI, the parameters governing the saturation amplitude of the turbulence are poorly understood and the existence of an asymptotic behavior in the Ohmic diffusion regime is not clearly established. We investigate the properties of the turbulent state in the small magnetic Prandtl number limit. Since this is extremely computationally expensive, we also study the relevance and range of applicability of the most common subgrid scale models for this problem. Unstratified shearing boxes simulations are performed both in the compressible and incompressible limits, with a resolution up to 800 cells per disc scale height. The latter constitutes the largest resolution ever attained for a simulation of MRI turbulence. In the presence of a mean magnetic field threading the domain, angular momentum transport converges to a finite value in the small Pm limit. When the mean vertical field amplitude is such that β, the ratio between the thermal and magnetic pressure, equals 1000, we find α~0.032 when Pm approaches zero. In the case of a mean toroidal field for which β=100, we find α~0.018 in the same limit. Both implicit LES and Chollet-Lesieur closure model reproduces these results for the α parameter and the power spectra. A reduction in computational cost of a factor at least 16 (and up to 256) is achieved when using such methods. MRI turbulence operates efficiently in the small Pm limit provided there is a mean magnetic field. Implicit LES offers a practical and efficient mean of investigation of this regime but should be used with care, particularly in the case of a vertical field. Chollet-Lesieur closure model is perfectly suited for simulations done with a spectral code.

Accepted for publication in A&A

References in corpus (13)

• Accretion disc viscosity: how big is alpha?
• A High Order Godunov Scheme with Constrained Transport and Adaptive Mesh Refinement for Astrophysical MHD
• Gaps, Rings, and Non-Axisymmetric Structures in Protoplanetary Disks - From Simulations to ALMA Observations
• MHD simulations of the magnetorotational instability in a shearing box with zero net flux. II. The effect of transport coefficients
• Impact of dimensionless numbers on the efficiency of MRI-induced turbulent transport
• Hall-effect Controlled Gas Dynamics in Protoplanetary Disks: II. Full 3D Simulations toward the Outer Disk
• Hyperviscosity, Galerkin truncation and bottlenecks in turbulence
• Magnetic Flux Concentration and Zonal Flows in Magnetorotational Instability Turbulence
• On the Magnetic Prandtl Number Behavior of Accretion Disks
• Aspect ratio dependence in magnetorotational instability shearing box simulations
• Numerical Measurements of the Spectrum in Magnetohydrodynamic Turbulence
• Spectral Modeling of Turbulent Flows and the Role of Helicity
• Dissipative effects on the sustainment of a magnetorotational dynamo in Keplerian shear flow

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