On the Non-linear Hydrodynamic Stability of Thin Keplerian Disks

The non-linear hydrodynamic stability of thin, compressible, Keplerian disks is studied on the large two-dimensional compressible scale, using a highorder accuracy spectral method. We find that purely hydrodynamical perturbations, can develop initially into either sheared disturbances or coherent vortices. However, the perturbations decay and do not evolve into a self-sustained turbulence. Temporarily, due to an inverse cascade of energy, which is characteristic of two-dimensional flows, energy is being transferred to the largest scale mode before being dissipated. In the case of an inner reflecting boundary condition, it is found that the innermost disk is globally unstable to non-axisymmetric modes which can evolve into turbulence. However, this turbulence cannot play a significant role in angular momentum transport in disks. Subject Headings: accretion, accretion disks hydrodynamics instabilities turbulence