Persistent accelerations disentangle Lagrangian turbulence

Particles in turbulence frequently encounter extreme accelerations between extended periods of quiescence. The occurrence of extreme events is closely related to the intermittent spatial distribution of intense flow structures such as vorticity filaments. This mixed history of flow conditions leads to very complex particle statistics with a pronounced scale dependence, which presents one of the major challenges on the way to a non-equilibrium statistical mechanics of turbulence. Here, we introduce the notion of persistent Lagrangian acceleration, quantified by the squared particle acceleration coarse-grained over a viscous time scale. Conditioning Lagrangian particle data from simulations on this coarse-grained acceleration, we find remarkably simple, close-to-Gaussian statistics for a range of Reynolds numbers. This opens the possibility to decompose the complex particle statistics into much simpler sub-ensembles. Based on this observation, we develop a comprehensive theoretical framework for Lagrangian single-particle statistics that captures the acceleration, velocity increments as well as single-particle dispersion

Transitions of turbulent superstructures in generalized Kolmogorov flow

Self-organized large-scale flow structures occur in a wide range of turbulent flows. Yet, their emergence, dynamics, and interplay with small-scale turbulence are not well understood. Here, we investigate such self-organized turbulent superstructures in three-dimensional turbulent Kolmogorov flow with large-scale drag. Through extensive simulations, we uncover their low-dimensional dynamics featuring transitions between several stable and meta-stable large-scale structures as a function of the damping parameter. The main dissipation mechanism for the turbulent superstructures is the generation of small-scale turbulence, whose local structure depends strongly on the large-scale flow. Our results elucidate the generic emergence and low-dimensional dynamics of large-scale flow structures in fully developed turbulence and reveal a strong coupling of large- and small-scale flow features.Comment: v2: Revised manuscrip

Bias in particle tracking acceleration measurement

We investigate sources of error in acceleration statistics from Lagrangian Particle Tracking (LPT) data and demonstrate techniques to eliminate or minimise bias errors introduced during processing. Numerical simulations of particle tracking experiments in isotropic turbulence show that the main sources of bias error arise from noise due to position uncertainty and selection biases introduced during numerical differentiation. We outline the use of independent measurements and filtering schemes to eliminate these biases. Moreover, we test the validity of our approach in estimating the statistical moments and probability densities of the Lagrangian acceleration. Finally, we apply these techniques to experimental particle tracking data and demonstrate their validity in practice with comparisons to available data from literature. The general approach, which is not limited to acceleration statistics, can be applied with as few as two cameras and permits a substantial reduction in the spatial resolution and sampling rate required to adequately measure statistics of Lagrangian acceleration

On the large-scale sweeping of small-scale eddies in turbulence -- A filtering approach

We present an analysis of the Navier-Stokes equations based on a spatial filtering technique to elucidate the multi-scale nature of fully developed turbulence. In particular, the advection of a band-pass-filtered small-scale contribution by larger scales is considered, and rigorous upper bounds are established for the various dynamically active scales. The analytical predictions are confirmed with direct numerical simulation data. The results are discussed with respect to the establishment of effective large-scale equations valid for turbulent flows.Comment: 14 pages, 6 figure

An Efficient Particle Tracking Algorithm for Large-Scale Parallel Pseudo-Spectral Simulations of Turbulence

Particle tracking in large-scale numerical simulations of turbulent flows presents one of the major bottlenecks in parallel performance and scaling efficiency. Here, we describe a particle tracking algorithm for large-scale parallel pseudo-spectral simulations of turbulence which scales well up to billions of tracer particles on modern high-performance computing architectures. We summarize the standard parallel methods used to solve the fluid equations in our hybrid MPI/OpenMP implementation. As the main focus, we describe the implementation of the particle tracking algorithm and document its computational performance. To address the extensive inter-process communication required by particle tracking, we introduce a task-based approach to overlap point-to-point communications with computations, thereby enabling improved resource utilization. We characterize the computational cost as a function of the number of particles tracked and compare it with the flow field computation, showing that the cost of particle tracking is very small for typical applications

The statistical geometry of material loops in turbulence

Material elements - which are lines, surfaces, or volumes behaving as passive, non-diffusive markers of dye - provide an inherently geometric window into the intricate dynamics of chaotic flows. Their stretching and folding dynamics has immediate implications for mixing in the oceans or the atmosphere, as well as the emergence of self-sustained dynamos in astrophysical settings. Here, we uncover robust statistical properties of an ensemble of material loops in a turbulent environment. Our approach combines high-resolution direct numerical simulations of Navier-Stokes turbulence, stochastic models, and dynamical systems techniques to reveal predictable, universal features of these complex objects. We show that the loop curvature statistics become stationary through a dynamical formation process of high-curvature slings, leading to distributions with power-law tails whose exponents are determined by the large-deviations statistics of finite-time Lyapunov exponents of the background flow. This prediction applies to advected material lines in a broad range of chaotic flows. To complement this dynamical picture, we confirm our theory in the analytically tractable Kraichnan model with an exact Fokker-Planck approach

Vortices within vortices: hierarchical nature of vortex tubes in turbulence

The JHU turbulence database [1] can be used with a state of the art visualisation tool [2] to generate high quality fluid dynamics videos. In this work we investigate the classical idea that smaller structures in turbulent flows, while engaged in their own internal dynamics, are advected by the larger structures. They are not advected undistorted, however. We see instead that the small scale structures are sheared and twisted by the larger scales. This illuminates the basic mechanisms of the turbulent cascade.Comment: 2 pages, 1 low quality video, 1 high quality vide

Emergence of phytoplankton patchiness at small scales in mild turbulence

Phytoplankton often encounter turbulence in their habitat. As most toxic phytoplankton species are motile, resolving the interplay of motility and turbulence has fundamental repercussions on our understanding of their own ecology and of the entire ecosystems they inhabit. The spatial distribution of motile phytoplankton cells exhibits patchiness at distances of decimeter to millimeter scale for numerous species with different motility strategies. The explanation of this general phenomenon remains challenging. Furthermore, hydrodynamic cell-cell interactions, which grow more relevant as the density in the patches increases, have been so far ignored. Here, we combine particle simulations and continuum theory to study the emergence of patchiness in motile microorganisms in three dimensions. By addressing the combined effects of motility, cell-cell interaction and turbulent flow conditions, we uncover a general mechanism: the coupling of cell-cell interactions to the turbulent dynamics favors the formation of dense patches. Identification of the important length and time scales, independently from the motility mode, allows us to elucidate a general physical mechanism underpinning the emergence of patchiness. Our results shed light on the dynamical characteristics necessary for the formation of patchiness, and complement current efforts to unravel planktonic ecological interactions