MHD simulations of the magnetorotational instability in a shearing box with zero net flux. II. The effect of transport coefficients

We study the influence of the choice of transport coefficients (viscosity and resistivity) on MHD turbulence driven by the magnetorotational instability (MRI) in accretion disks. We follow the methodology described in paper I: we adopt an unstratified shearing box model and focus on the case where the net vertical magnetic flux threading the box vanishes. For the most part we use the finite difference code ZEUS, including explicit transport coefficients in the calculations. However, we also compare our results with those obtained using other algorithms (NIRVANA, the PENCIL code and a spectral code) to demonstrate both the convergence of our results and their independence of the numerical scheme. We find that small scale dissipation affects the saturated state of MHD turbulence. In agreement with recent similar numerical simulations done in the presence of a net vertical magnetic flux, we find that turbulent activity (measured by the rate of angular momentum transport) is an increasing function of the magnetic Prandtl number Pm for all values of the Reynolds number Re that we investigated. We also found that turbulence disappears when the Prandtl number falls below a critical value Pm_c that is apparently a decreasing function of Re. For the limited region of parameter space that can be probed with current computational resources, we always obtained Pm_c>1. We conclude that the magnitudes of the transport coefficients are important in determining the properties of MHD turbulence in numerical simulations in the shearing box with zero net flux, at least for Reynolds numbers and magnetic Prandtl numbers that are such that transport is not dominated by numerical effects and thus can be probed using current computational resources.Comment: 10 pages, 13 figures, accepted in A&A. Numerical results improved, minor changes in the tex

The subcritical baroclinic instability in local accretion disc models

(abridged) Aims: We present new results exhibiting a subcritical baroclinic instability (SBI) in local shearing box models. We describe the 2D and 3D behaviour of this instability using numerical simulations and we present a simple analytical model describing the underlying physical process. Results: A subcritical baroclinic instability is observed in flows stable for the Solberg-Hoiland criterion using local simulations. This instability is found to be a nonlinear (or subcritical) instability, which cannot be described by ordinary linear approaches. It requires a radial entropy gradient weakly unstable for the Schwartzchild criterion and a strong thermal diffusivity (or equivalently a short cooling time). In compressible simulations, the instability produces density waves which transport angular momentum outward with typically alpha<3e-3, the exact value depending on the background temperature profile. Finally, the instability survives in 3D, vortex cores becoming turbulent due to parametric instabilities. Conclusions: The subcritical baroclinic instability is a robust phenomenon, which can be captured using local simulations. The instability survives in 3D thanks to a balance between the 2D SBI and 3D parametric instabilities. Finally, this instability can lead to a weak outward transport of angular momentum, due to the generation of density waves by the vortices.Comment: 12 pages, 17 figures, Accepted in A&

Magnetically driven accretion in protoplanetary discs

We characterize magnetically driven accretion at radii between 1 au and 100 au in protoplanetary discs, using a series of local non-ideal magnetohydrodynamic (MHD) simulations. The simulations assume a Minimum Mass Solar Nebula (MMSN) disc that is threaded by a net vertical magnetic field of specified strength. Confirming previous results, we find that the Hall effect has only a modest impact on accretion at 30 au, and essentially none at 100 au. At 1-10 au the Hall effect introduces a pronounced bi-modality in the accretion process, with vertical magnetic fields aligned to the disc rotation supporting a strong laminar Maxwell stress that is absent if the field is anti-aligned. In the anti-aligned case, we instead find evidence for bursts of turbulent stress at 5-10 au, which we tentatively identify with the non-axisymmetric Hall-shear instability. The presence or absence of these bursts depends upon the details of the adopted chemical model, which suggests that appreciable regions of actual protoplanetary discs might lie close to the borderline between laminar and turbulent behaviour. Given the number of important control parameters that have already been identified in MHD models, quantitative predictions for disc structure in terms of only radius and accretion rate appear to be difficult. Instead, we identify robust qualitative tests of magnetically driven accretion. These include the presence of turbulence in the outer disc, independent of the orientation of the vertical magnetic fields, and a Hall-mediated bi-modality in turbulent properties extending from the region of thermal ionization to 10 au.Comment: accepted to MNRAS after very minor revision

Space weather effects on drilling accuracy in the North Sea

The oil industry uses geomagnetic field information to aid directional drilling operations when drilling for oil and gas offshore. These operations involve continuous monitoring of the azimuth and inclination of the well path to ensure the target is reached and, for safety reasons, to avoid collisions with existing wells. Although the most accurate method of achieving this is through a gyroscopic survey, this can be time consuming and expensive. An alternative method is a magnetic survey, where measurements while drilling (MWD) are made along the well by magnetometers housed in a tool within the drill string. These MWD magnetic surveys require estimates of the Earth’s magnetic field at the drilling location to correct the downhole magnetometer readings. The most accurate corrections are obtained if all sources of the Earth’s magnetic field are considered. Estimates of the main field generated in the core and the local crustal field can be obtained using mathematical models derived from suitable data sets. In order to quantify the external field, an analysis of UK observatory data from 1983 to 2004 has been carried out. By accounting for the external field, the directional error associated with estimated field values at a mid-latitude oil well (55 N) in the North Sea is shown to be reduced by the order of 20%. This improvement varies with latitude, local time, season and phase of the geomagnetic activity cycle. By accounting for all sources of the field, using a technique called Interpolation In-Field Referencing (IIFR), directional drillers have access to data from a “virtual” magnetic observatory at the drill site. This leads to an error reduction in positional accuracy that is close to matching that of the gyroscopic survey method and provides a valuable independent technique for quality control purposes

The plasma-wall transition with collisions and an oblique magnetic field: reversal of potential drops at grazing incidences

International audienceThe plasma-wall transition is studied by using 1d3V particle-in-cell (PIC) simulations in the case of a one dimensional plasma bounded by two absorbing walls separated by 200 Debye lengths (λ d). A constant and oblique magnetic field is applied to the system, with an amplitude such that r < λ d < R, where r and R are the electron and ion Larmor radius respectively. Collisions with neutrals are taken into account and modelled by an energy conservative operator, which randomly reorients ion and electron velocities. The plasma-wall transition (PWT) is shown to depend on both the angle of incidence of the magnetic field with respect to the wall θ, and on the ion mean-free-path to Larmor radius ratio, λ ci /R. In the very low collisionality regime (λ ci R) and for a large angle of incidence, the PWT consists in the classical tri-layer structure (Debye sheath / Chodura sheath / Pre-sheath) from the wall towards the center of the plasma. The drops of potential within the different regions are well consistent with already published models. However, when sin θ ≤ R/λ ci or with the ordering λ ci < R , collisions can not be neglected, leading to the disappearance of the Chodura sheath. In these case, a collisional model yields analytic expressions for the potential drop in the quasi-neutral region, and explains, in qualitative and quantitative agreement with the simulation results, its reversal below a critical angle derived in the paper, a regime possibly met in the SOL of tokamaks. It is further shown that the potential drop in the Debye sheath slightly varies with the collision-ality for λ ci R. However, it tends to decrease with λ ci in the high collisionality regime, until the Debye sheath finally vanishes

On the vertical-shear instability in astrophysical discs

We explore the linear stability of astrophysical discs exhibiting vertical shear, which arises when there is a radial variation in the temperature or entropy. Such discs are subject to a ‘vertical-shear instability’, which recent non-linear simulations have shown to drive hydrodynamic activity in the MRI-stable regions of protoplanetary discs. We first revisit locally isothermal discs using the quasi-global reduced model derived by Nelson et al. This analysis is then extended to global axisymmetric perturbations in a cylindrical domain. We also derive and study a reduced model describing discs with power-law radial entropy profiles (‘locally polytropic discs’), which are somewhat more realistic in that they possess physical (as opposed to numerical) surfaces. The fastest growing modes have very short wavelengths and are localized at the disc surfaces (if present), where the vertical shear is maximal. An additional class of modestly growing vertically global body modes is excited, corresponding to destabilized classical inertial waves (‘r modes’). We discuss the properties of both types of modes, and stress that those that grow fastest occur on the shortest available length-scales (determined either by the numerical grid or the physical viscous length). This ill-posedness makes simulations of the instability difficult to interpret. We end with some brief speculation on the non-linear saturation and resulting angular momentum transport

Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic field generation in shear flows

The nature of dynamo action in shear flows prone to magnetohydrodynamic instabilities is investigated using the magnetorotational dynamo in Keplerian shear flow as a prototype problem. Using direct numerical simulations and Newton's method, we compute an exact time-periodic magnetorotational dynamo solution to the three-dimensional dissipative incompressible magnetohydrodynamic equations with rotation and shear. We discuss the physical mechanism behind the cycle and show that it results from a combination of linear and nonlinear interactions between a large-scale axisymmetric toroidal magnetic field and non-axisymmetric perturbations amplified by the magnetorotational instability. We demonstrate that this large scale dynamo mechanism is overall intrinsically nonlinear and not reducible to the standard mean-field dynamo formalism. Our results therefore provide clear evidence for a generic nonlinear generation mechanism of time-dependent coherent large-scale magnetic fields in shear flows and call for new theoretical dynamo models. These findings may offer important clues to understand the transitional and statistical properties of subcritical magnetorotational turbulence.Comment: 10 pages, 6 figures, accepted for publication in Physical Review

MHD simulations of the magnetorotational instability in a shearing box with zero net flux. I. The issue of convergence

We study the properties of MHD turbulence driven by the magnetorotational instability (MRI) in accretion disks. We adopt the local shearing box model and focus on the special case for which the initial magnetic flux threading the disk vanishes. We employ the finite difference code ZEUS to evolve the ideal MHD equations. Performing a set of numerical simulations in a fixed computational domain with increasing resolution, we demonstrate that turbulent activity decreases as resolution increases. We quantify the turbulent activity by measuring the rate of angular momentum transport through evaluating the standard alpha parameter. We find alpha=0.004 when (N_x,N_y,N_z)=(64,100,64), alpha=0.002 when (N_x,N_y,N_z)=(128,200,128) and alpha=0.001 when (N_x,N_y,N_z)=(256,400,256). This steady decline is an indication that numerical dissipation, occurring at the grid scale is an important determinant of the saturated form of the MHD turbulence. Analysing the results in Fourier space, we demonstrate that this is due to the MRI forcing significant flow energy all the way down to the grid dissipation scale. We also use our results to study the properties of the numerical dissipation in ZEUS. Its amplitude is characterised by the magnitude of an effective magnetic Reynolds number Re_M which increases from 10^4 to 10^5 as the number of grid points is increased from 64 to 256 per scale height. The simulations we have carried out do not produce results that are independent of the numerical dissipation scale, even at the highest resolution studied. Thus it is important to use physical dissipation, both viscous and resistive, and to quantify contributions from numerical effects, when performing numerical simulations of MHD turbulence with zero net flux in accretion disks at the resolutions normally considered.Comment: 10 pages, 15 figures, accepted in A&A. Numerical results improved, various numerical issues addressed (boundary conditions, box size, run durations