Twisted accretion disks. III - The time-dependent equations

We derive the equations governing the time-dependent structure of a twisted thin accretion disk in which the planes of the disk rings differ from one another by no more than a small angle. The equations separate into a 'time-dependent twist-equation' which determines the orientation of the planes of the different disk rings, and a set of time-dependent flat (nontwisted) disk equations which determine the remaining structure of the disk. The twist-equation can be written in the form of two coupled differential equations of the diffusion type. We study some of its properties on the basis of a number of simple (but very restricted) examples of twisted disks. The possible importance of these properties for disks in X-ray binary systems, and for warped galactic disks, is mentioned.