Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence

In a three-dimensional simulation higher-order derivative correlations, including skewness and flatness (or kurtosis) factors, are calculated for velocity and passive scalar fields and are compared with structures in the flow. Up to 128 3 grid points are used with periodic boundary conditions in all three directions to achieve R λ to 82. 9. The equations are forced to maintain steady-state turbulence and collect statistics. The scalar-derivative flatness is found to increase much faster with Reynolds number than the velocity-derivative flatness, and the velocity- and mixed-derivative skewnesses do not increase with Reynolds number. Separate exponents are found for the various fourth-order velocity-derivative correlations, with the vorticity-flatness exponent the largest. This does not support a major assumption of the lognormal and β models, but is consistent with some aspects of structural models of the small scales. Three-dimensional graphics show strong alignment between the vorticity, rate-of-strain, and scalar-gradient fields. The vorticity is concentrated in tubes with the scalar gradient and the largest principal rate of strain aligned perpendicular to the tubes. Velocity spectra, in Kolmogorov variables, collapse to a single curve and a short -53 spectral regime is observed.