We treat certain aspects of
the hydrodynamics of astrophysical accretion disks. 
We specifically consider non-self-gravitating disks
in the thin disk limit. These systems
are, in a hydrodynamic sense, stable according to the
Rayleigh criterion, and yet there is mounting evidence
that the dissipative and transport processes that must
be at work within these disks are hydrodynamic in nature
at least some of the time. 
We apply the developing theory of transition to turbulence
via large linear transient amplification of initial disturbances,
which depends upon the non-self-adjoint nature of the
differential operator that describes the dynamics of
perturbations to the background state in these systems.
We find that small initial perturbations can be tailored
to produce large growth in accretion disks, despite the
absence of any linear instability. Furthermore, perturbations
to the operator that governs the growth of perturbations
to the flow can create an operator that possesses modes
with unbounded growth. The size of the perturbation
to the operator that is necessary to make the governing
equations have unstable solutions is asymptotically 
small as a function of Reynolds number.