Local Hydrodynamic Stability of Accretion Disks

Abstract

We employ a variety of numerical simulations in the local shearing box system to investigate in greater depth the local hydrodynamic stability of Keplerian differential rotation. In particular, we explore the relationship of Keplerian shear to the nonlinear instabilities known to exist in simple Cartesian shear. The Coriolis force is the source of linear stabilization in differential rotation. We exploit the formal equivalence of constant angular momentum flows and simple Cartesian shear to examine the transition from stability to nonlinear instability. The manifestation of nonlinear instability in simple shear flows is known to be sensitive to initial perturbation and the amount of viscosity; marginally (linearly) stable differentially rotating flows exhibit this same sensitivity. Keplerian systems, however, are completely stable; stabilizing Coriolis forces easily overwhelm any destabilizing nonlinear effects. If anything, nonlinear effects speed the decay of applied turbulence by producing a rapid cascade of energy to high wavenumbers where dissipation occurs. We test our conclusions with grid-resolution experiments and by comparing the results of codes with very different diffusive properties. The detailed agreement of the decay of nonlinear disturbances found repeatedly in codes with very different diffusive behaviors strongly suggests that Keplerian stability is not a numerical artifact. The properties of hydrodynamic differential rotation are contrasted with magnetohydrodynamic differential rotation. A kinetic stress tensor couples to the outwardly increasing vorticity, which limits turbulence; a magnetic stress couples to the outwardly decreasing shear, which promotes turbulence. Thus magnetohydrodynamic turbulence is uniquely capable of acting as a turbulent angular momentum transport mechanism in disks.