Attractor Size in Intermittent Turbulence

C. Meneveau* and M. Nelkin+,
Mason Laboratory | Yale University | New Haven, CT 06520
*Present Address: Department of Mechanical Engineering
The Johns Hopkins University | Baltimore, MD 21218
+Physics Department | New York University | New York, NY 10003

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(a), the number of degrees of freedom is decreased by intermittency for space dimensionality D < 4, 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 thereduction in attractor size in three dimensions and find it to be very small. The possible dynamical significance of our result is briefly discussed.

Phys. Rev. A, 39, pp. 3732–3733

DOI: 10.1103/PhysRevA.39.3732 | Full PDF
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