Computation of anomalous scaling exponents of turbulence from self-similar instanton dynamics

TL;DR

This paper demonstrates that anomalous scaling exponents in turbulence are governed by self-similar instanton dynamics, with a simplified model capturing the creation process responsible for multiscaling properties.

Contribution

It introduces a novel perspective linking turbulence multiscaling to instanton dynamics and proposes a simplified model for instanton creation.

Findings

Anomalous exponents are determined by instanton creation.

Self-similar instanton structure explains multiscaling.

A simplified model accurately describes instanton-induced anomalies.

Abstract

We show that multiscaling properties of developed turbulence in shell models, which lead to anomalous scaling exponents in the inertial range, are determined exclusively by instanton dynamics. Instantons represent correlated extreme events localized in space-time, whose structure is described by self-similar statistics with a single universal scaling exponent. We show that anomalous scaling exponents appear due to the process of instanton creation. A simplified model of instanton creation is suggested, which adequately describes this anomaly.