  The perturbations of weakly-viscous, barotropic, non-self-gravitating,
Newtonian rotating fluids are analyzed via a single partial differential
equation. The results are then used to find an expression for the
viscosity-induced normal-mode complex eigenfrequency shift, with respect to the
case of adiabatic perturbations. However, the effects of viscosity are assumed
to have been incorporated in the unperturbed (equilibrium) model. This paper is
an extension of the normal-mode formalism developed by Ipser & Lindblom for
adiabatic pulsations of purely-rotating perfect fluids. The formulas derived
are readily applicable to the perturbations of thin and thick accretion disks.
We provide explicit expressions for thin disks, employing results from previous
relativistic analyses of adiabatic normal modes of oscillation. In this case,
we find that viscosity causes the fundamental p- and g- modes to grow while the
fundamental c-mode could have either sign of the damping rate.
