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

TL;DR

This paper reviews 25 years of research on multifractals in fully developed turbulence, highlighting key concepts, applications, and the influence of Giovanni Paladin's work in understanding turbulence's complex statistical properties.

Contribution

It provides a comprehensive overview of the development and application of the multifractal model in turbulence studies over the past 25 years, honoring Giovanni Paladin's contributions.

Findings

Multifractal models effectively describe turbulence intermittency.

The approach has advanced understanding of Eulerian and Lagrangian turbulence statistics.

The review highlights the evolution and impact of multifractal analysis in turbulence research.

Abstract

The paper {\it On the multifractal nature of fully developed turbulence and chaotic systems}, by R. Benzi {\it et al.} published in this journal in 1984 (vol {\bf 17}, page 3521) has been a starting point of many investigations on the different faces of selfsimilarity 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. In the occasion of the 50-th 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.