Intermittency from instanton calculus at the transition to turbulence and fusion rules

TL;DR

This paper introduces a novel method combining instanton calculus, fusion rules, and numerical data to analyze intermittency in turbulence, successfully capturing key scaling behaviors at the transition point.

Contribution

The authors develop a new approach to determine high-order structure function exponents in turbulence using instantons and fusion rules, validated against numerical simulations.

Findings

Method captures the crossover at Re_λ ≈ 1 in VG moments

Including fluctuations around instantons is essential for accuracy

The approach links instanton evaluation to turbulence intermittency scaling

Abstract

Understanding intermittency of turbulent systems from the underlying differential equations is an outstanding problem in fluid dynamics. Here, in the example of Burgers turbulence as a stringent test, we introduce a method that yields high-order structure function exponents by combining instanton calculus, fusion rule predictions, and low-order statistical inputs from direct numerical simulations. We use instantons to evaluate high velocity gradient (VG) moments at the onset of intermittency, and then infer scaling exponents in fully developed turbulence via fusion rules. We show that the method captures the crossover at $\mathrm{Re}_\lambda \approx 1$ in the VG moment scaling, highlight the necessity of including fluctuations around instantons, and discuss future extensions.