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, $d_c$ , 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.

The production of uncertainty in three-dimensional Navier–Stokes turbulence

“…Therefore, the internal production of uncertainty can be related to the strain self-amplification and vortex-stretching as speculated by Clark et al. (2022) in their conclusion, but also to the pressure Hessian. In (2.11) represents the influence of the external forcing on the strain rate tensor.…”

“…2020; Clark et al. 2021, 2022). It offers the advantage of setting the average turbulence dissipation a priori for statistically steady turbulence.…”

“…2020; Clark et al. 2021, 2022) and F2 differs from it only in terms of which is zero in F2 and non-zero in F1. In both F1 and F2 the perturbation is made to a fully developed statistically stationary turbulence whereas in F3 we follow the evolution of two velocity fields which are initially very weak in terms of energy and very close to each other, i.e.…”

“…From these results, Clark et al. (2022) speculated that vortex stretching and strain self-amplification, which are responsible for enstrophy generation, may also be important for uncertainty generation. The present paper is an effort in the direction of understanding uncertainty growth in terms of vortex stretching and compression dynamics and statistics.…”

“…Clark et al. (2021, 2022) investigated the dependence of uncertainty on spatial dimension (between two and eight) in DNS and in an EDQNM model of statistically stationary homogeneous turbulence. They found a critical dimension which is close to the dimension of maximum enstrophy production and above which the turbulence uncertainty is no longer ruled by chaoticity.…”