Small-scale statistics of turbulence at high Reynolds numbers by massive computation

Velocity field statistics in the inertial and dissipation ranges of three-dimensional, homogeneous, steady turbulent flow are studied using high-resolution direct numerical simulation (DNS) with up to N = 1024(3) grid points. The Taylor microscale Reynolds number is between 38 and 460. The Kolmogorov spectrum E(k) = Kepsilon(-2/3)k(-5/3) is observed clearly, and the value of the constant K is K = 1.64. The structure functions and their scaling exponents are measured and found to be anomalous. The statistics of the volume-averaged energy dissipation rate per unit mass are also examined. (C) 2002 Elsevier Science B.V. All rights reserved.