Reference solution to the Kelvin–Helmholtz problem with initial Mach number $\mathcal{M}$₀ = 10⁻². The solution was computed using PSH reconstruction and the LHLLC flux function on an 8192 × 4096 grid. The mass fraction X of the passive scalar is shown at four points in time: late in the linear growth of the instability (t = 0.2 $\mathcal{M}$₀⁻¹), at an early stage of nonlinear evolution (t = 0.4 $\mathcal{M}$₀⁻¹), at a stage when the primary vortices have fully formed (t = 0.8 $\mathcal{M}$₀⁻¹; the final time for all of our other Kelvin–Helmholtz simulations), and at a late stage when fine threads have formed inside the primary vortices (t = 1.6 $\mathcal{M}$₀⁻¹). We use the same color scale as in Figs. 4, D.2, and D.1, although 0 ≲ X & ≲ 1 in the reference solution.