Figure 8
Compensated 3rd-order structure functions (equation ( 23 )) for all the numerical methods and resolutions. The structure functions are compensated and scaled so that they should be close to one where the \(4/5\)-law (equation (25)) is verified. The data is plotted as a function of the dimensionless separation \(r/\Delta x\). The first five panels show the PPM_HLLC (upper left), PPM_HLLC_CFL0.8 (upper center), PPM_HLLE (upper right), TVD_HLLE (lower left) and WENOZ_HLLC (lower center) group of runs. The last panel (lower right) shows a comparison of all of the methods at the highest resolution (5123). The \(4/5\)-law is very well verified in our data suggesting that (1) anisotropic corrections are subdominant and (2) all of the simulations behave in a way consistent with large Reynolds numbers turbulence at the largest scales.