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.