We study the propagation properties of three-dimensional oscillating modes in a differentially rotating gaseous disk, without self-gravity. We consider mainly axisymmetric waves in a locally vertically isothermal disk and show that the wave structure can be determined analytically. Low-frequency axisymmetric g-modes propagate in a region that lies somewhere inside the wave resonance radius defined by omega = OMEGA(r), for wave frequency omega and disk angular speed OMEGA(r). High-frequency axisymmetric p-modes propagate in a region that lies somewhere outside this resonance. Waves exist that cause the disk midplane to oscillate vertically (corrugation waves), as well as waves that keep the disk midplane fixed. For a Keplerian disk, the p-modes and g-modes are separated by a forbidden region for all modes, except for the mode with no vertical nodes (n = 0). Inwardly propagating g-modes become increasingly focused toward the disk midplane, experience a rapidly decreasing radial group velocity, and increasing perturbing velocities near the disk midplane. Such waves can never reach the disk radial center and must almost certainly shock near midplane. We discuss briefly the extension of these results to nonaxisymmetric waves of low azimuthal wavenumber, which have been previously considered in accretion disks of close binary star systems.
