Kolmogorov microscale

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Kolmogorov microscale

Of the three standard turbulence length scales, the one that characterizes the smallest dissipation-scale eddies.

As the turbulence kinetic energy cascades from the largest scales down to the smallest scales, the dynamics of the small eddies become independent of the large-scale eddies. At the smallest scales, the rate at which energy is supplied must equal the rate at which it is dissipated by viscosity. Thus, parameters available to form length and velocity scales are the dissipation rate, ε, and the kinematic viscosity, ν. The Kolmogorov length, η, and velocity, υ, scales are:
ams2001glos-Ke7
ams2001glos-Ke8
Note that the Reynolds number formed from the Kolmogorov microscale is equal to one. Based on the observation that the large eddies lose their energy in about one large eddy turnover time, the dissipation rate may be scaled as ε = u3/L where L is the appropriate length scale. Thus, the ratio of the largest to the smallest length scales is
ams2001glos-Ke9
and the number of grid points necessary to resolve a turbulent flow in a numerical model is therefore proportional to R9/4.
Compare integral length scales, Taylor microscale;
see also isotropic turbulence, local isotropy, Reynolds number, turbulence kinetic energy, turbulence spectrum, viscous fluid.

Hinze, J. O. 1975. Turbulence. 2d ed., McGraw–Hill, . 790 pp.

Tennekes, H., and J. L. Lumley 1972. A First Course in Turbulence. MIT Press, . 300 pp.

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