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, SNe and AGN feedbacks into our code, so that the effect of turbulence heating for IGM can be exhibited to the most extent. By computing cross-correlation functions rm(k) for the density field and rv(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−1Mpc for density field, while as large as 23 h−1Mpc 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 SNe and AGN feedbacks.

The spatial distribution between dark matter and baryonic matter of the Universe is biased or deviates from each other. In this work, by comparing the results derived from IllustrisTNG and WIGEON simulations, we find that many results obtained from TNG are similar to those from WIGEON data, but differences between the two simulations do exist. For the ratio of density power spectrum between dark matter and baryonic matter, as scales become smaller and smaller, the power spectra for baryons are increasingly suppressed for WIGEON simulations; while for TNG simulations, the suppression stops at $k=15-20\, {h {\rm Mpc}^{-1}}$, and the power spectrum ratios increase when $k\gt 20\, {h {\rm Mpc}^{-1}}$. The suppression of power ratio for WIGEON is also redshift-dependent. From z = 1 to z = 0, the power ratio decreases from about 70 per cent to less than 50 per cent at $k=8\, {h {\rm Mpc}^{-1}}$. For TNG simulation, the suppression of power ratio is enhanced with decreasing redshifts in the scale range $k\gt 4\, {h {\rm Mpc}^{-1}}$, but is nearly unchanged with redshifts in $k\lt 4\, {h {\rm Mpc}^{-1}}$. These results indicate that turbulent heating can also have the consequence to suppress the power ratio between baryons and dark matter. Regarding the power suppression for TNG simulations as the norm, the power suppression by turbulence for WIGEON simulations is roughly estimated to be 45 per cent at $k=2\, {h {\rm Mpc}^{-1}}$, and gradually increases to 69 per cent at $k=8\, {h {\rm Mpc}^{-1}}$, indicating the impact of turbulence on the cosmic baryons are more significant on small scales.

Continuous wavelet analysis has been increasingly employed in various fields of science and engineering due to its remarkable ability to maintain optimal resolution in both space and scale. Here, we introduce wavelet-based statistics, including the wavelet power spectrum, wavelet cross correlation, and wavelet bicoherence, to analyze the large-scale clustering of matter. For this purpose, we perform wavelet transforms on the density distribution obtained from the one-dimensional Zel’dovich approximation and then measure the wavelet power spectra and wavelet bicoherences of this density distribution. Our results suggest that the wavelet power spectrum and wavelet bicoherence can identify the effects of local environments on the clustering at different scales. Moreover, we apply the statistics based on the three-dimensional isotropic wavelet to the IllustrisTNG simulation at z = 0, and investigate the environmental dependence of the matter clustering. We find that the clustering strength of the total matter increases with increasing local density except on the largest scales. Besides, we notice that the gas traces dark matter better than stars on large scales in all environments. On small scales, the cross correlation between the dark matter and gas first decreases and then increases with increasing density. This is related to the impacts of the active galactic nucleus feedback on the matter distribution, which also varies with the density environment in a similar trend to the cross correlation between dark matter and gas. Our findings are qualitatively consistent with previous studies on matter clustering.