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 $\backslash varepsilon$ is the average rate of dissipation of turbulence kinetic energy per unit mass, and $\backslash nu$ 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, $\backslash eta$ may be much smaller.George, William K. "Lectures in Turbulence for the 21st Century." Department of Thermo and Fluid Engineering, Chalmers University of Technology, GĂ¶teborg, Sweden (2005).p 64 nlinehttp://www.turbulence-online.com/Publications/Lecture_Notes/Turbulence_Lille/TB_16January2013.pdf
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 $\backslash varepsilon$ and $\backslash nu$. The definitions of the Kolmogorov microscales can be obtained using this idea and dimensional analysis. Since the dimension of kinematic viscosity is length^{2}/time, and the dimension of the energy dissipation rate per unit mass is length^{2}/time^{3}, the only combination that has the dimension of time is $\backslash tau\_\backslash eta=(\backslash nu\; /\; \backslash varepsilon)^$ which is the Kolmorogov time scale. Similarly, the Kolmogorov length scale is the only combination of $\backslash varepsilon$ and $\backslash nu$ that has dimension of length.
Alternatively, the definition of the Kolmogorov time scale can be obtained from the inverse of the mean square strain rate tensor, $\backslash tau\_\backslash eta\; =\; (2\; \backslash langle\; E\_\; E\_\; \backslash rangle)^$ which also gives $\backslash tau\_\backslash eta=(\backslash nu/\backslash varepsilon)^$ using the definition of the energy dissipation rate per unit mass $\backslash varepsilon\; =\; 2\; \backslash nu\; \backslash langle\; E\_\; E\_\; \backslash rangle$. Then the Kolmogorov length scale can be obtained as the scale at which the Reynolds number is equal to 1, $\backslash mathit\; =\; UL/\backslash nu\; =\; (\backslash eta/\backslash tau\_\backslash eta)\; \backslash eta\; /\; \backslash nu\; =\; 1$.
The Kolmogorov 1941 theory is a mean field theory since it assumes that the relevant dynamical parameter is the mean energy dissipation rate. In fluid turbulence, the energy dissipation rate fluctuates in space and time, so it is possible to think of the microscales as quantities that also vary in space and time. However, standard practice is to use mean field values since they represent the typical values of the smallest scales in a given flow.

See also

*Taylor microscale *Integral length scale *Batchelor scale

** References **

{{DEFAULTSORT:Kolmogorov Microscales
Category:Turbulence

See also

*Taylor microscale *Integral length scale *Batchelor scale