Shell model intermittency is the hidden self-similarity

TL;DR

This paper reveals that the intermittency in the Sabra shell model of turbulence is fundamentally linked to a hidden self-similarity, replacing traditional scaling symmetries with a new exact symmetry in rescaled coordinates.

Contribution

It introduces a novel hidden scaling symmetry in shell models and derives formulas for anomalous exponents using Perron-Frobenius eigenvalues, supported by numerical verification.

Findings

Intermittency linked to hidden self-similarity.

Derived formulas for anomalous scaling exponents.

Numerical simulations confirm theoretical predictions.

Abstract

We show that the intermittent dynamics observed in the inertial interval of Sabra shell model of turbulence can be rigorously related to the property of scaling self-similarity. In this connection, the space-time scaling symmetries (like in the K41 theory) are replaced by the new hidden scaling symmetry, which is an exact symmetry of inviscid dynamics represented in special rescaled coordinates and times. We derive the formulas expressing anomalous scaling exponents in terms of Perron-Frobenius eigenvalues of linear operators based on the self-similar statistics. Theoretical conclusions are verified by extensive numerical simulations.