Figure 7
Cumulated energy distribution (equation ( 29 )) for all methods and resolutions, normalized by a factor \(\pmb{2/v_{\mathrm{rms}}^{2}}\) to be equal to 1 for large k . As a reference for comparison we also plot the asymptotic profile expected from Kolmogorov’s theory (equation (31)). The different panels are, from left to right and from top to bottom, the results obtained with PPM_HLLC, PPM_HLLC_CFL0.8, PPM_HLLE, TVD_HLLE and WENOZ_HLLC. The bottom right panel show a comparison of all of the methods at 5123. At low resolution all of the schemes show an excess of energy at intermediate scales, due to the bottleneck. Only at the highest resolution at least, roughly, 80% of the energy is correctly resolved.