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Attractor size in intermittent turbulence

1989; American Institute of Physics; Volume: 39; Issue: 7 Linguagem: Inglês

10.1103/physreva.39.3732

0556-2791

Charles Meneveau, Mark Nelkin,

Financial Risk and Volatility Modeling

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(\ensuremath{\alpha}), the number of degrees of freedom is decreased by intermittency for space dimensionality 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.