On the Nonlinear Hydrodynamic Stability of Thin Keplerian Disks

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Abstract
The nonlinear hydrodynamic stability of thin, compressible, Keplerian disks is studied on the large two-dimensional compressible scale, using a high-order-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, because of 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 nonaxisymmetric modes which can evolve into turbulence. However, this turbulence cannot play a significant role in angular momentum transport in disks.