Quasi-geostrophic motions in a galactic flow

Abstract

We continue the theoretical investigation of geostrophically balanced motions of a star gas in a rotating galaxy. The method of small perturbations is employed to derive a quasi geostrophic vorticity equation suitable for solving initial value problems for ‘slow’ galactic eddying motions. The results derived for this simple theoretical model are then generalized to obtain approximate geostrophic forecast equations suitable for study of nonlinear galactic motions over a whole disk galaxy. A simple discussion of the stability of our approximate vorticity equation is presented. It is expected that in the absence of rapid gravitational instabilities, actual eddy motions observed in spiral galaxies will be at least approximately of the type of motion discussed in this paper. The Rossby adjustment problem is investigated in this context.