Reynolds number Kolmogorov

In his treatise "The local structure of turbulence in an incompressible viscous liquid at very high Reynolds numbers , Kolmogorov [289] considered the elements of free turbulence as random variables, which are in general terms accessible to probability theory. This assumes local isotropic turbulence. Thus the probability distribution law is independent of time, since a temporally steady-state condition is present. For these conditions Kolmogorov postulated two similarity hypotheses ... 

The ratio of the Kolmogorov scale and the turbulence integral scale can be expressed in terms of the turbulence Reynolds number by... 

Kolmogorov, A. N. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dolt Akad. NaukSSSR 30, 301 (1941). 

FIGURE 10.5. Parameter plane of nondimensional intensity and nondimensional Kolmogorov scale of turbulence for premixed turbulent combustion, showing regimes of combustion and lines for constant values of turbulence Reynolds numbers, nondimensional integral scale, and a Damkohler number. 

Earlier it was stated that the structure of a turbulent velocity field may be presented in terms of two parameters—the scale and the intensity of turbulence. The intensity was defined as the square root of the turbulent kinetic energy, which essentially gives a root-mean-square velocity fluctuation U. Three length scales were defined the integral scale /q, which characterizes the large eddies the Taylor microscale X, which is obtained from the rate of strain and the Kolmogorov microscale 1, which typifies the smallest dissipative eddies. These length scales and the intensity can be combined to form not one, but three turbulent Reynolds numbers Ri = U lo/v, Rx. = U X/v, and / k = U ly/v. From the relationship between Iq, X, and /k previously derived it is found that / ... 

Approximately stated Kolmogorov s hypothesis of local isotropy yields ([83] see also [121], p. 184) At sufficiently high Reynolds number, the small scale turbulent motions are statistically isotropic. 

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). 

Kolmogorov AN (1962) A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J Fluid Mech 13(l) 82-85... 

Kolmogorov AN (1941) Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Number, it Dokl Akad Nauk SSSR 30 301-306... 

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