  Direct numerical simulations of the forced Navier-Stokes equations were
performed, in which each shell-averaged quantity evolved from a value
appropriate to an initial Gaussian state, to fluctuate about a mean value. Once
the transient had passed, mean values (and their associated statistics) were
obtained by sampling the evolved time-series at intervals of the order of an
eddy-turnover time. This was repeated for a range of Taylor-Reynolds numbers
from 10.6 to 335.2. With increasing Reynolds number, our results for energy
spectra, transfer spectra and inertial flux supported the Kolmogorov-Obukhov
picture of turbulent energy transfer. In particular, we observed the onset of
scale-invariance of the inertial flux, accompanied by the onset of the -5/3
power law in the energy spectrum for the corresponding inertial range of
wavenumbers. Detailed comparisons showed that our results were in agreement
with those found in many other investigations. Flow visualization methods were
used to study the internal intermittency. This phenomenon is seen in single
realisations but was found to average out with increasing number of
realisations under ensemble-averaging. Following a critical review of the
literature relating to the controversy about intermittency effects versus
finite-Reynolds number corrections, it was concluded that, for the case of
stationary isotropic turbulence, internal intermittency cannot affect the
Kolmogorov-Obukhov picture, as this is constructed entirely in terms of
ensemble-averaged mean quantities.
