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Register a new userMagnetohydrodynamics in a Cylindrical Shearing Box
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We develop a framework for magnetohydrodynamical (MHD) simulations in a local cylindrical shearing box by extending the formulation of the Cartesian shearing box. We construct shearing-periodic conditions at the radial boundaries of a simulation box from the conservation relations of the basic MHD equations, taking into account the explicit radial dependence of physical quantities. We demonstrate quasi-steady mass accretion, which cannot be handled by the standard Cartesian shearing box model, with an ideal MHD simulation in a vertically unstratified cylindrical shearing box up to 200 rotations. In this demonstrative run we set up (i) net vertical magnetic flux, (ii) a locally isothermal equation of state, and (iii) a sub-Keplerian equilibrium rotation, whereas the sound velocity and the initial Alfven velocity have the same radial dependence as that of the Keplerian velocity. Inward mass accretion is induced to balance with the outward angular momentum flux of the MHD turbulence triggered by the magnetorotational instability in a self-consistent manner. We discuss detailed physical properties of the saturated magnetic field, in comparison to the results of a Cartesian shearing box simulation.
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The launching process of a magnetically driven outflow from an accretion disk is investigated in a local, shearing box model which allows a study of the feedback between accretion and angular momentum loss. The mass-flux instability found in previous linear analyses of this problem is recovered in a series of 2D (axisymmetric) simulations in the MRI-stable (high magnetic field strength) regime. At low field strengths that are still sufficient to suppress MRI, the instability develops on a short radial length scale and saturates at a modest amplitude. At high field strengths, a long-wavelength clump instability of large amplitude is observed, with growth times of a few orbits. As speculated before, the unstable connection between disk and outflow may be relevant for the time dependence observed in jet-producing disks. The success of the simulations is due in a large part to the implementation of an effective wave-transmitting upper boundary condition.
The dynamical evolution of protoplanetary disks is of key interest for building a comprehensive theory of planet formation and to explain the observational properties of these objects. Using the magnetohydrodynamics code Athena++, with an isothermal shearing box setup, we study the boundary between the active and dead zone, where the accretion rate changes and mass can accumulate. We quantify how the turbulence level is affected by the presence of a non uniform ohmic resistivity in the radial-x direction that leads to a region of inhibited turbulence (or dead zone). Comparing the turbulent activity to that of ideal simulations, the turbulence inhibited area shows density fluctuations and magnetic activity at its boundaries, driven by energy injection from the active (ideal) zone boundaries. We find magnetic dissipation to be significantly stronger in the ideal regions, and the turbulence penetration through the boundary of the dead zone is determined by the value of the resistivity itself, through the ohmic dissipation process, though the thickness of the transition does not play a significant role in changing the dissipation. We investigate the 1D spectra along the shearing direction: magnetic spectra appear flat at large scales both in ideal as well as resistive simulations, though a Kolmogorov scaling over more than one decade persists in the dead zone, suggesting the turbulent cascade is determined by the hydrodynamics of the system: MRI dynamo action is inhibited where sufficiently high resistivity is present.
Magnetohydrodynamic (MHD) turbulence driven by the magnetorotational instability can provide diffusive transport of angular momentum in astrophysical disks, and a widely studied computational model for this process is the ideal, stratified, isothermal shearing box. Here we report results of a convergence study of such boxes up to a resolution of $N = 256$ zones per scale height, performed on blue waters at NCSA with ramses-gpu. We find that the time and vertically integrated dimensionless shear stress $overline{alpha} sim N^{-1/3}$, i.e. the shear stress is resolution dependent. We also find that the magnetic field correlation length decreases with resolution, $lambda sim N^{-1/2}$. This variation is strongest at the disk midplane. We show that our measurements of $alpha$ are consistent with earlier studies. We discuss possible reasons for the lack of convergence.
Magnetic induction in magnetohydrodynamic fluids at magnetic Reynolds number (Rm) less than~1 has long been known to cause magnetic drag. Here, we show that when $mathrm{Rm} gg 1$ and the fluid is in a hydrodynamic-dominated regime in which the magnetic energy is much smaller than the kinetic energy, induction due to a mean shear flow leads to a magnetic eddy viscosity. The magnetic viscosity is derived from simple physical arguments, where a coherent response due to shear flow builds up in the magnetic field until decorrelated by turbulent motion. The dynamic viscosity coefficient is approximately $(B_p^2/2mu_0) tau_{rm corr}$, the poloidal magnetic energy density multiplied by the correlation time. We confirm the magnetic eddy viscosity through numerical simulations of two-dimensional incompressible magnetohydrodynamics. We also consider the three-dimensional case, and in cylindrical or spherical geometry, theoretical considerations similarly point to a nonzero viscosity whenever there is differential rotation. Hence, these results serve as a dynamical generalization of Ferraros law of isorotation. The magnetic eddy viscosity leads to transport of angular momentum and may be of importance to zonal flows in astrophysical domains such as the interior of some gas giants.
We describe a numerical scheme for magnetohydrodynamics simulations of dust-gas mixture by extending smoothed particle magnetohydrodynamics. We employ the single-species particle approach to describe dust-gas mixture with several modifications from the previous studies. We assume that the charged and neutral dusts can be treated as single-fluid and the electro-magnetic force acts on the gas and that on the charged dust is negligible. The validity of these assumption in the context of protostar formation is not obvious and is extensively evaluated. By investigating the electromagnetic force and electric current with terminal velocity approximation, it is found that as the dust size increases, the contribution of dust to them becomes smaller and negligible. We conclude that our assumptions of the electro-magnetic force on the dusts is negligible are valid for the dust size with a d & 10{mu}m. On the other hand, they do not produce the numerical artifact for the dust a d . 10{mu}m in envelope and disk where the perfect coupling between gas and dusts realizes. However, we also found that our assumptions may break down in outflow (or under environment with very strong magnetic field and low density) for the dust a d . 10{mu}m. We conclude that our assumptions are valid in almost all cases where macroscopic dust dynamics is important in the context of protostar formation. We conduct numerical tests of dusty wave, dusty magnetohydrodynamics shock, and gravitational collapse of magnetized cloud core with our simulation code. The results show that our numerical scheme well reproduces the dust dynamics in the magnetized medium.
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