Instability of a shock wave formed in a disk accretion on to a non-rotating black hole

The results of stability analysis for a steady state shock wave, formed in disk accretion on to a non-rotating black hole, are considered. The stability of such a shock in the framework of linear analysis is reduced to solution of Stourm-Liouville problem between the shock front and the sonic point with corresponding outer and inner boundary conditions. The results of an eigenvalue problem demonstrated the instability of the shock wave against azimuthal perturbations. Numerical 2D modelling shows good agreement with the result of linear semi-analitical analysis at the linear regime. At nonlinear stage the instability saturates at a low level and a strongly deformed asymmetric shock wave is formed.