Li, J., Si, W., Li, Y. orcid.org/0000-0001-7907-5176 et al. (1 more author) (2025) Intrinsic relationship between synchronisation thresholds and Lyapunov vectors: evidence from large eddy simulations and shell models. Journal of Fluid Mechanics, 1008. A27. ISSN 0022-1120
Abstract
An important parameter characterising the synchronisation of turbulent flows is the thresh9 old coupling wavenumber. This study investigates the relationship between the threshold coupling wavenumber and the leading Lyapunov vector using large eddy simulations and the SABRA model. Various subgrid-scale stress models, Reynolds numbers, and different coupling methods are examined. A new scaling relation is identified for the leading Lyapunov exponents in large eddy simulations, showing that they approximate those of filtered direct numerical simulations. This interpretation provides a physical basis for results related to the Lyapunov exponents of large eddy simulations, including those related to synchronisation. Synchronization experiments show that the peak wavenumber of the energy spectrum of the leading Lyapunov vector coincides with the threshold coupling wavenumber, in large eddy simulations of box turbulence with standard Smagorinsky or dynamic mixed models as well as in the SABRA model, replicating results from direct numerical simulations of box turbulence. Although the dynamic Smagorinsky model exhibit different behaviour, the totality of the results suggests that the relationship is an intrinsic property of a certain class of chaotic systems. We also confirm that conditional Lyapunov exponents characterize the synchronization process in indirectly coupled systems as they do in directly coupled ones, with their values insensitive to the nature of the master flow. These findings advance the understanding of the role of the Lyapunov vector in the synchronization of turbulence.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s), 2025. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited. |
Keywords: | Nonlinear Dynamical Systems: Chaos; Turbulent Flows: Turbulence simulation; Turbulent Flows: Turbulence modelling |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematical and Physical Sciences |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 31 Jan 2025 10:55 |
Last Modified: | 03 Apr 2025 10:33 |
Status: | Published |
Publisher: | Cambridge University Press |
Refereed: | Yes |
Identification Number: | 10.1017/jfm.2025.133 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:222358 |