  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.
