Universality in turbulent pair-dispersion

When a group of particles is released into a turbulent flow, they tend to be carried  away from each other, making the typical separation distance between pairs of particles grow with time. This process, which dominates the spreading and mixing of matter in the oceans and the atmosphere, is called pair dispersion. In 1926, Richardson predicted that the mean squared distance between particle pairs in turbulence grows super-diffusively, with a time exponent of 3. However, since its discovery nearly a century ago and despite its central role in turbulence theory, Richardson’s law evaded unequivocal experimental confirmation ever since. Among the issues that make its verification difficult are having too small Reynolds numbers, an intrinsic intermittency of the process, and an innate dependence on initial distances and velocities. To overcome these issues, our work reveals a new property of turbulent pair dispersion:  the average of the angle that is formed between the separation and the relative velocity vectors is a conserved quantity in turbulence and it has a universal value. We confirm these predictions through experimental and DNS resutls. This novel discovery  allows identifying whether Richardson’s self-similar regime exists and at which scales in future experiments, independently of the flow parameters. It thus allows confirming Richardson’s theory, with significant consequences for predicting dispersion and mixing of in the oceans and in the atmosphere