Why is there a breakdown in Kolmogorov scaling in turbulence?

Question

Why is there a breakdown of Kolmogorov scaling in turbulence? What causes intermittency?

Answer 1

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$):

... It may be thought that the possibility exists in principle of obtaining a universal formula, applicable to any turbulent flow, which should give $B_{rr}$ and $B_{tt}$ for all distances $r$ that are small compared with $l$. In fact, however, there can be no such formula, as we see from the following argument. The instantaneous value of $(v_{2i}-v_{1i})(v_{2k}-v_{1k})$ might in principle be expressed as a universal function of the energy dissipation $\epsilon$ at the instant considered. When we average these expressions, however, an important part will be played by the manner of variation of $\epsilon$ over times of the order of the periods of large eddies (with size $\sim l$) and this variation is different for different flows. The result of averaging therefore cannot be universal.

(Fluid Mechanics, Landau and Lifshitz, chapter 34.)