Intermittency and cascades

The theory of intermittency in multiplicative cascades is reviewed, with special, but not exclusive, emphasis on its applications to turbulence. It is noted that, in many physical systems, this theory is incomplete, and two of its limitations are discussed in some detail. It is first argued that large fluctuations will in most cases behave differently from the lower-level background, since the overall mean introduces an intensity scale that breaks self-similarity, and that they will, under the right conditions, evolve into coherent structures decoupled from the rest of the system. The effect of non-local interactions is then addressed. It is shown that the results depend on the nature of the interaction, and that it is possible to generate non-local cascades which are less intermittent, as intermittent, or even more intermittent, than local ones. It is finally stressed that the multiplicative theory of cascades is a kinematic description, and that its relation with the real dynamics is not straightforward.