  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.
