Local Hydrodynamic Stability of Accretion Disks

We employ a variety of numerical simulations in the local shearing box systemto investigate in greater depth the local hydrodynamic stability of Kepleriandifferential rotation. In particular we explore the relationship of Keplerianshear to the nonlinear instabilities known to exist in simple Cartesian shear.The Coriolis force is the source of linear stabilization in differentialrotation. We exploit the formal equivalence of constant angular momentum flowsand simple Cartesian shear to examine the transition from stability tononlinear instability. The manifestation of nonlinear instability in shearflows is known to be sensitive to initial perturbation and to the amount ofviscosity; marginally (linearly) stable differentially rotating flows exhibitthis same sensitivity. Keplerian systems, however, are completely stable; thestrength of the stabilizing Coriolis force easily overwhelms any destabilizingnonlinear effects. In fact, nonlinear effects speed the decay of appliedturbulence by producing a rapid cascade of energy to high wavenumbers wheredissipation occurs. Our conclusions are tested with grid resolution experimentsand by comparison with results from a code that employs an alternativenumerical algorithm. The properties of hydrodynamic differential rotation arecontrasted with magnetohydrodynamic differential rotation. The kinetic stresscouples to the vorticity which limits turbulence, while the magnetic stresscouples to the shear which promotes turbulence. Thus magnetohydrodynamicturbulence is uniquely capable of acting as a turbulent angular momentumtransport mechanism in disks.Comment: 27 pages (including 10 figures), Latex, submitted to Ap