  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 collision-less 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 collision-less 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 mass-angular momentum relation, power spectrum of density fluctuations.
They all point the concordant value for the constant energy flow per mass: $0.3
cm^2/sec^3$, which may be understood as the speed of the hierarchical
coalescence process in the cosmic structure formation.

Astrophysics