INTERMITTENCY AND PREDICTABILITY IN TURBULENCE

We discuss the relation between predictability and the sensitive dependence on initial conditions in turbulent flows. We find that the maximum Lyapunov exponent lambda and the variance of the effective Lyapunov exponent diverge as a power of the Reynolds number with scaling exponents which can be calculated from the eddy turnover time at the Kolmogorov length using the multifractal approach. The intermittency leads to long tails in the distribution of the predictability time. The typical predictability time T is related to the value of lambda-1. We provide numerical evidence of this picture within the framework of a cascade model for three-dimensional fully developed turbulence.