  Dark matter, if exists, accounts for five times as much as the ordinary
baryonic matter. Compared to hydrodynamic turbulence, the flow of dark matter
might possess the widest presence in our universe. This paper presents a
statistical theory for the flow of dark matter that is compared with N-body
simulations. By contrast to hydrodynamics of normal fluids, dark matter flow is
self-gravitating, long-range, and collisionless with a scale dependent flow
behavior. The peculiar velocity field is of constant divergence nature on small
scale and irrotational on large scale. The statistical measures, i.e.
correlation, structure, dispersion, and spectrum functions are modeled on both
small and large scales, respectively. Kinematic relations between statistical
measures are fully developed for incompressible, constant divergence, and
irrotational flow. Incompressible and constant divergence flow share same
kinematic relations for even order correlations. The limiting correlation of
velocity $\rho_L=1/2$ on the smallest scale ($r=0$) is a unique feature of
collisionless flow ($\rho_L=1$ for incompressible flow). On large scale,
transverse velocity correlation has an exponential form $T_2\propto e^{-r/r_2}$
with a constant comoving scale $r_2$=21.3Mpc/h that maybe related to the
horizon size at matter-radiation equality. All other correlation, structure,
dispersion, and spectrum functions for velocity, density, and potential fields
are derived analytically from kinematic relations for irrotational flow. On
small scale, longitudinal structure function follows one-fourth law of
$S^l_2\propto r^{1/4}$. All other statistical measures can be obtained from
kinematic relations for constant divergence flow. Vorticity is negatively
correlated for scale $r$ between 1 and 7Mpc/h. Divergence is negatively
correlated for $r$>30Mpc/h that leads to a negative density correlation.
