Internal structure of a thin transonic disk
  The internal structure of the thin transonic disk accreting onto a nonrotating black hole inside the last stable orbit ($r < 3r_{\rm g}$) is considered within the hydrodynamical version of the Grad-Shafranov equation. It is shown that in the vicinity of the sonic surface takes place a sharp diminishing of the disk thickness. As a result, in the vertical balance equation the dynamical forces $\rho[({\bf v}\nabla){\bf v}]_{\theta}$ become important, these on the sonic surface being of the same order as the pressure gradient $\nabla_{\theta} P$. In the supersonic region the thickness of the disk is determined by the form of ballistic trajectories rather than by the pressure gradient. 
V.S. Beskin, A.D. Tchekhovskoy