Ballistic versus diffusive pair dispersion in the Richardson regime

Two-particle dispersion in fully developed turbulence is modeled within an asymmetric Lévy-walk framework which yields the Richardson $t^3$ law and which recovers recently observed results on the probability distribution function of pair separations in two-dimensional turbulence [M.C. Jullien, J. Paret, and P. Tabeling, Phys. Rev. Lett. 82, 2872 (1999)]. The ballistic nature of the Richardson dispersion is discussed in terms of the persistence parameter and compared with the Richardson diffusive behavior.