Instantons and the path to intermittency in turbulent flows

TL;DR

This paper investigates the role of instantons, or optimal trajectories, in the emergence of intermittency and non-Gaussian statistics in turbulent flows, using a stochastic Langevin framework derived from experimental data.

Contribution

It introduces a novel instanton-based approach to analyze intermittency in turbulence through a Langevin process with multiplicative noise, conditioned on entropy exchange.

Findings

Instantons with negative entropy are linked to non-Gaussian small-scale turbulence statistics.

The effective action for trajectories is derived from measured data.

Selected trajectories concentrate around optimal paths called instantons.

Abstract

Processes leading to anomalous fluctuations in turbulent flows, referred to as intermittency, are still challenging. We consider cascade trajectories through scales as realizations of a stochastic Langevin process for which multiplicative noise is an intrinsic feature of the turbulent state. The trajectories are conditioned on their entropy exchange. Such selected trajectories concentrate around an optimal path, called instanton, which is the minimum of an effective action. The action is derived from the Langevin equation, estimated from measured data. In particular instantons with negative entropy pinpoint the trajectories responsible for the emergence of non-Gaussian statistics at small-scales.