On the Perturbations of Viscous Rotating Newtonian Fluids

The perturbations of weakly-viscous, barotropic, non-self-gravitating,Newtonian rotating fluids are analyzed via a single partial differentialequation. The results are then used to find an expression for theviscosity-induced normal-mode complex eigenfrequency shift, with respect to thecase of adiabatic perturbations. However, the effects of viscosity are assumedto have been incorporated in the unperturbed (equilibrium) model. This paper isan extension of the normal-mode formalism developed by Ipser & Lindblom foradiabatic pulsations of purely-rotating perfect fluids. The formulas derivedare readily applicable to the perturbations of thin and thick accretion disks.We provide explicit expressions for thin disks, employing results from previousrelativistic analyses of adiabatic normal modes of oscillation. In this case,we find that viscosity causes the fundamental p- and g- modes to grow while thefundamental c-mode could have either sign of the damping rate.Comment: Accepted for publication by The Astrophysical Journal. 11 pages, no figure