Many scaling relations have been observed for self-gravitating systems (SGS) in the universe. We explore a consistent understanding of them from a simple principle based on the proposal that the collision-less dark matter (DM) fluid terns into a turbulent state, i.e. dark turbulence, 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 several observations such as the scale-dependent velocity dispersion, mass-luminosity ratio, and mass-angular momentum relation. They all point the concordant value for the constant energy flow per mass: 0.3 cm2/s3, which may be understood as the speed of the hierarchical coalescence process in the cosmic structure formation.