 Viscous-convective scalar range

For scalar diffusivity much smaller than kinematic viscosity, a scalar has structure below the Kolmogorov length scale while the velocity is smooth. The strain rate $s\sim (ϵ/\nu {)}^{1/2}$ transfers scalar variance, giving $d{S}_C/dr\sim {ϵ}_c/(sr)$. Integration produces a logarithm plus an additive matching constant.