CHAOTIC CASCADES WITH KOLMOGOROV 1941 SCALING

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.