A statistically stationary isotropic turbulence is of quasi-closure, i.e. i
ts high-order statistical moments can be derived from its low-order moments
. A workable quasi-closure scheme is developed for the structure functions
of incompressible homogeneous isotropic turbulence based upon a non-Gaussia
n statistical model. The second order structure function is obtained by sol
ving the spectral dynamic equation or by using an empirical formula such as
the Batchelor fit, and then the high-order structure functions is calculat
ed by the quasi-closure scheme. We study the absolute and relative scaling
of the structure functions of isotropic turbulence in connection with Kolmo
gorovs' 1941 theory (K41) and his 1962 theory (K62). In contrast to K62 and
various intermittency models, our results suggest a different picture of s
caling of isotropic turbulence: the anomalous scaling of structure function
s observed in experiments and numerical simulations is a finite Reynolds nu
mber effect, and the K41 normal scaling is valid in the real Kolmogorov ine
rtial range corresponding to an infinite Reynolds number.