Mixing in Active Turbulence: from fully developed turbulence to labyrinthine arrest

Abstract

Active fluids represent a new paradigm in non-equilibrium physics. Even at low Reynolds numbers, they can develop spontaneous flows that resemble inertial turbulence in chaotic behaviour, also with a universal scaling law. However, unlike classical turbulence, active turbulence lacks an energy cascade. Instead, it self-organizes the scales at which energy is injected and dissipated. This suggests we may be dealing with a new class of turbulence—one we are still learning how to describe. This thesis is the first to study mixing in this rich scenario, in which two qualitatively different turbulence limits emerge: one characterized by fully developed turbulence and another where labyrinth-like patterns form and the system becomes dynamically arrested. We study the mixing of a passive scalar and the movement of tracer particles within these simulated flows. We aim to characterize each flow regime using our mixing analysis. We find that tracer particles provide a more effective way to probe the transport properties of each regime, particularly through quantities like the ballistic time and the excess kurtosis, which clearly distinguish the two types of flow and point towards a non-diffusive stationary state of the labyrinths. Interestingly, also in the labyrinthine regime, tracer particles show a heavy-tailed distribution in concentration, indicating clustering and the possible formation of particle caustics. Although this study is still in progress, our results already point toward labyrinthine flows as a distinct form of quantitative and qualitative turbulence, with unique transport properties.