Stochastic chaos in a turbulent swirling flow

TL;DR

This paper provides experimental evidence of a stochastic attractor in turbulent swirling flow, demonstrating that stochastic Duffing equations can accurately model its chaotic dynamics and transition properties.

Contribution

It introduces a novel experimental approach to identify a stochastic attractor in turbulence and shows that stochastic Duffing models effectively capture its complex behavior.

Findings

Experimental turbulent flow exhibits a stochastic attractor.

Stochastic Duffing equations match flow's transition rates and dimensions.

Deterministic models fail to reproduce observed properties.

Abstract

We report the experimental evidence of the existence of a random attractor in a fully developed turbulent swirling flow. By defining a global observable which tracks the asymmetry in the flux of angular momentum imparted to the flow, we can first reconstruct the associated turbulent attractor and then follow its route towards chaos. We further show that the experimental attractor can be modeled by stochastic Duffing equations, that match the quantitative properties of the experimental flow, namely the number of quasi-stationary states and transition rates among them, the effective dimensions, and the continuity of the first Lyapunov exponents. Such properties can neither be recovered using deterministic models nor using stochastic differential equations based on effective potentials obtained by inverting the probability distributions of the experimental global observables. Our findings open the way to low dimensional modeling of systems featuring a large number of degrees of freedom and multiple quasi-stationary states.