13 research outputs found
Linear stability analysis of purely elastic travelling wave solutions in pressure driven channel flows
Recent studies of pressure-driven flows of dilute polymer solutions in
straight channels demonstrated the existence of two-dimensional coherent
structures that are disconnected from the laminar state and appear through a
sub-critical bifurcation from infinity. These travelling-wave solutions were
suggested to organise the phase-space dynamics of purely elastic and
elasto-inertial chaotic channel flows. Here, we consider a wide range of
parameters, covering the purely-elastic and elasto-inertial cases, and
demonstrate that the two-dimensional travelling-wave solutions are unstable
when embedded in sufficiently wide three-dimensional domains. Our work
demonstrates that studies of purely elastic and elasto-inertial turbulence in
straight channels require three-dimensional simulations, and no reliable
conclusions can be drawn from studying strictly two-dimensional channel flows.Comment: 10 pages, 5 page
Purely elastic linear instabilities in parallel shear flows with free-slip boundary conditions
Using Machine Learning to predict extreme events in the Hénon map
Machine Learning (ML) inspired algorithms provide a flexible set of tools for
analyzing and forecasting chaotic dynamical systems. We here analyze the
performance of one algorithm for the prediction of extreme events in the
two-dimensional H\'enon map at the classical parameters. The task is to
determine whether a trajectory will exceed a threshold after a set number of
time steps into the future. This task has a geometric interpretation within the
dynamics of the H\'enon map, which we use to gauge the performance of the
neural networks that are used in this work. We analyze the dependence of the
success rate of the ML models on the prediction time , the number of
training samples and the size of the network . We observe that in
order to maintain a certain accuracy, and , where is the topological entropy. Similar relations between the
intrinsic chaotic properties of the dynamics and ML parameters might be
observable in other systems as well.Comment: 9 pages, 12 figure
Explaining wall-bounded turbulence through deep learning
Despite its great scientific and technological importance, wall-bounded
turbulence is an unresolved problem that requires new perspectives to be
tackled. One of the key strategies has been to study interactions among the
coherent structures in the flow. Such interactions are explored in this study
for the first time using an explainable deep-learning method. The instantaneous
velocity field in a turbulent channel is used to predict the velocity field in
time through a convolutional neural network. Based on the predicted flow, we
assess the importance of each structure for this prediction using the
game-theoretic algorithm of SHapley Additive exPlanations (SHAP). This work
provides results in agreement with previous observations in the literature and
extends them by quantifying the importance of the Reynolds-stress structures,
finding a connection between these structures and the dynamics of the flow. The
process, based on deep-learning explainability, has the potential to shed light
on numerous fundamental phenomena of wall-bounded turbulence, including the
objective definition of new types of flow structures
Effects of anisotropy on the geometry of tracer particle trajectories in turbulent flows
Using curvature and torsion to describe Lagrangian trajectories gives a full
description of these as well as an insight into small and large time scales as
temporal derivatives up to order 3 are involved. One might expect that the
statistics of these properties depend on the geometry of the flow. Therefore,
we calculated curvature and torsion probability density functions (PDFs) of
experimental Lagrangian trajectories processed using the Shake-the-Box
algorithm of turbulent von K\'arm\'an flow, Rayleigh-B\'enard convection and a
zero-pressure-gradient turbulent boundary layer over a flat plate. The results
for the von K\'arm\'an flow compare well with previous experimental results for
the curvature PDF and numerical simulation of homogeneous and isotropic
turbulence for the torsion PDF. Results for Rayleigh-B\'enard convection agree
with those obtained for K\'arm\'an flow, while results for the logarithmic
layer within the boundary layer differ slightly, and we provide a potential
explanation. To detect and quantify the effect of anisotropy either resulting
from a mean flow or large-scale coherent motions on the geometry or tracer
particle trajectories, we introduce the curvature vector. We connect its
statistics with those of velocity fluctuations and demonstrate that strong
large-scale motion in a given spatial direction results in meandering rather
than helical trajectories
Effects of anisotropy on the geometry of tracer particle trajectories in turbulent flows
Using curvature and torsion to describe Lagrangian trajectories gives a full description of these as well as an insight into small and large time scales as temporal derivatives up to order 3 are involved. One might expect that the statistics of these properties depend on the geometry of the flow. Therefore, we calculated curvature and torsion probability density functions (PDFs) of experimental Lagrangian trajectories processed using the Shake-the-Box algorithm of turbulent von Kármán flow, Rayleigh-Bénard convection and a zero-pressuregradient boundary layer over a flat plate. The results for the von-Kármán flow compare well with experimental results for the curvature PDF and numerical simulation of homogeneous and isotropic turbulence for the torsion PDF. For the experimental Rayleigh-Bénard convection, the power law tails found agree with those measured for von-Kármán flow. Results for the logarithmic layer within the boundary layer differ slightly, we give some potential explanation below. To detect and quantify the effect of anisotropy either resulting from a mean flow or large-scale coherent motions on the geometry or tracer particle trajectories, we introduce the curvature vector. We connect its statistics with those of velocity fluctuations and demonstrate that strong large-scale motion in a given spatial direction results in meandering rather than helical trajectories
Interpreted machine learning in fluid dynamics: Explaining relaminarisation events in wall-bounded shear flows
Machine Learning (ML) is becoming increasingly popular in fluid dynamics.
Powerful ML algorithms such as neural networks or ensemble methods are
notoriously difficult to interpret. Here, we introduce the novel Shapley
Additive Explanations (SHAP) algorithm (Lundberg & Lee, 2017), a game-theoretic
approach that explains the output of a given ML model, in the fluid dynamics
context. We give a proof of concept concerning SHAP as an explainable AI method
providing useful and human-interpretable insight for fluid dynamics. To show
that the feature importance ranking provided by SHAP can be interpreted
physically, we first consider data from an established low-dimensional model
based on the self-sustaining process (SSP) in wall-bounded shear flows, where
each data feature has a clear physical and dynamical interpretation in terms of
known representative features of the near-wall dynamics, i.e. streamwise
vortices, streaks and linear streak instabilities. SHAP determines consistently
that only the laminar profile, the streamwise vortex, and a specific streak
instability play a major role in the prediction. We demonstrate that the method
can be applied to larger fluid dynamics datasets by a SHAP evaluation on plane
Couette flow in a minimal flow unit focussing on the relevance of streaks and
their instabilities for the prediction of relaminarisation events. Here, we
find that the prediction is based on proxies for streak modulations
corresponding to linear streak instabilities within the SSP. That is, the SHAP
analysis suggests that the break-up of the self-sustaining cycle is connected
with a suppression of streak instabilities.Comment: 29 pages, 10 figure
Data for "Interpreted machine learning in fluid dynamics" Lellep et al., Journal of Fluid Mechanics, 2022
This dataset is the supplementary data for the publication https://arxiv.org/abs/2102.05541. Machine Learning (ML) is becoming increasingly popular in fluid dynamics. Powerful ML algorithms such as neural networks or ensemble methods are notoriously difficult to interpret. Here, we introduce the novel Shapley additive explanations (SHAP) algorithm (Lundberg & Lee, Advances in Neural Information Processing Systems, 2017, pp. 4765–4774), a game-theoretic approach that explains the output of a given ML model in the fluid dynamics context. We give a proof of concept concerning SHAP as an explainable artificial intelligence method providing useful and human-interpretable insight for fluid dynamics. To show that the feature importance ranking provided by SHAP can be interpreted physically, we first consider data from an established low-dimensional model based on the self-sustaining process (SSP) in wall-bounded shear flows, where each data feature has a clear physical and dynamical interpretation in terms of known representative features of the near-wall dynamics, i.e. streamwise vortices, streaks and linear streak instabilities. SHAP determines consistently that only the laminar profile, the streamwise vortex and a specific streak instability play a major role in the prediction. We demonstrate that the method can be applied to larger fluid dynamics datasets by a SHAP evaluation on plane Couette flow in a minimal flow unit focussing on the relevance of streaks and their instabilities for the prediction of relaminarisation events. Here, we find that the prediction is based on proxies for streak modulations corresponding to linear streak instabilities within the SSP. That is, the SHAP analysis suggests that the break-up of the self-sustaining cycle is connected with a suppression of streak instabilities.Lellep, Martin; Linkmann, Moritz. (2022). Data for "Interpreted machine learning in fluid dynamics" Lellep et al., Journal of Fluid Mechanics, 2022, [dataset]. https://doi.org/10.7488/ds/3450
Effects of anisotropy on the geometry of tracer particle trajectories in turbulent flows
Using curvature and torsion to describe Lagrangian trajectories gives a full description of these as well as an insight into small and large time scales as temporal derivatives up to order 3 are involved. One might expect that the statistics of these properties depend on the geometry of the flow. Therefore, we calculated curvature and torsion probability density functions (PDFs) of Lagrangian trajectories obtained from experimental data using the Shake-the-Box algorithm. We analyse three datasets, turbulent von Kármán flow, Rayleigh-Bénard convection and a zero-pressure-gradient (ZPG) boundary layer over a flat plate. The results for the von Kármán flow compare well with experimental results for the curvature PDF and numerical simulation of homogeneous and isotropic turbulence for the torsion PDF. For Rayleigh-Bénard convection, the power law tails found agree with those measured for von Kármán flow. Results for the logarithmic layer within the boundary layer differ. To detect and quantify the effect of anisotropy either resulting from a mean flow or large-scale coherent motions on the geometry of tracer particle trajectories, we introduce the curvature vector. We connect its statistics with those of velocity fluctuations and demonstrate that strong large-scale motion in a given spatial direction results in meandering rather than helical trajectories. For the turbulent boundary layer, this is commensurate with the current understanding of turbulent superstructures