%0 Journal Article
%T Chaotic Cascades with Kolmogorov 1941 Scaling
%A L. Biferale
%A M. Blank
%A U. Frisch
%J Physics
%D 1993
%I arXiv
%R 10.1007/BF02186743
%X 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.
%U http://arxiv.org/abs/cond-mat/9311006v1