  Despite observational evidence for cold neutral astrophysical accretion
disks, the viscous process which may drive the accretion in such systems is not
yet understood. While molecular viscosity is too small to explain the observed
accretion efficiencies by more than ten orders of magnitude, the absence of any
linear instability in Keplerian accretion flows is often used to rule out the
possibility of turbulent viscosity. Recently, the fact that some fine tuned
disturbances of any inviscid shear flow can reach arbitrarily large transient
growth has been proposed as an alternative route to turbulence in these
systems. We present an analytic study of this process for 3D plane wave
disturbances of a general rotating shear flow in Lagrangian coordinates, and
demonstrate that large transient growth is the generic feature of
non-axisymmetric disturbances with near radial leading wave vectors. The
maximum energy growth is slower than quadratic, but faster than linear in time.
The fastest growth occurs for two dimensional perturbations, and is only
limited by viscosity, and ultimately by the disk vertical thickness.
  After including viscosity and vertical structure, we find that, as a function
of the Reynolds number, R, the maximum energy growth is approximately 0.4
(R/log R)^{2/3}, and put forth a heuristic argument for why R > 10^4 is
required to sustain turbulence in Keplerian disks. Therefore, assuming that
there exists a non-linear feedback process to replenish the seeds for transient
growth, astrophysical accretion disks must be well within the turbulent regime.
However, large 3D numerical simulations running for many orbital times, and/or
with fine tuned initial conditions, are required to confirm Keplerian
hydrodynamic turbulence on the computer.
