Recording of Leray-type singular events in a high speed wind tunnel

TL;DR

This paper presents experimental evidence from a high-speed wind tunnel indicating that large velocity fluctuations are correlated with accelerations consistent with Leray's finite-time singularities, challenging classical Kolmogorov turbulence models.

Contribution

It provides the first experimental recording of Leray-type singular events in turbulent flows, linking theoretical singularities to observable phenomena.

Findings

Correlations between large velocities and accelerations match Leray's scaling laws.

Experimental data contradict Kolmogorov's turbulence cascade model.

Singular events are distinct from classical turbulence cascades.

Abstract

It has long been suspected that flows of incompressible fluids at very large or infinite Reynolds may present finite time singularities. We review briefly the theoretical situation on this point. Then we show that single point records of velocity fluctuations in the Modane wind tunnel show correlations between large velocities and large accelerations that are in agreement with the scaling laws for such singularities as derived by Leray in 1934. Conversely the experimental correlations between velocity and acceleration are not explainable by Kolmogorov scalings. This implies in particular that the singularities cannot be seen as the end of a cascade in the sense of Kolmogorov, but are best described as singular events in the sense of Leray.