Histogram of the compression frequency −∇ ⋅ v in the entire domain. The negative (positive) frequency population represents expansions (compressions) and is coloured in blue (magenta). The green line represents the histogram of compression frequencies corresponding to $-\mathrm{\nabla }·\mathbf{v}\le \frac{c_s}{ϵ.ds}$, with ϵ = 6 (see Eq. 1)). We use a darker shade of magenta to highlight compressions attributed to non-linear shocks.