Kolmogorov's similarity hypotheses

From Glossary of Meteorology

Kolmogorov's similarity hypotheses

(Also called local similarity hypotheses, universal equilibrium hypotheses.) Statements of the factors determining the transfer and dissipation of kinetic energy at the high wavenumber end of the spectrum of turbulence.

Kolmogorov considers the large anisotropic eddies as the sources of energy, which is transferred down the size scale. At some point the eddies lose all structure; they become homogeneous and isotropic, that is, "similar." In this region, their energy is determined only by the rate of transfer from the larger eddies and the rate of dissipation by the smaller ones. Kolmogorov stated two similarity hypotheses:
  1. At large Reynolds numbers the local average properties of the small- scale components of any turbulent motion are determined entirely by kinematic viscosity and average rate of dissipation per unit mass.
  2. There is an upper subrange (the inertial subrange) in this bandwidth of small eddies in which the local average properties are determined only by the rate of dissipation per unit mass.

    It is a consequence of these hypotheses that in the inertial subrange the energy is partitioned among the eddies in proportion to k-5/3, where k is the wavenumber.

Sutton, O. G. 1953. Micrometeorology. 100–101.