View source for Kolmogorov's similarity hypotheses



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== Kolmogorov's similarity hypotheses ==
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<div class="definition"><div class="short_definition">(<br/>''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]].</div><br/> <div class="paragraph">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, &ldquo;similar.&rdquo; 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:
#<div class="list_item">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.</div> 
#<div class="list_item">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.</div><br/> It is a consequence of these hypotheses that in the inertial  subrange the energy is partitioned among the eddies in proportion to ''k''<sup>&minus;5/3</sup>, where ''k'' is the [[wavenumber]].</div><br/></div><div class="reference">Sutton,  O. G. 1953. Micrometeorology.  100&ndash;101. </div><br/> 
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