 9453 L. Biferale, M. Blank and U. Frisch
 Chaotic cascades with Kolmogorov 1941 scaling
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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 zeronoise limit can be handled by
PerronFrobenius theory, just as the zerodiffusivity limit for the
fast dynamo problem. Random multiplicative models do not possess
Kolmogorov 1941 (K41) scaling because of a largedeviations 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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