Inertial-diffusive scalar range ($S_C(r)\simeq {ϵ}_c{r}^2/(3\alpha )$)

For scalar diffusivity much larger than kinematic viscosity, scalar diffusion dominates at lengths between the Kolmogorov and scalar cutoff scales. The velocity may still have inertial-range variations, but the scalar is smooth to leading order. The leading isotropic scalar structure function is quadratic, with coefficient fixed by the mean-square gradient and the scalar dissipation rate, rather than by a continuing inertial-convective two-thirds law.

In the large-diffusivity regime, equate diffusion rate $\alpha /r^2$ with inertial eddy rate ${ϵ}^{1/3}{r}^{-2/3}$. This gives the Corrsin scalar microscale, which exceeds the Kolmogorov length scale when $\alpha \gg \nu$.