DYNAMICS OF THE MAGNETIC SHEARING INSTABILITY AND MAGNETOHYDRODYNAMICTURBULENCE IN ACCRETION DISKS .1. VERTICAL MAGNETIC-FIELD

Recently, the magnetic shearing instability (MSI) has been proposed as a dynamical mechanism for angular momentum transport in accretion dis ks (Balbus & Hawley 1991; Hawley and Balbus 1991). In this paper, the nonlinear dynamics of MSI modes in the presence of a vertical magnetic field B, is discussed. In particular, the saturation levels of the fl uctuating fields, the angular momentum flux, and the energy dissipatio n mechanism, are examined in detail. It is shown that MSI induces stro ng magnetohydrodynamic (MHD) turbulence in a range of wavenumbers H-1< k less than or equal to Omega/V-Ao, where H is the thickness, Omega is the rotation frequency of the disk, and V-Ao, is the Alfven velocity. Despite the fact that the linear growth rate of MSI is maximal at sma ll-scale (i.e., k similar to Omega/V-Ao,), angular momentum transport due to MSI turbulence is dominated by the magnetic Reynolds stress dri ven by large-scale modes (k similar to H--l). It is shown that the amp litude of low k, MSI eddies is limited primarily by subscale shear how instability. Thus, dominant MSI cells are quasi-isotropic. In a stati onary state, the effective Shakura-Sunyaev ''alpha'' value is predicte d to be of order V-AD/C-s. In addition, the vertical magnetic-field-in duced MSI cells convert vertical magnetic field B-0 into azimuthal mag netic field B-0 in the disk. The generation of azimuthal magnetic fiel d in turn introduces new physical processes, such as dynamo activity a nd azimuthal MSI turbulence. We conclude that it is not possible to de couple vertical MSI saturation from azimuthal MSI evolution. Low-frequ ency MSI cells are shown to co-exist with high-frequency radial buoyan cy or internal waves. We show that modulational interaction between wa ves in these two frequency ranges is usually weak in the case when mea n magnetic field is vertical. Thus, MSI and internal wave dynamics mus t be treated on an equal footing.