  We employ the IllustrisTNG simulation data to investigate the turbulent and
thermal motions of the cosmic baryonic fluid. With continuous wavelet transform
techniques, we define the pressure spectra, or density-weighted velocity power
spectra, as well as the spectral ratios, for both turbulent and thermal
motions. We find that the magnitude of the turbulent pressure spectrum grows
slightly from $z=4$ to $2$ and increases significantly from $z=2$ to $1$ at
large scales, suggesting progressive turbulence injection into the cosmic
fluid, whereas from $z=1$ to $0$, the spectrum remains nearly constant,
indicating that turbulence may be balanced by energy transfer and dissipation.
The magnitude of the turbulent pressure spectra also increases with
environmental density, with the highest density regions showing a turbulent
pressure up to six times that of thermal pressure. We also explore the
dynamical effects of turbulence and thermal motions, discovering that while
thermal pressure provides support against structure collapse, turbulent
pressure almost counteracts this support, challenging the common belief that
turbulent pressure supports gas against overcooling.
