Intermittency and Predictability in a Shell Model for Three-Dimensional turbulence

We review some recent work on scaling laws in turbulence. The Navier-Stokes equations and the equation for the transport of passive scalar fields are formulated in terms of shell models in Fourier space, which incorporate the appropriate conservation laws. We find that the Kolmogorov scaling for the energy cascade and the Obukhov-Corrsin scaling for the passive scalar cascade are dynamically unstable. This fact gives rise to corrections to classical values of the scaling exponents. We relate these corrections to the dynamical behavior of the intermittency bursts present in the shell models. Our numerical results are in good quantitative agreement with the experimental results in fluids. Finally we discuss the problem of predictability.