Chameleon attractors in turbulent flows

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 use a recently proposed formalism to trace the evolution of the structural characteristics of phase-space trajectories across scales in a fully developed turbulent flow featuring a huge number of degrees of freedom. Our results demonstrate the failure of the concept of universality of turbulent attractors since their properties depend on the scale we are focusing on. More specifically, we observe that the geometrical and topological properties depend on the large-scale forcing, with a breakdown of statistical universality emerging at the beginning of the inertial range, where nonlinear interactions controlling the energy cascade mechanism develop. Given the changing nature of such attractors in time and scales we term them chameleon attractors.