Kolmogorov microscales ($\eta ,v_{\eta },{\tau }_{\eta }$)

The Kolmogorov length, velocity and time are $\eta =({\nu }^3/ϵ{)}^{1/4}$, $v_{\eta }=(\nu ϵ{)}^{1/4}$ and ${\tau }_{\eta }=(\nu /ϵ{)}^{1/2}$. With $ϵ\sim u^3/\ell$, their ratios to the integral scales of turbulence are powers of the Reynolds number. They describe a mean scale balance; intermittent dissipative structures can have other local scales.

The Kolmogorov length scale is the length among the Kolmogorov microscales. Kinematic viscosity $\nu$ and mean energy dissipation per unit mass $ϵ$ give the displayed dimensional scale. The associated speed is $(\nu ϵ{)}^{1/4}$, so the Reynolds number formed at this length is one.