Kolmogorov microscales

The micro- scale of Kolmogorov is the smallest scale when considering the energy cascade of turbulent flow.

According to Richardson splits the spectrum of turbulent flow in three wavelength ranges. The injection area absorbs the energy, the Inertialbereich transports and in the dissipation of very small wavelengths, the energy is converted into heat by friction. Kolmogorov was 1941 not only a universal formula for the spectral density in the Inertialbereich, the 5/3-Gesetz, but also described as the designated micro scale of Kolmogorov the dissipation, which depends only on the dissipation rate and the viscosity:

Here, the mean value of the dissipation rate per unit mass and the kinematic viscosity of the fluid.

In his theory of Kolmogorov assumes that the length scale is the same for each turbulent flow, ie only by and dependent. The definition of scale can be obtained using this assumption and a dimensional analysis. Since the dimension of kinematic viscosity is Länge2/Zeit and the dimension of the dissipation rate per unit mass Länge2/Zeit3 is obtained as a combination to obtain the dimension of time, the relationship. Because of the assumption of a constant mean dissipation rate is at its approach to a molecular field.

Swell

• M. T. Landahl, E. Mollo -Christensen: Turbulence and Random Processes in Fluid Mechanics, Cambridge, second edition, 1992.