On the viability of the shearing box approximation for numerical studies of MHD turbulence in accretion disks

Abstract

Most of our knowledge on the nonlinear development of the magneto-rotational instability (MRI) relies on the results of numerical simulations employing the shearing box (SB) approximation. A number of difficulties arising from this approach have recently been pointed out in the literature. We thoroughly examine the effects of the assumptions made and numerical techniques employed in SB simulations. This is done in order to clarify and gain better understanding of those difficulties as well as of a number of additional serious problems, raised here for the first time, and of their impact on the results. Analytical derivations and estimates as well as comparative analysis to methods used in the numerical study of turbulence are used. Numerical experiments are performed to support some of our claims and conjectures. The following problems, arising from the (virtually exclusive) use of the SB simulations as a tool for the understanding and quantification of the nonlinear MRI development in disks, are analyzed and discussed: (i) inconsistencies in the application of the SB approximation itself; (ii) the limited spatial scale of the SB; (iii) the lack of convergence of most ideal MHD simulations; (iv) side-effects of the SB symmetry and the non-trivial nature of the linear MRI; (v) physical artifacts arising on the too small box scale due to periodic boundary conditions. The computational and theoretical challenge posed by the MHD turbulence problem in accretion disks cannot be met by the SB approximation, as it has been used to date. A new strategy to confront this challenge is proposed, based on techniques widely used in numerical studies of turbulent flows - developing (e.g., with the help of local numerical studies) a sub-grid turbulence model and implementing it in global calculations.

arXiv commentAccepted for publication in Astronomy and Astrophysics

References in corpus (28)

• Accretion disc viscosity: how big is alpha?
• Simulations of small-scale turbulent dynamo
• Enhanced Angular Momentum Transport in Accretion Disks
• Angular Momentum Transport by MHD Turbulence in Accretion Disks: Gas Pressure Dependence of the Saturation Level of the Magnetorotational Instability
• 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
• MHD simulations of the magnetorotational instability in a shearing box with zero net flux. I. The issue of convergence
• Experimental observation and characterization of the magnetorotational instability
• Magnetorotational Instability in a Rotating Liquid Metal Annulus
• The Effect of the Hall Term on the Nonlinear Evolution of the Magnetorotational Instability: I. Local Axisymmetric Simulations
• On magnetic field generation in Kolmogorov turbulence
• Experimental evidence for magnetorotational instability in a helical magnetic field
• New type of magneto-rotational instability in cylindrical Taylor-Couette flow
• Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers
• Angular Momentum Transport in Accretion Disks: Scaling Laws in MRI-driven Turbulence
• The onset of a small-scale turbulent dynamo at low magnetic Prandtl numbers
• Global MHD Simulations of Cylindrical Keplerian Disks
• Saturation and Thermalization of the Magnetorotational Instability: Recurrent Channel Flows and Reconnections
• Hydrodynamic stability of rotationally supported flows: Linear and nonlinear 2D shearing box results
• A self-sustaining nonlinear dynamo process in Keplerian shear flows
• Mean-Field Magnetohydrodynamics of Accretion Disks
• Magnetorotational Instability in Liquid Metal Couette Flow
• A weakly nonlinear analysis of the magnetorotational instability in a model channel flow
• Simulations of Magnetorotational Instability in a Magnetized Couette Flow
• Ballooning Modes in Thin Accretion Disks: Limits for their Excitation
• Traveling waves in magnetized Taylor-Couette flow
• On the nonlinear saturation of the magnetorotational instability near threshold in a thin-gap Taylor-Couette setup
• Energetics in MRI driven Turbulence

Cited by in corpus (41)

• The subcritical baroclinic instability in local accretion disc models
• Semi-global simulations of the magneto-rotational instability in core collapse supernovae
• Implementation of the Shearing Box Approximation in Athena
• On the Stability of Elliptical Vortices in Accretion Discs
• The magnetorotational instability as a jet launching mechanism
• The baroclinic instability in the context of layered accretion. Self-sustained vortices and their magnetic stability in local compressible unstratified models of protoplanetary disks
• On Self-Sustained Dynamo Cycles in Accretion Discs
• A conservative orbital advection scheme for simulations of magnetized shear flows with the PLUTO code
• Turbulent resistivity evaluation in MRI generated turbulence
• High accretion rates in magnetised Keplerian discs mediated by a Parker instability driven dynamo
• On the dynamics of planetesimals embedded in turbulent protoplanetary discs
• MRI-driven turbulent transport: the role of dissipation, channel modes and their parasites
• The Boussinesq approximation in rapidly rotating flows
• On the angular momentum transport due to vertical convection in accretion discs
• Connections Between Local and Global Turbulence in Accretion Disks
• Angular momentum transport and turbulence in laboratory models of Keplerian flows
• On the dynamics of planetesimals embedded in turbulent protoplanetary discs with dead zones
• Nonlinear energy transfers in accretion discs MRI turbulence. I-Net vertical field case
• Magnetorotational turbulence transports angular momentum in stratified disks with low magnetic Prandtl number but magnetic Reynolds number above a critical value
• Local models of astrophysical discs
• Symmetries, scaling laws and convergence in shearing-box simulations of MRI driven turbulence
• Vorticity production through rotation, shear and baroclinicity
• Global simulations of magnetorotational turbulence I: convergence and the quasi-steady state
• The weakly nonlinear magnetorotational instability in a local geometry
• Motivation and challenge to capture both large scale and local transport in next generation accretion theory
• On the local stability of vortices in differentially rotating discs
• Equilibrium disks, MRI mode excitation, and steady state turbulence in global accretion disk simulations
• 3D global simulations of RIAFs: convergence, effects of azimuthal extent and dynamo
• On characterizing nonlocality and anisotropy for the magnetorotational instability
• Radially Dependent Large Scale Dynamos in Global Cylindrical Shear Flows and the Local Cartesian Limit
• Sensitivity of the Magnetorotational Instability to the shear parameter in stratified simulations
• Transient dynamics of perturbations in astrophysical disks
• Transport properties of the Azimuthal Magnetorotational Instability
• Simulating cold shear flows on a moving mesh
• Spectral and algebraic instabilities in thin Keplerian discs under poloidal and toroidal magnetic fields
• Non-exponential hydrodynamical growth in density-stratified thin Keplerian discs
• Low magnetic-Prandtl number flow configurations for cold astrophysical disk models: speculation and analysis
• Hydrodynamical activity in thin accretion disks
• Regimes of the non-exponential temporal growth in thin Keplerian discs under toroidally-dominated magnetic fields
• Hydrodynamic response of rotationally supported flows in the Small Shearing Box model
• Fully kinetic shearing-box simulations of magnetorotational turbulence in 2D and 3D. I. Pair plasmas