Critical transition to a non-chaotic regime in isotropic turbulence

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Article numberA17
Pages (from-to)1-28
Number of pages28
JournalJournal of Fluid Mechanics
Early online date10 Nov 2021
Publication statusPublished - 10 Jan 2022


  • physics.flu-dyn


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