  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.
