Many scaling relations have been observed forself-gravitating systems (SGS) in the universe. We explore a consistentunderstanding of them from a simple principle based on the proposal that thecollision-less dark matter (DM) fluid terns into a turbulent state, i.e. darkturbulence, after crossing the caustic surface in the non-linear stage.After deriving Kolmogorov scaling laws from Navier-Stokes and Jeans equations by the method used in solving the Smoluchowski coagulation equation, we apply this to severalobservations such as the scale-dependent velocity dispersion,mass-luminosity ratio, and mass-angular momentum relation. They all pointthe concordant value for the constant energy flow per mass: 0.3 cm2/s3, which may be understood as the speed of the hierarchicalcoalescence process in the cosmic structure formation.