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Exact coherent structures and shadowing in turbulent Taylor–Couette flow

Published online by Cambridge University Press:  23 July 2021

Michael C. Krygier Open the ORCID record for Michael C. Krygier [Opens in a new window] ,
Joshua L. Pughe-Sanford Open the ORCID record for Joshua L. Pughe-Sanford [Opens in a new window]  and
Roman O. Grigoriev Open the ORCID record for Roman O. Grigoriev [Opens in a new window]
Michael C. Krygier
Affiliation:
School of Physics, Georgia Institute of Technology, Atlanta, GA30332, USA
Joshua L. Pughe-Sanford
Affiliation:
School of Physics, Georgia Institute of Technology, Atlanta, GA30332, USA
Roman O. Grigoriev*
Affiliation:
School of Physics, Georgia Institute of Technology, Atlanta, GA30332, USA
*
†Email address for correspondence: [email protected]
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Abstract

We investigate a theoretical framework for modelling fluid turbulence based on the formalism of exact coherent structures (ECSs). Although highly promising, existing evidence for the role of ECSs in turbulent flows is largely circumstantial and comes primarily from idealized numerical simulations. In particular, it remains unclear whether three-dimensional turbulent flows in experiment shadow any ECSs. In order to conclusively answer this question, a hierarchy of ECSs should be computed on a domain and with boundary conditions exactly matching experiment. The present study makes the first step in this direction by investigating a small-aspect-ratio Taylor–Couette flow with naturally periodic boundary conditions in the azimuthal direction. We describe the structure of the chaotic set underlying turbulent flow driven by counter-rotating cylinders and present direct numerical evidence for shadowing of a collection of unstable relative periodic orbits and a travelling wave, setting the stage for further experimental tests of the framework.

JFM classification

Nonlinear Dynamical Systems: Chaos Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 923 , 25 September 2021 , A7
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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Krygier et al. Supplementary Movie 1

Shadowing event for RPO05 in lobe 1.
Download Krygier et al. Supplementary Movie 1(Video)
Video 9.8 MB

Krygier et al. Supplementary Movie 2

Shadowing event for reflected copy of RPO05 in lobe 1.

Download Krygier et al. Supplementary Movie 2(Video)
Video 12.8 MB

Krygier et al. Supplementary Movie 3

Shadowing event for RPO01 in lobe 1.

Download Krygier et al. Supplementary Movie 3(Video)
Video 14.4 MB

Krygier et al. Supplementary movie 4

Shadowing event for TW01 in lobe 1.

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Video 11.3 MB

Krygier et al. Supplementary Movie 5

Shadowing event for RPO15 in lobe 3.

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Video 3.3 MB

Krygier et al. Supplementary Movie 6

RPO07 and RPO12 shadowing each other.

Download Krygier et al. Supplementary Movie 6(Video)
Video 22.9 MB