CHAOTIC CASCADES WITH KOLMOGOROV 1941 SCALING

Citation
L. Biferale et al., CHAOTIC CASCADES WITH KOLMOGOROV 1941 SCALING, Journal of statistical physics, 75(5-6), 1994, pp. 781-795
Citations number
31
Categorie Soggetti
Mathematical Method, Physical Science","Physycs, Mathematical
ISSN journal
00224715
Volume
75
Issue
5-6
Year of publication
1994
Pages
781 - 795
Database
ISI
SICI code
0022-4715(1994)75:5-6<781:CCWK1S>2.0.ZU;2-N
Abstract
We define a (chaotic) deterministic variant of random multiplicative c ascade models of turbulence. It preserves the hierarchical tree struct ure, thanks to the addition of infinitesimal noise. The zero-noise lim it can be handled by Perron-Frobenius theory, just like the zero-diffu sivity limit for the fast dynamo problem. Random multiplicative models do not possess Kolmogorov 1941 (K41) scaling because of a large-devia tions effect. Our numerical studies indicate that deterministic multip licative models can be chaotic and still have exact K41 scaling. A mec hanism is suggested for avoiding large deviations, which is present in maps with a neutrally unstable fixed point.