Corrugation waves in a differentially-rotating gas layer

The perturbations of a differentially-rotating galactic gas layer, uniform parallel to the plane, are considered. The gas is assumed to be moving in a fixed stellar potential, and motion in the vertical direction out of the plane is included. Using a local approximation the linearized hydrodynamic equations are solved asymptotically in the limit of weak shear, and a dispersion relation for the perturbations obtained. The solutions of this dispersion relation can be classified by frequency as (a) fast waves, with frequencies closely related to the oscillation frequency of a particle in the vertical potential, and (b) slow waves, with frequencies close to the epicyclic frequency. There are an infinite number of modes of each class, each mode having a different structure in the vertical direction, and all of them, with the exception of the simplest slow mode, involve vertical motion and a corrugated density structure. (author)