Intermittency, chaos and singular fluctuations in the mixed Obukhov-Novikov shell model of turbulence

TL;DR

This paper explores the multiscaling and chaotic behavior in the mixed Obukhov-Novikov shell model of turbulence, identifying key singular fluctuations and their impact on turbulence dynamics through numerical analysis.

Contribution

It introduces a new method to track singular fluctuations and compares the model's properties with the complex GOY model, highlighting the role of Novikov interactions in chaos.

Findings

Self-similar solutions align with large order statistics when deviating from Kolmogorov scaling.

Complex time singularities are trapped in the last shells beyond a critical Novikov interaction proportion.

The boundary between chaos and regularity is linked to the critical Novikov interaction threshold.

Abstract

The multiscaling properties of the mixed Obukhov-Novikov shell model of turbulence are investigated numerically and compared with those of the complex GOY model, mostly studied in the 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 inhibiting the cascade and promoting chaos. A simple and robust method is proposed to track these objects. It is shown that the scaling exponent of self-similar solutions selected by the dynamics is compatible with large order statistics whenever it departs enough from the Kolmogorov value. Complex time singularities on the other hand get trapped on the last shells, when the proportion of Novikov interactions exceeds a critical value which is argued to mark the boundary between chaotic and regular dynamics in the limit of infinite Reynolds number.