Two-dimensional structure of thin transonic discs: theory and   observational manifestations
  We study the two-dimensional structure of thin transonic accretion discs in the vicinity of black holes. We use the hydrodynamical version of the Grad-Shafranov equation and focus on the region inside the marginally stable orbit. We show that all components of the dynamical force in the disc become significant near the sonic surface and especially important in the supersonic region. Under certain conditions, the disc structure is shown to be far from radial, and we review the affected disc properties, in particular the role of the critical condition at the sonic surface: it determines neither the accretion rate nor the angular momentum in the accretion disc. Finally, we present a simple model explaining quasi-periodical oscillations that have been observed in the infrared and X-ray radiation of the Galactic Centre. 
V. S. Beskin, A. D. Tchekhovskoy