  We sample a velocity field that has an inertial spectrum and a skewness that
matches experimental data. In particular, we compute a self-consistent
correction to the Kolmogorov exponent and find that for our model it is zero.
We find that the higher order structure functions diverge for orders larger
than a certain threshold, as theorized in some recent work. The significance of
the results for the statistical theory of homogeneous turbulence is reviewed.
