Braid Entropy of Two-Dimensional Turbulence

A Hydrodynamic Analog of the Casimir Effect in Wave-Driven Turbulent Flows

We present experimental results on a fluctuation-induced force observed in Faraday wave-driven turbulence. As recently reported, a long-range attraction force arises between two walls that confine the wave-driven turbulent flow. In the Faraday waves system, the turbulent fluid motion is coupled with the disordered wave motion. This study describes the emergence of the fluctuation-induced force from the viewpoint of the wave dynamics. The wave amplitude is unaffected by the confinement while the wave erratic motion is. As the wall spacing decreases, the wave motion becomes less energetic and more anisotropic in the cavity formed by the walls, giving rise to a stronger attraction. These results clarify why the modelling of the attraction force in this system cannot be based on the wave amplitude but has to be built upon the wave-fluid motion coupling. When the wall spacing is comparable to the wavelength, an intermittent wave resonance is observed, and it leads to a complex short-range interaction. These results contribute to the study of aggregation processes in the presence of turbulence and its related problems such as the accumulation of plastic debris in coastal marine ecosystems or the modelling of planetary formation.

Nonequilibrium Thermodynamics of Turbulence-Driven Rotors

We characterize a process of energy extraction via rectification of strongly turbulent flow by using tools of stochastic thermodynamics. We study the dynamics of an asymmetric autonomous rotor that shows biased direction of rotation when placed in a stream. We give experimental evidence that a fluctuation theorem can be used to describe the work injected in the rotor via its coupling with the turbulent flow structure. This approach allows to measure the mean power extracted from the chaotic fluid motion over a broad range of turbulent kinetic energy. A nontrivial dependence of the rotor power on flow kinetic energy is identified. This observation is described by a model taking into account the dissipation of the rotor energy and the temporal memory of coherent structures present in the turbulent flow.

Material coherence from trajectories via Burau eigenanalysis of braids

In this paper, we provide a numerical tool to study a material's coherence from a set of 2D Lagrangian trajectories sampling a dynamical system, i.e., from the motion of passive tracers. We show that eigenvectors of the Burau representation of a topological braid derived from the trajectories have levelsets corresponding to components of the Nielsen-Thurston decomposition of the dynamical system. One can thus detect and identify clusters of space-time trajectories corresponding to coherent regions of the dynamical system by solving an eigenvalue problem. Unlike previous methods, the scalable computational complexity of our braid-based approach allows the analysis of large amounts of trajectories.