Pair dispersion in synthetic fully developed turbulence

The Lagrangian statistics of relative dispersion in fully developed turbule nce is numerically investigated. A scaling range spanning many decades is a chieved by generating a two-dimensional velocity field by means of a stocha stic process with prescribed statistics and of a dynamical model (shell mod el) with fluctuating characteristic times. When the velocity field obeys Ko lmogorov similarity, the Lagrangian statistics is self similar and agrees w ith Richardson's predictions [Proc. R. Sec. London Ser. A 110, 709 (1926)]. For intermittent velocity fields the scaling laws for the Lagrangian stati stics are found to depend on the Eulerian intermittency in agreement with t he multifractal description. As a consequence of the Kolmogorov law the Ric hardson law for the variance of pair separation is, however, not affected b y intermittency corrections. Moreover, Lagrangian exponents do not depend o n the particular Eulerian dynamics. A method of data analysis, based on fix ed scale statistics rather than usual fixed time statistics, is shown to gi ve much wider scaling range, and should be preferred for the analysis of ex perimental data. [S1063-651X(99)09112-6].