31 research outputs found
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
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
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
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