  The Lagrangian statistics of relative dispersion in fully developed
turbulence is numerically investigated. A scaling range spanning many decades
is achieved by generating a synthetic velocity field with prescribed Eulerian
statistical features. When the velocity field obeys Kolmogorov similarity, the
Lagrangian statistics is self similar too, and in agreement with Richardson's
predictions. For an intermittent velocity field the scaling laws for the
Lagrangian statistics are found to depend on Eulerian intermittency in
agreement with a multifractal description. As a consequence of the Kolmogorov
law the Richardson law for the variance of pair separation is not affected by
intermittency corrections. A new analysis method, based on fixed scale averages
instead of usual fixed time statistics, is shown to give much wider scaling
range and should be preferred for the analysis of experimental data.
