A rare event algorithm links transitions in turbulent flows with activated nucleations

TL;DR

This paper introduces a rare event algorithm that enables detailed analysis of abrupt transitions in turbulent flows, revealing nucleation processes and Arrhenius laws, thus bridging turbulence and non-equilibrium statistical mechanics.

Contribution

The study applies adaptive multilevel splitting to turbulent flows, demonstrating transition path concentration near instantons and establishing Arrhenius laws in turbulence.

Findings

Transition paths concentrate near instantons.

Transitions are noise-activated nucleations of vorticity bands.

Existence of Arrhenius laws in turbulent flows.

Abstract

Many turbulent flows undergo drastic and abrupt configuration changes with huge impacts. As a paradigmatic example we study the multistability of jet dynamics in a barotropic beta plane model of atmosphere dynamics. It is considered as the Ising model for Jupiter troposphere dynamics. Using the adaptive multilevel splitting, a rare event algorithm, we are able to get a very large statistics of transition paths, the extremely rare transitions from one state of the system to another. This new approach opens the way for addressing a set of questions that are out of reach through direct numerical simulations. We demonstrate for the first time the concentration of transition paths close to instantons, in a numerical simulation of genuine turbulent flows. We show that the transition is a noise-activated nucleation of vorticity bands. We address for the first time the existence of Arrhenius laws in turbulent flows. The methodology we developed shall prove useful to study many other transitions related to drastic changes for the turbulent dynamics of climate, geophysical, astrophysical and engineering applications. This opens a new range of studies impossible so far, and bring turbulent phenomena in the realm of non-equilibrium statistical mechanics.