Julian Weigel

Heidelberg University

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Florian Huhn

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

Matteo Novara

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

Johannes Bosbach

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

Andreas Schröder

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

Yasmin Hengster

Maxwell Institute for Mathematical Sciences

Martin Lellep

University of Edinburgh

Christian J. Kähler

Universität der Bundeswehr München

Matthew Bross

Universität der Bundeswehr München

Daniel Schanz

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

Moritz Linkmann

University of Edinburgh

Cooperative Institutions

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

Universidade de Santiago de Compostela

University of Edinburgh

China Aerodynamics Research and Development Center

Maxwell Institute for Mathematical Sciences

Philipps University of Marburg

Universität der Bundeswehr München

Ferdinand-Braun-Institut

ETH Zurich

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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.

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Particle (ecology)

10.2139/ssrn.4355466

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

European Journal of Mechanics - B/Fluids (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 observables 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 turbulent boundary layer over a flat plate. The results for the von Kármán flow compare well with experimental results for the curvature PDF and results obtained by numerical simulations of homogeneous and isotropic turbulence for the torsion PDF. Results for Rayleigh–Bénard convection agree with those measured for von Kármán flow, while results for the logarithmic layer within the boundary layer differ slightly. We provide a potential explanation for the latter. 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.

10.1016/j.euromechflu.2023.10.008

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