Kolmogorov similarity hypothesis

Approximately stated Kolmogorov s first similarity hypothesis 3uelds ([83] see also [121], p. 185) In every turbulent flow at sufficiently high Re3molds number, the statistics of the small scale motions have a universal form that is uniquely determined by i/ and e. 

The phrases similarity hypothesis and universal form refer to a mathematical consequence of the Kolmogorov h3q)othesis denoting that on the small scales all high-Reynolds-number turbulent velocity fields are statistically similar. That is, they are statistically identical when they are scaled by the Kolmogorov velocity scale ([121], p. 186). 

Stolovitzky G, Sreenivasan KR. (1994) Kolmogorov s refined similarity hypothesis for turbulence and general stochastic processes. Rev. Mod. Phys., 66 229-236. 

Approximately stated Kolmogorov s second similarity hypothesis yields ([84] see also [122], p. 186) In every turbulent flow at sufficiently high Reynolds numbers, the statistics of the motions of scale I in the range L A Z 3> have a universal... 

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