Journal of Fluid Mechanics · 1985 · 662 citations · 40 references
A three‑dimensional periodic simulation with up to 1283 grid points (Rλ≈82.9) is used to compute higher‑order derivative correlations (skewness, flatness) of velocity and passive scalar fields, maintaining steady‑state turbulence through forcing and collecting statistics for comparison with flow structures. The study finds that scalar‑derivative flatness increases much faster with Reynolds number than velocity‑derivative flatness, while velocity and mixed‑derivative skewnesses remain unchanged; distinct fourth‑order exponents are identified, with the largest for vorticity flatness, contradicting lognormal and β models but supporting structural models; 3‑D visualizations show strong alignment of vorticity, rate‑of‑strain, and scalar‑gradient fields, with vorticity tubes perpendicular to the largest strain direction, and velocity spectra collapse to a single Kolmogorov curve with a short spectral regime.
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 1283 grid points are used with periodic boundary conditions in all three directions to achieve Rλ 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 spectral regime is observed.
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