Hydrodynamic Turbulence in Accretion Disks
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Turbulent viscosity in cold accretion disks is likely to be hydrodynamic in origin. We investigate the growth of hydrodynamic perturbations in a small region of a disk, which we model as a linear shear flow with Coriolis force, between two parallel walls. Although there are no exponentially growing eigenmodes in this system, because of the non-normal nature of the modes, it is possible to have a large transient growth in the energy of certain perturbations. For a constant angular momentum disk, the energy grows by more than a factor of 1000 for a Reynolds number of only 1000, and so turbulence is easily excited. For a Keplerian disk, the growth is more modest, and energy growth by a factor of 1000 requires a Reynolds number of nearly a million. Accretion disks have even larger Reynolds numbers than this. Therefore, transient growth of perturbations could seed turbulence in such disks.
6 pages including 5 figures. To appear in the proceedings of 22nd Texas Symposium on Relativistic Astrophysics, Stanford University, December 13-17, 2004
6 pages including 5 figures. To appear in the proceedings of 22nd Texas Symposium on Relativistic Astrophysics, Stanford University, December 13-17, 2004