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Synchronization of low Reynolds number plane Couette turbulence

Published online by Cambridge University Press:  17 December 2021

Marios-Andreas Nikolaidis Open the ORCID record for Marios-Andreas Nikolaidis [Opens in a new window]  and
Petros J. Ioannou Open the ORCID record for Petros J. Ioannou [Opens in a new window]
Marios-Andreas Nikolaidis*
Affiliation:
Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, Athens, 157 84, Greece
Petros J. Ioannou
Affiliation:
Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, Athens, 157 84, Greece Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA 02138, USA
*
†Email address for correspondence: mnikolaidis@phys.uoa.gr
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Abstract

We demonstrate that in plane Couette turbulence a separation of the velocity field in large and small scales according to a streamwise Fourier decomposition allows us to identify an active subspace comprising a small number of the gravest streamwise components of the flow that can synchronize all the remaining streamwise flow components. The critical streamwise wavelength, $\ell _{x c}$, that separates the active from the synchronized passive subspace is identified as the streamwise wavelength at which perturbations to the time-dependent turbulent flow with streamwise wavelengths $\ell _x<\ell _{xc}$ have negative characteristic Lyapunov exponents. The critical wavelength is found to be approximately 130 wall units and obeys viscous scaling at these Reynolds numbers.

JFM classification

Nonlinear Dynamical Systems: Chaos Turbulent Flows: Turbulence simulation

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JFM Papers
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Journal of Fluid Mechanics , Volume 933 , 25 February 2022 , A5
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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