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Chaotic Cascades with Kolmogorov 1941 Scaling

L. Biferale·M. Blank·U. Frisch
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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 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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L. Biferale, M. Blank, U. Frisch. 1993-11-02. Chaotic Cascades with Kolmogorov 1941 Scaling. https://doi.org/10.1007/bf02186743

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