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

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.