STRUCTURES AND STRUCTURE FUNCTIONS IN THE INERTIAL RANGE OF TURBULENCE

The deviations from the Kolmogorov 1941 laws of inertial range of turb ulence are investigated using the results from the direct numerical si mulations of an unforced flow starting from a high-symmetry initial co ndition by Kida [J. Phys. Soc. Jpn. 54, 2132 (1985)]. The resolution i s 300(3) points (1200(3) 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 s tructure function (for p between 2 and 16) are computed using differen t methods with particular focus on a recent method by Benzi and collab orators [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 m ore than the longitudinal. A systematic methodology (strain-enstrophy state) is developed to relate the K-41 deviations to different structu res in the field. Enstrophy-dominated structures are found to contribu te mainly to the deviations in lateral direction whereas the strain-do minated structures to longitudinal direction, albeit in an imbalanced proportion, the lateral deviations being much stronger. Structures who se enstrophy and strain are comparable in magnitude contribute to devi ations in both directions. Results are compared to several intermitten cy models and experiments. Special focus is given to the recent She-Le veque model [Phys. Rev. Lett. 72, 336 (1994)] whose predictions gave v ery good agreement if compared to the longitudinal exponents. The mode l is rewritten for a family of free parameters, giving predictions as good as the original one. The lateral scaling exponents disagree with both the She-Leveque model and the experimental results (from longitud inal velocity measurements) suggesting that the dominant contribution to intermittency can only be detected from the lateral structure funct ion measurements. (C) 1997 American Institute of Physics.