Critical transition to a non-chaotic regime in isotropic turbulence

TL;DR

This paper investigates how isotropic turbulence transitions from chaotic to non-chaotic behavior as the spatial dimension increases, identifying a critical dimension around 5.88 where chaos diminishes.

Contribution

It reveals a critical dimension for turbulence where chaos disappears, using both DNS and EDQNM closure methods to analyze energy cascade properties.

Findings

Transition to non-chaotic regime above d_c≈5.88

Closure results show a significant change in turbulence behavior at critical dimension

Energy cascade properties vary with spatial dimension

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 (DNS) and numerical calculations of the Eddy Damped Quasi Normal Markovian (EDQNM) closure approximation. Our closure results show a remarkable transition to a non-chaotic regime above critical dimension $d_c\approx 5.88$. 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.