In fluid dynamics, Kolmogorov microscales are the smallest scales in turbulent flow.
They are defined[1] by where 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, η may be much smaller.
[2] In 1941, Andrey Kolmogorov introduced the hypothesis that the smallest scales of turbulence are universal (similar for every turbulent flow) and that they depend only on ε and ν.
[3] The definitions of the Kolmogorov microscales can be obtained using this idea and dimensional analysis.
Alternatively, the definition of the Kolmogorov time scale can be obtained from the inverse of the mean square strain rate tensor,
using the definition of the energy dissipation rate per unit mass
Then the Kolmogorov length scale can be obtained as the scale at which the Reynolds number (Re) is equal to 1, Kolmogorov's 1941 theory is a mean field theory since it assumes that the relevant dynamical parameter is the mean energy dissipation rate.
In 1961, Kolomogorov published a refined version of the similarity hypotheses that accounts for the log-normal distribution of the dissipation rate.