Universal statistics of non-linear energy transfer in turbulent models

Abstract

A class of shell models for turbulent energy transfer at varying the inter-shell separation, $\lambda$, is investigated. Intermittent corrections in the continuous limit of infinitely close shells ($\lambda \rightarrow 1$) have been measured. Although the model becomes, in this limit, non-intermittent, we found universal aspects of the velocity statistics which can be interpreted in the framework of log-poisson distributions, as proposed by She and Waymire (1995, Phys. Rev. Lett. 74, 262). We suggest that non-universal aspects of intermittency can be adsorbed in the parameters describing statistics and properties of the most singular structure. On the other hand, universal aspects can be found by looking at corrections to the monofractal scaling of the most singular structure. Connections with similar results reported in other shell models investigations and in real turbulent flows are discussed.