  Countless processes in nature and industry, from rain droplet nucleation to
plankton interaction in the ocean, are intimately related to turbulent
fluctuations of local concentrations of advected matter. These fluctuations can
be described by considering the change of the separation between particle
pairs, known as pair dispersion, which is believed to obey a cubic in time
growth according to Richardson's theory. Our work reveals a universal,
scale-invariant alignment between the relative velocity and position vectors of
dispersing particles at a mean angle that we show to be a universal constant of
turbulence. We connect the value of this mean angle to Richardson's traditional
theory and find agreement with data from a numerical simulation and a
laboratory experiment. While the Richardson's cubic regime has been observed
for small initial particle separations only, the constancy of the mean angle
manifests throughout the entire inertial range of turbulence. Thus, our work
reveals the universal nature of turbulent pair dispersion through a geometrical
paradigm whose validity goes beyond the classical theory, and provides a novel
framework for understanding and modeling transport and mixing processes.
