  A deterministic multi-scale dynamical system is introduced and discussed as
prototype model for relative dispersion in stationary, homogeneous and
isotropic turbulence. Unlike stochastic diffusion models, here trajectory
transport and mixing properties are entirely controlled by Lagrangian Chaos.
The anomalous "sweeping effect", a known drawback common to kinematic
simulations, is removed thanks to the use of quasi-Lagrangian coordinates.
Lagrangian dispersion statistics of the model are accurately analysed by
computing the Finite-Scale Lyapunov Exponent (FSLE), which is the optimal
measure of the scaling properties of dispersion. FSLE scaling exponents provide
a severe test to decide whether model simulations are in agreement with
theoretical expectations and/or observation. The results of our numerical
experiments cover a wide range of "Reynolds numbers" and show that chaotic
deterministic flows can be very efficient, and numerically low-cost, models of
turbulent trajectories in stationary, homogeneous and isotropic conditions. The
mathematics of the model is relatively simple and, in a geophysical context,
potential applications may regard small-scale parametrization issues in general
circulation models, mixed layer and/or boundary layer turbulence models as well
as Lagrangian predictability studies.
