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Intermittency, chaos and singular fluctuations in the mixed Obukhov-Novikov shell model of turbulence. (English) Zbl 0947.76042
Summary: The multiscaling properties of the mixed Obukhov-Novikov (ON) shell model of turbulence are investigated numerically and compared with those of the complex Gledzer-Okhitani-Yamada (GOY) model, mostly studied in recent years. Two types of generic singular fluctuations are identified: first, self-similar solutions propagating from large to small scales and building up intermittency, second, complex-time singularities which are argued to encode “blockings” in the cascade. A robust dynamic rescaling method is developed to characterize these objects. It is shown that the scaling exponent of self-similar solutions selected by the dynamics is compatible with large-order statistics, only when it departs enough from the Kolmogorov value. Complex-time singularities on the other hand suffer a “depinning” transition which, in a remarkable way, is found to occur in the phase diagrams of both the ON and GOY models at a place such that the scaling exponent of corresponding self-similar solutions take the same value $$\approx 0.855$$.

MSC:
 76F99 Turbulence
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