Intermittency of energy dissipation in high-resolution direct numerical simulation of turbulence

The statistics of energy dissipation rate in turbulence and the ratio alpha(n) equivalent to is an element of(n+1)/is an element of(n) is studied using the data of direct numerical simulations of incompressible turbulence with up to 2048(3) grid points, where is an element of(n) is the average of (is an element of) over tilde over a sphere of radius r(n) with r(n)/r(n+1) = const > 1. The data do not support the well-known assumption of the scale-independence of the statistics of alpha(n) nor that of the statistical independence of alpha(n)'s from each other, but suggest the existence of a scale range where the correlation between log alpha(n) and log alpha(n+k) is insensitive to n. A simple zero-cumulant approximation compatible with these observations yields an estimate of the moment <(is an element of(n))(p)> for given < log alpha(n)>'s, in good agreement with the simulations for approximately vertical bar p vertical bar <= 4.