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Critical transition to a non-chaotic regime in isotropic turbulence

Published online by Cambridge University Press:  10 November 2021

Daniel Clark Open the ORCID record for Daniel Clark [Opens in a new window] ,
Andres Armua Open the ORCID record for Andres Armua [Opens in a new window] ,
Richard D.J.G. Ho Open the ORCID record for Richard D.J.G. Ho [Opens in a new window]  and
Arjun Berera Open the ORCID record for Arjun Berera [Opens in a new window]
Daniel Clark*
Affiliation:
SUPA, School of Physics and Astronomy, University of Edinburgh, JCMB, King's Buildings, Peter Guthrie Tait Road, EdinburghEH9 3FD, UK
Andres Armua
Affiliation:
SUPA, School of Physics and Astronomy, University of Edinburgh, JCMB, King's Buildings, Peter Guthrie Tait Road, EdinburghEH9 3FD, UK
Richard D.J.G. Ho
Affiliation:
Institute of Theoretical Physics, Jagiellonian University, Łojasiewicza 11, 30-348Kraków, Poland
Arjun Berera
Affiliation:
SUPA, School of Physics and Astronomy, University of Edinburgh, JCMB, King's Buildings, Peter Guthrie Tait Road, EdinburghEH9 3FD, UK
*
†Email address for correspondence: daniel-clark@ed.ac.uk
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Abstract

We study the properties of homogeneous and isotropic turbulence in higher spatial dimensions through the lens of chaos and predictability using numerical simulations. We employ both direct numerical simulations and numerical calculations of the eddy damped quasi-normal Markovian closure approximation. Our closure results show a remarkable transition to a non-chaotic regime above the critical dimension, $d_c$, which is found to be approximately 5.88. We relate these results to the properties of the energy cascade as a function of spatial dimension in the context of the idea of a critical dimension for turbulence where Kolmogorov's 1941 theory becomes exact.

JFM classification

Nonlinear Dynamical Systems: Chaos Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 930 , 10 January 2022 , A17
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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