Many scaling relations are observed for self-gravitating systems in the universe. We explore the consistent understanding of them from a simple principle based on the proposal that the collisionless dark matter fluid terns into a turbulent state, i.e. dark turbulence, after crossing the caustic surface in the non-linear stage. The dark turbulence will not eddy dominant reflecting the collisionless property. After deriving Kolmogorov scaling laws from Navier-Stokes equation by the method similar to the one for Smoluchowski coagulation equation, we apply this to several observations such as the scale-dependent velocity dispersion, mass-luminosity ratio, magnetic fields, and massangular momentum relation, power spectrum of density fluctuations. They all point the concordant value for the constant energy flow per mass: 0.3cm 2 /sec 3 , which may be understood as the speed of the hierarchical coalescence process in the cosmic structure formation. PACS numbers: Cosmology: theory, Gravitation, Turbulence, Cosmology: dark matter, Cosmology: observations, Hydrodynamics 98.80.-k 95.35 +d 98.65.-r