Geometry of Lagrangian Dispersion in Turbulence

Turbulent flows disperse Lagrangian particles resulting not only in the growth of pairwise separations but, for sets of three or more particles, in a non-trivial dynamics of their configuration. The shape of such Lagrangian point clusters provides information about the structure of turbulent fluctuations which goes beyond simple scaling. It is determined dynamically by the relative importance of the coherent strain acting on the particles compared to their independent random motion due to small scale velocity fluctuations. We introduce a statistical description of the geometry of the Lagrangian clusters and predict a non-trivial self-similar distribution of shapes which should be observable in the inertial range of scales in high Reynolds numbers flows.