The interface animation shows h(x,t) = h₀e^Re(s)tcos(kx + Im(s)t) for the fastest-growing mode, shaded into billows once the amplitude passes a threshold. It is linear theory: real KH billows roll up into vortex cores that this model cannot produce, so treat the late-time picture as suggestive, not literal. The lower plot is the honest part — the exact dispersion relation.