(a) Probability-density-function of s = lnρ for varying Mach and Reynolds numbers. Colours from dark blue to yellow correspond to increasing Reynolds numbers as shown in the legend. The grey dashed lines are the associated Gaussian distributions (Eq. (3)). (b) Evolution of the variance σ_s² with respect to Ma. The prediction (Eq. (4)) is also plotted for different type of forcing (compressive, solenoidal, mixed). The shaded regions represent the statistical uncertainty which affects only the far tails of the PDFs (a) and thus marginally the variance σ_s² (b).