Attractor size in intermittent turbulence

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Abstract
We estimate the number of degrees of freedom in intermittent fully developed turbulence using the multifractal formalism. We find that for any reasonable distribution f(α), the number of degrees of freedom is decreased by intermittency for space dimensionality D, and increased for D>4. This is in agreement with a result of Kraichnan [Phys. Fluids 28, 10 (1985)] obtained for the special case of fractally homogeneous turbulence. We calculate the reduction in attractor size in three dimensions and find it to be very small. The possible dynamical significance of our result is briefly discussed.