  Cold accretion disks such as those in star-forming systems, quiescent
cataclysmic variables, and some active galactic nuclei, are expected to have
neutral gas which does not couple well to magnetic fields. The turbulent
viscosity in such disks must be hydrodynamic in origin, not
magnetohydrodynamic. We investigate the growth of hydrodynamic perturbations in
a linear shear flow sandwiched between two parallel walls. The unperturbed flow
is similar to plane Couette flow but with a Coriolis force included. Although
there are no exponentially growing eigenmodes in this system, nevertheless,
because of the non-normal nature of the eigenmodes, it is possible to have a
large transient growth in the energy of perturbations. For a constant angular
momentum disk, we find that the perturbation with maximum growth has a
wave-vector in the vertical direction. The energy grows by more than a factor
of 100 for a Reynolds number R=300 and more than a factor of 1000 for R=1000.
Turbulence can be easily excited in such a disk, as found in previous numerical
simulations. For a Keplerian disk, on the other hand, similar vertical
perturbations grow by no more than a factor of 4, explaining why the same
simulations did not find turbulence in this system. However, certain other
two-dimensional perturbations with no vertical structure do exhibit modest
growth. For the optimum two-dimensional perturbation, the energy grows by a
factor of ~100 for R~10^4.5 and by a factor of 1000 for R~10^6. It is
conceivable that these two-dimensional disturbances might lead to
self-sustained turbulence. The Reynolds numbers of cold astrophysical disks are
much larger even than 10^6, therefore, hydrodynamic turbulence may be possible
in disks.
