Intermittency and Leray singularities

Yves Pomeau
Ladhyx Ecole polytechnique Palaiseau, France
Real turbulent flows display intense and short lived velocity fluctuations. This is the phenomenon of intermittency. In 1934 Leray introduced the idea of finite time singularities of the incompressible fluid equations with smooth initial data. Leray singularities occur at given points of space and time. Their analysis give a precise relation between the large velocity and the large acceleration one should observe, a result opposite to the prediction of K41 scaling laws. Leray-like scaling are amazingly well verified in the velocity records of turbulence measured in Modane wind tunnel. I'll introduce Leray's idea and make the connection with the presentation by Christophe Josserand at this conference.