Multifractal approach to fully developed turbulence

Abstract
The idea of the multifractals is basically contained in the large deviation theory; however, the introduction of the multifractal description in the 1980s had an important role in statistical physics, chaos and disordered systems. In particular, it clarified rather neatly that the usual idea, coming from critical phenomena, that just a few scaling exponents are relevant, is not completely correct, and an infinite set of exponents is indeed necessary for a complete characterization of the scaling features. I discuss the  multifractal approach  to  fully developed turbulence, and in particular  some nontrivial predictions for the statistical properties of the velocity gradients, the existence of an intermediate dissipative range and Lagrangian statistics.

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