Local hydrodynamic stability of accretion disks

We employ a variety of numerical simulations in the local shearing box syst em to investigate in greater depth the local hydrodynamic stability of Kepl erian differential rotation. In particular, we explore the relationship of Keplerian shear to the nonlinear instabilities known to exist in simple Car tesian shear. The Coriolis force is the source of linear stabilization in d ifferential rotation. We exploit the formal equivalence of constant angular momentum flows and simple Cartesian shear to examine the transition from s tability to nonlinear instability. The manifestation of nonlinear instabili ty in simple shear flows is known to be sensitive to initial perturbation a nd the amount of viscosity; marginally (linearly) stable differentially rot ating flows exhibit this same sensitivity. Keplerian systems, however, are completely stable; stabilizing Coriolis forces easily overwhelm any destabi lizing nonlinear effects. If anything, nonlinear effects speed the decay of applied turbulence by producing a rapid cascade of energy to high wavenumb ers where dissipation occurs. We test our conclusions with grid-resolution experiments and by comparing the results of codes with very different diffu sive properties. The detailed agreement of the decay of nonlinear disturban ces found repeatedly in codes with very different diffusive behaviors stron gly suggests that Keplerian stability is not a numerical artifact. The prop erties of hydrodynamic differential rotation are contrasted with magnetohyd rodynamic differential rotation, a kinetic stress tensor couples to the out wardly increasing vorticity, which limits turbulence; a magnetic stress cou ples to the outwardly decreasing shear, which promotes turbulence. Thus mag netohydrodynamic turbulence is uniquely capable of acting as a turbulent an gular momentum transport mechanism in disks.