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Topological colouring of fluid particles unravels finite-time coherent sets

Published online by Cambridge University Press:  27 July 2021

Gisela D. Charó Open the ORCID record for Gisela D. Charó [Opens in a new window] ,
Guillermo Artana Open the ORCID record for Guillermo Artana [Opens in a new window]  and
Denisse Sciamarella Open the ORCID record for Denisse Sciamarella [Opens in a new window]
Gisela D. Charó*
Affiliation:
CONICET – Universidad de Buenos Aires, Centro de Investigaciones del Mar y la Atmósfera (CIMA), C1428EGA CABA, Argentina CNRS – IRD – CONICET – UBA, Institut Franco-Argentin d’Ètudes sur le Climat et ses Impacts (IRL 3351 IFAECI), C1428EGA CABA, Argentina CONICET – Consejo Nacional de Investigaciones Científicas y Técnicas, C1425FQD CABA, Argentina
Guillermo Artana
Affiliation:
CONICET – Consejo Nacional de Investigaciones Científicas y Técnicas, C1425FQD CABA, Argentina Laboratorio de Fluidodinámica, Facultad de Ingeniería, Universidad de Buenos Aires, C1063ACV CABA, Argentina
Denisse Sciamarella
Affiliation:
CNRS – IRD – CONICET – UBA, Institut Franco-Argentin d’Ètudes sur le Climat et ses Impacts (IRL 3351 IFAECI), C1428EGA CABA, Argentina CNRS – Centre National de la Recherche Scientifique, 75795 Paris, France
*
†Email address for correspondence: gisela.charo@cima.fcen.uba.ar
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Abstract

This work describes the application of a technique that extracts branched manifolds from time series to study numerically generated fluid particle behaviour in the wake past a cylinder performing a rotary oscillation at low Reynolds numbers, and compares it with the results obtained for a paradigmatic analytical model of Lagrangian motion: the driven double gyre. The approach does not require prior knowledge of the underlying equations defining the dataset. The time series taken as input corresponds to the evolution of a position coordinate of an individual fluid particle. A delay embedding is used to reconstruct the dynamics in phase space, and a cell complex is built to characterize the topology of the embedding. Fluid particles are said to belong to the same topological class when the Betti numbers, orientability chains and weak boundaries of the associated cell complexes coincide. Topological colouring consists of labelling or ‘colouring’ advected particles with the topological class obtained in their finite-time analyses. The results suggest that topological colouring can be used to distinguish between regions of the flow where trajectories exhibit different finite-time dynamics.

JFM classification

Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Mathematical Foundations: General fluid mechanics Mixing: Chaotic advection

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JFM Papers
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Journal of Fluid Mechanics , Volume 923 , 25 September 2021 , A17
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© The Author(s), 2021. Published by Cambridge University Press

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References

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Charó et al. Supplementary Movie 1

Advection of particles in the rotary oscillatory cylinder system. Particles are coloured following their topological classification: class I in green, class II in magenta and class III in blue (table 1).

Download Charó et al. Supplementary Movie 1(Video)
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Charó et al. Supplementary Movie 2

Advection of particles in the driven double gyre system. Particles are coloured following their topological classification: class I in green, class II in magenta, class III in blue, class IV in red, and class V in orange (table 2).

Download Charó et al. Supplementary Movie 2(Video)
Video 1.7 MB