Twenty-five years of multifractals in fully developed turbulence: a tribute to Giovanni Paladin

The paper On the multifractal nature of fully developed turbulence and chaotic systems, by Benzi et al (1984 J. Phys. A: Math. Gen. 17 3521) has been a starting point of many investigations on the different faces of self-similarity and intermittency in turbulent phenomena. Since then, the multifractal model has become a useful tool for the study of small-scale turbulence, in particular for detailed predictions of different Eulerian and Lagrangian statistical properties. On the occasion of the 50th birthday of our unforgettable friend and colleague Giovanni Paladin (1958-1996), we review here the basic concepts and some applications of the multifractal model for turbulence.