Chaotic Cascades with Kolmogorov 1941 Scaling
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.
Keywords
Cite
@article{arxiv.cond-mat/9311006,
title = {Chaotic Cascades with Kolmogorov 1941 Scaling},
author = {L. Biferale and M. Blank and U. Frisch},
journal= {arXiv preprint arXiv:cond-mat/9311006},
year = {2009}
}
Comments
14 pages, plain LaTex, 6 figures available upon request as hard copy (no local report #)