Kolmogorov microscales

Kolmogorov microscales are the smallest scales in turbulent flow. At the Kolmogorov scale, viscosity dominates and the turbulent kinetic energy is dissipated into heat. They are defined by

where ${\displaystyle \varepsilon }$ is the average rate of dissipation of turbulence kinetic energy per unit mass, and ${\displaystyle \nu }$ is the kinematic viscosity of the fluid. Typical values of the Kolmogorov length scale, for atmospheric motion in which the large eddies have length scales on the order of kilometers, range from 0.1 to 10 millimeters; for smaller flows such as in laboratory systems, ${\displaystyle \eta }$ may be much smaller.

In his 1941 theory, Andrey Kolmogorov introduced the idea that the smallest scales of turbulence are universal (similar for every turbulent flow) and that they depend only on ${\displaystyle \varepsilon }$ and ${\displaystyle \nu }$. The definitions of the Kolmogorov microscales can be obtained using this idea and dimensional analysis. Since the dimension of kinematic viscosity is length²/time, and the dimension of the energy dissipation rate per unit mass is length²/time³, the only combination that has the dimension of time is ${\displaystyle \tau _{\eta }=(\nu /\varepsilon )^{1/2}}$ which is the Kolmorogov time scale. Similarly, the Kolmogorov length scale is the only combination of ${\displaystyle \varepsilon }$ and ${\displaystyle \nu }$ that has dimension of length.

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