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.