Large scale properties in turbulent spherically symmetric accretion

In this investigation to study the role of turbulence in a spherically symmetric accreting system, it has been seen that on very large spatial scales of the system, i.e. in the subsonic region of the accreting system (where the accreting fluid may be treated as weakly compressible), the coupling of the mean flow and the fluctuations, gives rise to a scaling relation for the effective "turbulent viscosity". This in its turn, leads to a dynamic scaling for sound propagation in accretion processes. On large length scales of the accreting system, the scaling behaviour of the speed of sound has been found to go as the one third power of the length scale. As a consequence, the sonic horizon of the transonic inflow solution is shifted inwards, in comparison with the inviscid situation. This effect of a significantly large "turbulent viscosity" has been seen to be compatible with the conclusions drawn about the effect of the presence of molecular viscosity, as given in the Navier-Stokes equation