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

Abstract

Context. Angular momentum transport in accretion discs is often believed to be due to magnetohydrodynamic turbulence mediated by the magnetorotational instability (MRI). 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 behaviour in the Ohmic diffusion regime has not been clearly established. Aims. 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. Methods. Unstratified shearing box simulations are performed both in the compressible and incompressible limits, with a resolution up to 800 cells per disc scale height. This is the highest resolution ever attained for a simulation of MRI turbulence. Different magnetic field geometry and a wide range of dimensionless dissipative coefficients are considered. We also systematically investigate the relevance of using large eddy simulations (LES) in place of direct numerical simulations. Results. 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 10 3 , we find α ∼ 3.2 × 10 −2 when Pm approaches zero. In the case of a mean toroidal field for which β = 100, we find α ∼ 1.8 × 10 −2 in the same limit. Implicit LES and the Chollet-Lesieur closure model both reproduce these results for the α parameter and the power spectra. A reduction in computational cost by a factor of at least 16 (and up to 256) is achieved when using such methods. Conclusions. MRI turbulence operates efficiently in the small Pm limit provided there is a mean magnetic field. Implicit LES offers a practical and efficient means of investigation of this regime but should be used with care, particularly in the case of a vertical field. The Chollet-Lesieur closure model is perfectly suited for simulations done with a spectral code.

Transport Properties of the Azimuthal Magnetorotational Instability

“…The ratio of Maxwell to Reynolds stresses is solely determined by Rm and increases from 0 to 1 as Rm is increased. This is in agreement with Meheut et al (2015), who performed shearing-box simulations of MRI turbulence at two magnetic Reynolds numbers Rm = 400 and 2600, while varying either Pm. At each Rm they found a constant, but different, ratio of Maxwell to Reynolds stress for both azimuthal and axial magnetic fields, with Maxwell stresses growing with Rm.…”

Linear growth of streaming instability in pressure bumps

“…Numerical simulations of visco-turbulent discs exhibit values of α ∼ 10 −3 − 10 −2 (e.g. Meheut et al 2015). Dust grains are assumed to be compact, spherical, uncharged, of constant size and density.…”

Nonlinear Transverse Cascade and Sustenance of MRI Turbulence in Keplerian Disks with an Azimuthal Magnetic Field

“…It is also about twice larger than the mean field B0y = 0.1 (Table 1). turbulence in disks with a net azimuthal field (Hawley et al 1995;Guan et al 2009;Meheut et al 2015). For all the models, the time-and volume-averaged quantities over the whole quasi-steady state, between t = 100 and the end of the run at t f , are listed in Table 1.…”

“…Fleming et al (2000) in local model and Flock et al (2012b) in global model addressed the influence of resistivity and established a critical value of magnetic Reynolds number for the existence of turbulence. and Meheut et al (2015) included also viscosity together with resistivity and showed that at fixed field strength the saturation amplitude mainly depends on the magnetic Prandtl number, that is, the ratio of viscosity to resistivity, if the latter is larger than unity and the Reynolds number is high enough. On the other hand, at Prandtl numbers smaller than unity the turbulence sustenance is more delicate: it appears to be independent of the Prandtl number and mainly determined by the magnetic Reynolds number.…”