  We investigate the time behavior of the fragmentation model with Kolmogorov
time scales and space contraction resembling the random $\beta$-model of
turbulence. The space averages computed at any instant using the entire spatial
realization of the velocity field are shown to fluctuate strongly in time, and
in this sense they are not observable. The time averaging required to achieve
the steady-state distributions in the case of constant energy supply are found.
The fluctuations of the probability distribution functions (PDFs) have
intermittency properties different from those of PDFs.
