Three-dimensional compressible hydrodynamic simulations of vortices in disks

We carry out three-dimensional, high-resolution (up to 1024² × 256) hydrodynamic simulations of the evolution of vortices in vertically unstratified Keplerian disks using the shearing sheet approximation. The transient amplification of incompressible, linear amplitude leading waves (which has been proposed as a possible route to nonlinear hydrodynamic turbulence in disks) is used as one test of our algorithms; our methods accurately capture the predicted amplification, converge at second order, and are free from aliasing. Waves that are expected to reach nonlinear amplitude at peak amplification become unstable to Kelvin-Helmholtz modes when | W_max | ≳ Ω (where W_max is the local maximum of vorticity and Ω the angular velocity). We study the evolution of a power-law distribution of vorticity consistent with Kolmogorov turbulence; in two dimensions long-lived vortices emerge and decay slowly, similar to previous studies. In three dimensions, however, vortices are unstable to bending modes, leading to rapid decay. Only vortices with a length-to-width ratio smaller than 1 survive; in three dimensions the residual kinetic energy and shear stress is at least 1 order of magnitude smaller than in two dimensions. No evidence for sustained hydrodynamic turbulence and transport is observed in three dimensions. Instead, at late times the residual transport is determined by the amplitude of slowly decaying, large-scale vortices (with horizontal extent comparable to the scale height of the disk), with additional contributions from nearly incompressible inertial waves possible. Evaluating the role that large-scale vortices play in astrophysical accretion disks will require understanding the mechanisms that generate and destroy them.