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 shear flows is known to be sensitive to initial perturbation and to the amount of viscosity; marginally (linearly) stable differentially rotating flows exhibit this same sensitivity. Keplerian systems, however, are completely stable; the strength of the stabilizing Coriolis force easily overwhelms any destabilizing nonlinear effects. In fact, nonlinear effects speed the decay of applied turbulence by producing a rapid cascade of energy to high wavenumbers where dissipation occurs. Our conclusions are tested with grid resolution experiments and by comparison with results from a code that employs an alternative numerical algorithm. The properties of hydrodynamic differential rotation are contrasted with magnetohydrodynamic differential rotation. The kinetic stress couples to the vorticity which limits turbulence, while the magnetic stress couples to the shear which promotes turbulence. Thus magnetohydrodynamic turbulence is uniquely capable of acting as a turbulent angular momentum transport mechanism in disks.