  The cosmic baryonic fluid at low redshifts is similar to a fully developed
turbulence. In this work, we use simulation samples produced by the hybrid
cosmological hydrodynamical/N-body code, to investigate on what scale the
deviation of spatial distributions between baryons and dark matter is caused by
turbulence. For this purpose, we do not include the physical processes such as
star formation, supernovae (SNe) and active galactic nucleus (AGN) feedback
into our code, so that the effect of turbulence heating for IGM can be
exhibited to the most extent. By computing cross-correlation functions $r_m(k)$
for the density field and $r_v(k)$ for the velocity field of both baryons and
dark matter, we find that deviations between the two matter components for both
density field and velocity field, as expected, are scale-dependent. That is,
the deviations are the most significant at small scales and gradually diminish
on larger and larger scales. Also, the deviations are time-dependent, i.e. they
become larger and larger with increasing cosmic time. The most emphasized
result is that the spatial deviations between baryons and dark matter revealed
by velocity field are more significant than that by density field. At z = 0, at
the 1% level of deviation, the deviation scale is about 3.7 $h^{-1}$Mpc for
density field, while as large as 23 $h^{-1}$Mpc for velocity field, a scale
that falls within the weakly non-linear regime for the structure formation
paradigm. Our results indicate that the effect of turbulence heating is indeed
comparable to that of these processes such as SN and AGN feedback.
