Chameleon attractors in a turbulent flow

TL;DR

This paper introduces a new formalism to analyze turbulent flow attractors, revealing their scale-dependent properties and the emergence of intrinsic timescales that influence their geometry and topology.

Contribution

It presents a novel method to characterize the evolving structure of turbulent attractors across scales, highlighting the concept of chameleon attractors in fluid dynamics.

Findings

Attractors depend on the scale of observation.

An intrinsic timescale emerges from nonlinear interactions.

Attractors exhibit scale-dependent geometrical and topological features.

Abstract

Turbulent flows present rich dynamics originating from non-trivial energy fluxes across scales, non-stationary forcings and geometrical constraints. This complexity manifests in non-hyperbolic chaos, randomness, state-dependent persistence and unpredictability. All these features have prevented a full characterization of the underlying turbulent (stochastic) attractor, which will be the key object to unpin this complexity. Here we propose a novel formalism to trace the evolution of the structural characteristics of phase-space trajectories across scales, providing a full characterization of the attractor. We demonstrate that the properties of the dynamically invariant objects depend on the scale we are focusing on. In the case of laboratory experiments on fluids we observe the emergence of an intrinsic timescale, solely determined by nonlinear interactions, controlling the geometrical and topological properties of phase-space trajectories. Given the changing nature of such attractors in time and scales we term them chameleon attractors.