Amplitude spectrum (arbitrary units) of the averaged total energy of the perturbations for the thin-layer case at the end of the simulation for both numerical and linear analytic results. The vertical dot-dashed orange lines denote the maximum phase-mixing-generated wave number, k_maxR ≈ 33, obtained from Eq. (1), and an estimated wave number for which numerical diffusion starts to play a role, k_diffR ≈ 500. The red line is a least-squares linear fit for k_max <  k_⊥ <  k_diff in log-log scale whose slope is −1.83 ± 0.01. The green line is the same fit but for k_⊥ >  k_diff, whose slope is −3.28 ± 0.07.