Why is there a breakdown of Kolmogorov scaling in turbulence? What causes intermittency?
The basic Kolomogorov theory is a mean-field theory -- dissipation rate is considered to be constant over the whole volume of liquid. While the dissipation rate should depend on position -- that is where intermittency comes from.
Somewhere in 60's Kolmogorov and Obukhov attempted to account for this effect. But the problem is that there is the "Landau objection" -- the impossibility to devise universal formula, independent on the geometry of the problem (with scale $l$) for relatively small scales (which are $ \ll l$):
(Fluid Mechanics, Landau and Lifshitz, chapter 34.)