Hierarchical coupled map lattices as cascade models for hydrodynamical turbulence

We consider hierarchical coupled map lattices as models for hydrodynamical turbulence at large Reynolds numbers. These lattice dynamical systems allow for an efficient simulation of spatio-temporal stochastic processes that have properties similar to those of fully developed turbulent flows. Relative scaling exponents and probability densities are calculated. They are in very good agreement with turbulence experiments. Some visualisations of spatio-temporal flow patterns are presented.