A case of strong non linearity: intermittency in highly turbulent flows

TL;DR

This paper explores the nonlinear intermittency in highly turbulent flows, examining theoretical singularities and experimental velocity-acceleration correlations that challenge classical turbulence scaling laws.

Contribution

It provides a review of the theoretical possibility of finite-time singularities and presents experimental evidence of velocity-acceleration correlations inconsistent with Kolmogorov's laws.

Findings

Velocity-acceleration correlations align with Leray's self-similar singular solutions.

Experimental data contradict Kolmogorov scaling laws.

Small viscosity effects influence self-similar solutions in turbulence.

Abstract

It has long been suspected that flows of incompressible fluids at large or infinite Reynolds number (namely at small or zero viscosity) may present finite time singularities. We review briefly the theoretical situation on this point. We discuss the effect of a small viscosity on the self-similar solution of the Euler equations for inviscid fluids. Then we show that single point records of velocity fluctuations in the Modane wind tunnel display correlations between large velocities and large accelerations in full agreement with scaling laws derived from Leray's equations (1934) for self-similar singular solutions of the fluid equations. Conversely those experimental velocity-acceleration correlations are contradictory to the Kolmogorov scaling laws.