Three-Dimensional Simulations of the MHD Shearing Instability in Accretion Disks

Details Three-Dimensional Simulations of the MHD Shearing Instability in Accretion Disks Three-Dimensional Simulations of the MHD Shearing Instability in Accretion Disks

Dec 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992aas...181.7105h&link_type=abstract

American Astronomical Society, 181st AAS Meeting, #71.05; Bulletin of the American Astronomical Society, Vol. 24, p.1234

Astronomy and Astrophysics

Astronomy

3

Scientific paper

We continue with our investigation of the local MHD shearing instability recently put forward by the authors as the underlying cause of the anomalous viscosity in accretion disks (Balbus & Hawley 1991, ApJ, 376, 214). To determine more fully the consequences of this instability for accretion disks requires understanding its nonlinear behavior, and this requires numerical simulations. Previous axisymmetric simulations have demonstrated the efficacy of the instability in transporting angular momentum and generating poloidal field (Hawley & Balbus 1992, ApJ, 400, in press). Here we relax the assumption of axisymmetry and perform full three-dimensional (3D) simulations. We employ the shearing sheet approximation which assumes that the radial width of the simulation box is much smaller than the distance from the central gravitating mass. This allows us to neglect geometric terms in the equations and to use periodic boundary conditions in both the radial and vertical directions. We thus consider the evolution of a small, local, magnetized ``patch'' within a Keplerian accretion disk. As predicted by the 3D linear perturbation analysis (Balbus & Hawley 1992, ApJ, 400, in press) we find that initial poloidal field distributions remain unstable in 3D, and pure toroidal initial field distributions are also unstable. The instability quickly leads to turbulence and accompanying angular momentum transport. The rate of angular momentum transport is proportional to the poloidal magnetic pressure, hence the anomalous viscosity parameter ``alpha'' is approximately equal to Pmag/Pgas.

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