Universality of the Kolmogorov constant in numerical simulations of turbulence

Abstract

Motivated by a recent survey of experimental data [K. R. Sreenivasan, Phys. Fluids 7, 2778 (1995)], we examine data on the Kolmogorov spectrum constant in numerical simulations of isotropic turbulence, using results both from previous studies and from new direct numerical simulations over a range of Reynolds numbers (up to 240 on the Taylor scale) at grid resolutions up to [Formula Presented] It is noted that in addition to [Formula Presented] scaling, identification of a true inertial range requires spectral isotropy in the same wave-number range. The new simulations indicate approximate inertial range behavior at lower wave numbers than previously thought, with proportionality constants [Formula Presented] and [Formula Presented] in the one- and three-dimensional energy spectra, respectively, about 0.60 and 1.62. The latter suggests [Formula Presented] in excellent agreement with experiments. However, the one- and three-dimensional estimates are not fully consistent, because of departures (due to numerical and statistical limitations) from isotropy of the computed spectra at low wave numbers. The inertial scaling of structure functions in physical space is briefly addressed. © 1997 The American Physical Society.