  We discuss non-self-gravitating hydrodynamic disks in the thin disk limit.
These systems are stable according to the Rayleigh criterion, and yet there is
some evidence that the dissipative and transport processes in these disks are
hydrodynamic in nature at least some of the time. We draw on recent work on the
hydrodynamics of laboratory shear flows. Such flows are often experimentally
unstable even in the absence of a linear instability. The transition to
turbulence in these systems, as well as the large linear transient
amplification of initial disturbances, may depend upon the non-self-adjoint
nature of the differential operator that describes the dynamics of
perturbations to the background state. We find that small initial perturbations
can produce large growth in accretion disks in the shearing sheet approximation
with shearing box boundary conditions, despite the absence of any linear
instability. Furthermore, the differential operator that propagates initial
conditions forward in time is asymptotically close (as a function of Reynolds
number) to possessing growing eigenmodes. The similarity to the dynamics of
laboratory shear flows is suggestive that accretion disks might be
hydrodynamically unstable despite the lack of any known instability mechanism.
