Predictability of velocity and temperature fields in intermittent turbulence

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Abstract
We discuss the relation between predictability and the sensitive dependence on initial conditions in turbulent flows. The dependence on the Reynolds number of the maximum Lyapunov exponent of the flow is evaluated within the multifractal model. The temporal intermittency of the degree of chaos is found to localize on the degrees of freedom corresponding to high wavenumbers. We discuss the consequences for the mechanism for the growth of small perturbations. We show that intermittency causes long tails in the distribution of the predictability times both in the velocity field and in a passively advected scalar field, though there is no simple relation between these two times. Numerical evidence of this picture is provided within the framework of a cascade model for velocity and temperature fields in fully developed turbulence.