Dynamical Models for Fully Developed Turbulence

We discuss a shell-model for the 3D fully developed turbulence. By calculating the structure functions we find corrections to the Kolmogorov theory due to an intermittent structure of energy dissipation. The intermittency can be described in terms of a multifractal scaling and it is related to the Lyapunov exponents and eigenvectors. Moreover we obtain that the maximum Lyapunov exponent λ and the variance of the effective Lyapunov exponent diverge as a power of the Reynolds number with scaling exponents which can be calculated in terms of a multifractal spectrum