Chaotic cascade model for turbulent velocity distributions

A coupled map lattice is introduced that simulates the time evolution of velocity differences in fully developed turbulent flows. The model considered is an extension of the Langevin theory to chaotic driving forces acting on a self-similar cascade of spatial levels. Compared to full simulations of the Navier-Stokes equation, the amount of necessary computing time is negligible. Despite its simplicity, the model is in perfect agreement with experimentally observed results, provided the chaotic driving force is generated by the fully developed logistic map with parameter value μ=2. The shape of the velocity distributions, the slight asymmetry, the stretched exponential tails, as well as the moment scaling exponents ${\mathrm{\zeta }}_{\mathit{m}}$, come out in precisely the same way as in experimental measurements of high Reynolds number flows.