Chaotic Cascades with Kolmogorov 1941 Scaling

Details Chaotic Cascades with Kolmogorov 1941 Scaling Chaotic Cascades with Kolmogorov 1941 Scaling

1993-11-02

arxiv.org/abs/cond-mat/9311006v1

Physics

Condensed Matter

14 pages, plain LaTex, 6 figures available upon request as hard copy (no local report #)

Scientific paper

10.1007/BF02186743

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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