Geometry of Lagrangian dispersion in turbulence.

Turbulent flows disperse Lagrangian particles resulting in the growth of pairwise separations and, for sets of three or more particles, in a nontrivial dynamics of their configuration. The shape of such clusters is controlled by the competition between coherent straining of the cluster and the independent random motion of the particles due to small scale velocity fluctuations. We introduce a statistical description of the geometry of the Lagrangian clusters and predict a self-similar distribution of shapes, which should be observable in the inertial range of scales in high Reynolds numbers flows.