Speaker
Description
Perturbation theory is a powerful tool of the modern fluid dynamics. Various perturbation methods have been successfully applied in many difficult problems of aerodynamics and hydrodynamics. In the context of geometrically thin accretion flows, a regular perturbation method has been recently used by Kluzniak and Kita for consistent treatment of coupled radial and vertical structure of thin disks. Their analysis revealed nontrivial velocity field, including equatorial back-flows and vertical shear of the rotation velocity. The radial structure in their solution has however the same draw back as the standard Shakura-Sunyaev disk model. In the leading order, it is governed by algebraic equations leading to singular behavior of the solution near the radii where the viscous torque vanishes. In our view this problem is related to the use of the regular perturbation method. In this contribution, we use a singular perturbation method based on matched asymptotic expansions to describe the flow in the vicinity of the zero-torque radii. This way we find a global three-dimensional structure of black-hole accretion disks including the flow near the inner edge of the disk and the plunging region, as well as the structure of the flow in boundary layers in the innermost regions of neutron-stars accretion disks.