Critical transition to a non-chaotic regime in isotropic turbulence

Daniel Clark; Andres Armua; Richard DJG Ho; Arjun Berera

doi:10.1017/jfm.2021.878

Critical transition to a non-chaotic regime in isotropic turbulence

Daniel Clark^*, Andres Armua, Richard DJG Ho, Arjun Berera

^*Corresponding author for this work

School of Physics and Astronomy

Research output: Contribution to journal › Article › peer-review

Abstract / Description of output

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, dc, 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.

Original language	English
Article number	A17
Pages (from-to)	1-28
Number of pages	28
Journal	Journal of Fluid Mechanics
Volume	930
Early online date	10 Nov 2021
DOIs	https://doi.org/10.1017/jfm.2021.878
Publication status	Published - 10 Jan 2022

Keywords / Materials (for Non-textual outputs)

chaos
isotropic turbulence
turbulence theory

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10.1017/jfm.2021.878

mainAccepted author manuscript, 630 KB

https://arxiv.org/abs/2105.15163

Particle Theory at the Higgs Centre
Ball, R., Berera, A., Boyle, P., Callison-Burch, C., Del Debbio, L., Gardi, E., Kennedy, A., O'Connell, D., Zwicky, R., Berera, A., Boyle, P., Buckley, A., Del Debbio, L., Gardi, E., Horsley, R., Kennedy, A., Kenway, R., O'Connell, D., Smillie, J. & Zwicky, R.
STFC
1/10/14 → 30/09/18
Project: Research

Cite this

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title = "Critical transition to a non-chaotic regime in isotropic turbulence",

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, dc, 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.",

keywords = "chaos, isotropic turbulence, turbulence theory",

author = "Daniel Clark and Andres Armua and Ho, {Richard DJG} and Arjun Berera",

note = "28 pages, 13 figures, In Press Journal of Fluid Mechanics, 2022 Funding Information: D.C. and A.A. are supported by the University of Edinburgh. A.B. acknowledges partial funding from the UK Science and Technology Facilities Council. Publisher Copyright: {\textcopyright}",

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doi = "10.1017/jfm.2021.878",

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T1 - Critical transition to a non-chaotic regime in isotropic turbulence

AU - Clark, Daniel

AU - Armua, Andres

AU - Ho, Richard DJG

AU - Berera, Arjun

N1 - 28 pages, 13 figures, In Press Journal of Fluid Mechanics, 2022 Funding Information: D.C. and A.A. are supported by the University of Edinburgh. A.B. acknowledges partial funding from the UK Science and Technology Facilities Council. Publisher Copyright: ©

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Y1 - 2022/1/10

N2 - 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, dc, 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.

AB - 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, dc, 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.

KW - chaos

KW - isotropic turbulence

KW - turbulence theory

U2 - 10.1017/jfm.2021.878

DO - 10.1017/jfm.2021.878

M3 - Article

SN - 0022-1120

VL - 930

SP - 1

EP - 28

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

M1 - A17

ER -

Critical transition to a non-chaotic regime in isotropic turbulence

Abstract / Description of output

Keywords / Materials (for Non-textual outputs)

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Particle Theory at the Higgs Centre

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