Martin Lellep

University of Edinburgh

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Moritz Linkmann

University of Edinburgh

Alexander Morozov

University of Edinburgh

Bruno Eckhardt

Philipps University of Marburg

Florian Huhn

Deutsches Zentrum für Luft- und Raumfahrt e. V. (DLR)

Ricardo Vinuesa

KTH Royal Institute of Technology

Matteo Novara

Deutsches Zentrum für Luft- und Raumfahrt e. V. (DLR)

Johannes Bosbach

Deutsches Zentrum für Luft- und Raumfahrt e. V. (DLR)

Julian Weigel

Heidelberg University

Sergio Hoyas

Universitat Politècnica de València

Jonathan Prexl

Universität der Bundeswehr München

Cooperative Institutions

Deutsches Zentrum für Luft- und Raumfahrt e. V. (DLR)

University of Melbourne

Universitat Politècnica de València

Philipps University of Marburg

Weatherford College

Google (United States)

Universidade de Santiago de Compostela

KTH Royal Institute of Technology

University of Edinburgh

Delft University of Technology

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Effects of Anisotropy on the Geometry of Tracer Particle Trajectories in Turbulent Flows

Yasmin Hengster Martin Lellep Julian Weigel Matthew Bross Johannes Bosbach

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-pressure-gradient 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.

TRACER

Particle (ecology)

10.2139/ssrn.4355466

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Interpreted machine learning in fluid dynamics: Explaining relaminarization events in wall-bounded shear flows

APS Division of Fluid Dynamics Meeting Abstracts (2020)

Martin Lellep Jonathan Prexl Moritz Linkmann Bruno Eckhardt

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Purely elastic linear instabilities in parallel shear flows with free-slip boundary conditions

Journal of Fluid Mechanics (2021)

Martin Lellep Moritz Linkmann Bruno Eckhardt Alexander Morozov

We perform a linear stability analysis of viscoelastic plane Couette and plane Poiseuille flows with free-slip boundary conditions. The fluid is described by the Oldroyd-B constitutive model, and the flows are driven by a suitable body force. We find that both types of flow become linearly unstable, and we characterise the spatial structure of the unstable modes. By performing a boundary condition homotopy from the free-slip to no-slip boundaries, we demonstrate that the unstable modes are directly related to the least stable modes of the no-slip problem, destabilised under the free-slip situation. We discuss how our observations can be used to study recently discovered purely elastic turbulence in parallel shear flows.

Hagen–Poiseuille equation

Slip line field

10.1017/jfm.2021.840

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Purely elastic linear instabilities in parallel shear flows with free-slip boundary conditions

arXiv (Cornell University) (2021)

Martin Lellep Moritz Linkmann Bruno Eckhardt Alexander Morozov

Hagen–Poiseuille equation

Slip line field

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Using machine learning to predict extreme events in the Hénon map

Chaos An Interdisciplinary Journal of Nonlinear Science (2020)

Martin Lellep Jonathan Prexl Moritz Linkmann Bruno Eckhardt

Machine Learning (ML) inspired algorithms provide a flexible set of tools for analyzing and forecasting chaotic dynamical systems. We analyze here the performance of one algorithm for the prediction of extreme events in the two-dimensional Hénon 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 Hénon 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 T, the number of training samples NT, and the size of the network Np. We observe that in order to maintain a certain accuracy, NT∝exp⁡(2hT) and Np∝exp⁡(hT), where h 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.

10.1063/1.5121844

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Citations (26)

Effects of anisotropy on the geometry of tracer particle trajectories in turbulent flows

arXiv (Cornell University) (2023)

Yasmin Hengster Martin Lellep Julian Weigel Matthew Bross Johannes Bosbach

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.

10.48550/arxiv.2302.01844

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Self-consistent determination of attached eddies in rotating plane Couette flow

Bulletin of the American Physical Society (2017)

Bruno Eckhardt Marina Pausch Martin Lellep Stefan Zammert

Eddy

Taylor–Couette flow

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Linear stability analysis of purely elastic travelling wave solutions in pressure driven channel flows

arXiv (Cornell University) (2022)

Martin Lellep Moritz Linkmann Alexander Morozov

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.

Inertial wave

10.48550/arxiv.2211.09063

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Purely elastic turbulence in pressure-driven channel flows

arXiv (Cornell University) (2023)

Martin Lellep Moritz Linkmann Alexander Morozov

Solutions of long, flexible polymer molecules are complex fluids that simultaneously exhibit fluid-like and solid-like behaviour. When subjected to an external flow, dilute polymer solutions exhibit elastic turbulence - a unique, chaotic flow state absent in Newtonian fluids, like water. Unlike its Newtonian counterpart, elastic turbulence is caused by polymer molecules stretching and aligning in the flow, and can occur at vanishing inertia. While experimental realisations of elastic turbulence are well-documented, there is currently no understanding of its mechanism. Here, we present large-scale direct numerical simulations of elastic turbulence in pressure-driven flows through straight channels. We demonstrate that the transition to elastic turbulence is sub-critical, giving rise to spot-like flow structures that, further away from the transition, eventually spread throughout the domain. We provide evidence that elastic turbulence is organised around unstable coherent states that are localised close to the channel midplane.

10.48550/arxiv.2312.08091

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Identifying regions of importance in wall-bounded turbulence through explainable deep learning

arXiv (Cornell University) (2023)

Andres Cremades Sergio Hoyas Pedro A. Quintero Martin Lellep Moritz Linkmann

Despite its great scientific and technological importance, wall-bounded turbulence is an unresolved problem in classical physics that requires new perspectives to be tackled. One of the key strategies has been to study interactions among the energy-containing 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 obtained from a turbulent channel flow simulation is used to predict the velocity field in time through a U-net architecture. 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 revealing that the most important structures in the flow are not necessarily the ones with the highest contribution to the Reynolds shear stress. We also apply the method to an experimental database, where we can identify completely new structures based on their importance score. This framework has the potential to shed light on numerous fundamental phenomena of wall-bounded turbulence, including novel strategies for flow control.

Reynolds stress

10.48550/arxiv.2302.01250

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