## 2. Basic non-stationary accretion disk equationIn the approximation of Newtonian potential we assume that the
velocity of a free particle orbiting at distance where is the Kepler angular
velocity; The height-integrated Euler equation on
and the continuity equation along the
height where is the angular velocity in the disk; - the surface density of the matter, and is the height-integrated viscous shear stresses between adjacent layers. The time-independent angular velocity is assumed although there can possibly be certain variations of in the non-Keplerian advective disks when a time-dependent pressure gradient is involved (see, e.g. Ogilvie 1999). It is convenient to introduce the following variables: , henceforth means the total moment of viscous forces acting between the adjacent layers, - the specific angular momentum of the matter in the disk, and . From Eq. (2) in view of (1) it follows that Substituting (4) in (3) and expressing In the case of the Keplerian disk . The advection-dominated solution by Narayan and Yi (1994) yields , where is a dimensionless constant. © European Southern Observatory (ESO) 2000 Online publication: March 28, 2000 |