Fully developed turbulence and the multifractal conjecture

TL;DR

This paper reviews the multifractal formalism for turbulence, discusses statistical fluctuations of the dissipative scale, and presents new results applying the formalism to shell models, highlighting Reynolds number effects and vortex dynamics.

Contribution

It provides a comprehensive review of the multifractal formalism in turbulence and introduces new applications to shell models, exploring Reynolds number dependence and vortex structures.

Findings

Multifractal formalism effectively describes turbulence statistics.

Application to shell models reveals Reynolds number effects.

Vorticity and vortex filaments influence turbulent dissipation.

Abstract

We review the Parisi-Frisch MultiFractal formalism for Navier--Stokes turbulence with particular emphasis on the issue of statistical fluctuations of the dissipative scale. We do it for both Eulerian and Lagrangian Turbulence. We also show new results concerning the application of the formalism to the case of Shell Models for turbulence. The latter case will allow us to discuss the issue of Reynolds number dependence and the role played by vorticity and vortex filaments in real turbulent flows.