  We study the two-dimensional structure of thin transonic accretion discs in
the vicinity of a non-spinning black hole within the framework of
hydrodynamical version of the Grad-Shafranov equation. Our analysis focuses on
the region inside the marginally stable orbit (MSO), r < r_{ms}. We show that
all components of the dynamical force in the disc become significant near the
sonic surface and (especially) in the supersonic region. Under certain
conditions, the disc structure can be far from radial, and we review the
affected disc properties, in particular the role of the critical condition at
the sonic surface. Finally, we present a simple model aimed at explaining
quasi-periodical oscillations that have been observed in the infra-red and
X-ray radiation of the Galactic Centre.
