Geometry of Lagrangian dispersion in turbulence

Turbulent flows disperse Lagrangian particles resulting in the growth of pa irwise separations and, for sets of three or more particles, in a nontrivia l dynamics of their configuration. The shape of such clusters is controlled by the competition between coherent straining of the cluster and the indep endent random motion of the particles due to small scale velocity fluctuati ons. We introduce a statistical description of the geometry of the Lagrangi an clusters and predict a self-similar distribution of shapes, which should be observable in the inertial range of scales in high Reynolds numbers flo ws.