94-53 L. Biferale, M. Blank and U. Frisch

Chaotic cascades with Kolmogorov 1941 scaling (32K, LaTeX) Mar 3, 94

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Abstract. We define a (chaotic) deterministic variant of random multiplicative cascade models of turbulence. It preserves the hierarchical tree structure, thanks to the addition of infinitesimal noise. The zero-noise limit can be handled by Perron-Frobenius theory, just as the zero-diffusivity limit for the fast dynamo problem. Random multiplicative models do not possess Kolmogorov 1941 (K41) scaling because of a large-deviations effect. Our numerical studies indicate that {\it deterministic} multiplicative models can be chaotic and still have exact K41 scaling. A mechanism is suggested for avoiding large deviations, which is present in maps with a neutrally unstable fixed point.

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