The turbulence dissipation constant is not universal because of its universal dependence on large-scale flow topography

The dimensionless dissipation rate constant $C_{\epsilon}$ of homogeneous isotropic turbulence is such that $C_{\epsilon} = f(\log Re_{\lambda}) {C'}_s^3$ where $f(\log Re_{\lambda})$ is a dimensionless function of $\log Re_{\lambda}$ which tends to 0.26 (by extrapolation) in the limit where $\log Re_{\lambda} \gg 1$ (as opposed to just $Re_{\lambda} \gg 1$) if the assumption is made that a finite such limit exists. The dimensionless number $C'_{s}$ reflects the number of large-scale eddies and is therefore non-universal. The non-universal asymptotic values of $C_{\epsilon}$ stem, therefore, from its universal dependence on $C'_{s}$. The Reynolds number dependence of $C_{\epsilon}$ at values of $\log Re_{\lambda}$ close to and not much larger than 1 is primarily governed by the slow growth (with Reynolds number) of the range of viscous scales of the turbulence. An eventual Reynolds number independence of $C_{\epsilon}$ can be achieved, in principle, by an eventual balance between this slow growth and the increasing non-gaussianity of the small-scales. The turbulence is characterised by five length-scales in the following order of increasing magnitude: the Kolmogorov microscale $\eta$, the inner cutoff scale $\eta_{*} \approx \eta (7.8 + 9.1\log Re_{\lambda})$, the Taylor microscale $\lambda \sim {Re_{\lambda}}^{1/2} \eta$, the voids length-scale $\lambda_{v} \sim {Re_{\lambda}}^{1/3} \lambda$ and the integral length scale $L\sim {Re_{\lambda}}^{2/3} \lambda_{v}$.