Properties of Accretion Shock Waves in Viscous Flows Around Black Holes
  Accretion flows having low angular momentum and low viscosity can have standing shock waves. These shocks arise due to the presence of multiple sonic points in the flow. We study the region of the parameter space in which multiple sonic points occur in viscous flows in the absence of cooling. We also separate the parameter space in regions allowing steady shocks and oscillating shocks. We quantify the nature of two critical viscosities which separate the flow topologies. A post-shock region being hotter, it emits harder X-rays and oscillating shocks cause oscillating X-ray intensities giving rise to quasi-periodic oscillations. We show that with the increase in viscosity parameter, the shock always moves closer to the black hole. This implies an enhancement of the quasi-periodic oscillation frequency as viscosity is increased 
Sandip K. Chakrabarti and Santabrata Das