Gaseous flows in disk galaxies

The equations of motion and continuity which determine the structure of the gaseous component of a thin disk galaxy have been studied for the case in which the spiral structure is stationary in a coordinate system rotating with the spiral pattern. The solution depends on a Fourier analysis of the relevant physical quantities in the angular coordinate, and approximate solutions are presented for both the 20 and 40 modes. It is necessary to assume that a parameter of smallness E can be associated with each Fourier mode, and that terms of order E2 or higher can be ignored in equations of order unity. In this sense, the solutions are approximate; and as one would expect, the solutions for the 20 mode coincide with the hydrodynamical results of the purely linearized theory of Lin and Shu. Subject headings: galactic structure - galaxies - hydrodynamics