|The statistical properties of velocity fields
along the trajectories of fluid particles transported
by a fully developed turbulent flow are investigated
by means of high resolution Direct Numerical Simulations.
We present results for single particle observables
(Lagrangian velocity structure functions and particles' acceleration) for pair dispersion and for the geometry
of clusters of four particles (tetrahedra).
I will discuss in details the phenomenological
interpretation of the Lagrangian intermittency of the
velocity field and of the self-similar distribution of tetraedhra shapes.