Structures and structure functions in the inertial range of turbulence

The deviations from the Kolmogorov 1941 laws of inertial range of turbulence are investigated using the results from the direct numerical simulations of an unforced flow starting from a high-symmetry initial condition by Kida [J. Phys. Soc. Jpn. 54, 2132 (1985)]. The resolution is 3003 points (12003 with symmetries, maximum wavenumber 400 after dealiasing), and the Taylor scale Reynolds number is in the order of 100. The scaling exponents of the pth order longitudinal and lateral structure function (for p between 2 and 16) are computed using different methods with particular focus on a recent method by Benzi and collaborators [Phys. Rev. E 48, R29 (1993); Europhys. Lett. 32, 709 (1995)]. Both longitudinal and lateral scaling exponents deviate considerably from Kolmogorov 1941 (K-41) scaling laws, the lateral deviating much more than the longitudinal. A systematic methodology (strain–enstrophy state) is developed to relate the K-41 deviations to different structures in the field. Enstrophy-dominated struct...

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