ON THE ADIABATIC PULSATIONS OF ACCRETION DISKS AND ROTATING STARS

The adiabatic pulsations of rotating Newtonian fluids, including nonbarotropic configurations, are represented completely in terms of two scalar potentials. The second-order equations that determine these potentials are more convenient to solve numerically than the standard Lagrangian-displacement form of the equations. A variational principle is derived for these equations from which estimates of the frequencies of the modes may be obtained. This analysis generalizes previous work by describing the adiabatic pulsations of fluids having any (including nonbarotropic) equation of state, any (including differential) rotation law, and self-gravitation. It is applicable, therefore, to the pulsations of rotating stars or thick accretion disks.