IUTAM Symposium on Geometry and Statistics of Turbulence

This text places emphasis on the fact that the statistical laws in turbulence are not disconnected with the coherent structures distributing randomly in space and forming/decaying spontaneously in time, and that the anomalous scaling laws of a passive scalar in turbulence are captured from the first principle. Existence of such coherences in the stochastic processes of turbulence leads to the intermittency and also non-Gaussian statistics. Details of the geometrical structures are investigated how they are described in terms of vortices of shear layers.