Pair Dispersion in Turbulence: The Subdominant Role of Scaling

The mixing properties of turbulent flows are, at first order, related to the dynamics of separation of particle pairs. Scaling laws for the evolution in time of the mean distance between particle pairs < r(2)>(t) have been proposed since the pioneering work of Richardson. We analyze a model which shares some features with 3D experimental and numerical turbulence, and suggest that pure scaling laws are only subdominant. The dynamics is dominated by a very wide distribution of "delay times" t(d), the duration for which particle pairs remain together before their separation increases significantly. The delay time distribution is exponential for small separations and evolves towards a flat distribution at large separations. The observed < r(2)>(t) behavior is best understood as an average over separations that individually follow the Richardson-Obukhov scaling, r(2) proportional to t(3), but each only after a fluctuating time delay t(d), where t(d) is distributed uniformly.