Intermittency in turbulence is a topic which has been actively investigated for several decades, and a major part of Frisch's book (1995) is devoted to the subject.

Dynamical systems are often characterized by long quiescent periods interrupted by bursts of activity. This kind of dynamics is called intermittent. A way of quantifying this could be by high pass filtering the dynamical signal. If the signal has purely Gaussian statistics, which would be natural for a system of many degrees of freedom, high pass filtering is a linear operation and the high pass filtered signal would be Gaussian as well. If the high pass signal differs from the Gaussian by having heavier tails, it is intermittent. Thus intermittency could be formally defined by the deviation from Gaussian statistics. In this case, intermittency could be a sign of dynamics not merely governed by simple statistics given by the central limit theorem or equilibrium statistical mechanics. In the case of a turbulent velocity field, high pass filtering roughly corresponds to extracting information on velocity differences below or at some cutoff length scale. As described previously, the statistics of velocity increments in turbulence is found not to be Gaussian. The self-similarity of the flow assumed in K41 theory is not valid and there will be corrections to the scaling exponents for the moments of the velocity increments as expressed in (1.64).

Kolmogorov's lognormal correction

The dynamical origin of the deviation from the K41 value for the scaling exponents is a very non-uniform distribution of the energy dissipation.