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We study numerically the dynamical evolution of global equilibrium models of weakly magnetized accretion tori. The tori are orbiting around a central point--mass and are embedded in a hot, isothermal, non--rotating, spherically symmetric corona. Matter in each torus has initially an $n=3/2$ polytropic structure and obeys a power--law rotation law of the form $\Omega\propto R^{-q}$. The magnetic field is initially parallel to the rotation axis and extends out through the corona. We have performed magnetohydrodynamical simulations in 2.5 and in three dimensions of pressure--supported models with a constant specific angular momentum profile ($q=2$) and with a nearly Keplerian rotation profile ($q=1.51$). Three processes appear to dominate model evolutions at different times. Within the first few orbits, torsional Alfv\'en waves transport angular momentum from the surface layers to the surrounding corona. The surface layers slide down toward the central point--mass pulling along magnetic field lines. Matter inflow is thus initiated, but only becomes important when the deep interior is significantly perturbed by the magnetorotational instability of Balbus \& Hawley (1991). This instability causes dramatic redistribution of angular momentum and ultimately forces frequent magnetic reconnection. It drives radial inflow of matter that has lost angular momentum and a compensating outflow of matter with excess specific angular momentum. Reconnection leads to formation of disordered magnetic and velocity fields that are dominated by many loops and eddies. At later times, inflow/outflow continues but, in the absence of cooling, a torus does not become vertically thinner. Because of efficient redistribution of mass and momentum by eddies, the igh--density regions develop turbulence that provides some vertical support, slows down radial flow, and limits field growth to one or two orders of magnitude in energy.
\noindent This work is supported in part by NASA grant NAGW--1510 and by supercomputer time allocations from SDSC and NCSA.
\noindent Balbus, S. A., \& Hawley, J. F. 1991, ApJ, 376, 214
