  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. 
Turbulence-induced deviation between baryonic field and dark matter   field in the spatial distribution of the Universe