A NUMERICAL STUDY OF VISCOUS FLOWS IN AXISYMMETRICAL ALPHA-ACCRETION DISKS

Two-dimensional axisymmetric solutions of the equations of hydrodynami cs, including radiation transport and local energy generation due to v iscosity, are presented for the case of non-self-gravitating protoplan etary disks around young solar-type stars. The parameters that are var ied include the accretion rate in the disk, the magnitude of the visco sity parameter alpha, the boundary conditions, and the initial conditi ons. In general, for alpha > 0.05 and for distances >0.5 AU, the flow pattern is found to consist of a radial outflow near the equatorial pl ane and a radial inflow near the disk surface. Unlike one-dimensional vertical structure models in this regime, the flow is stable to convec tion, implying a physically inconsistent model in which the convective turbulence required to generate the viscosity is actually not present . Reduction of alpha to order 10(-3) is necessary to regain consistenc y. However, in the warmer regions interior to 0.5 AU, where the opacit y rises steeply as a consequence of hydrogen ionization, a physically consistent turbulent flow is found even for alpha = 0.05. Model result s are compared with one-dimensional vertical structure calculations.