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where ε is the average rate of dissipation of turbulence kinetic energy per unit mass, and; ν is the kinematic viscosity of the fluid.; Typical values of the Kolmogorov length scale, for atmospheric motion in which the large eddies have length scales on the order of kilometers, range from 0.1 to 10 millimeters; for smaller flows such as in laboratory systems, η may be much smaller.
These scales are very large compared with the Kolmogorov length, but still very small compared with the large scale of the flow (i.e. η ≪ r ≪ L). Since eddies in this range are much larger than the dissipative eddies that exist at Kolmogorov scales, kinetic energy is essentially not dissipated in this range, and it is merely transferred to ...
The largest motions, or eddies, of turbulence contain most of the kinetic energy, whereas the smallest eddies are responsible for the viscous dissipation of turbulence kinetic energy. Kolmogorov hypothesized that when these scales are well separated, the intermediate range of length scales would be statistically isotropic, and that its ...
Here l is the turbulence or eddy length scale, given below, and c μ is a k – ε model parameter whose value is typically given as 0.09; =. The turbulent length scale can be estimated as =, with L a characteristic length. For internal flows this may take the value of the inlet duct (or pipe) width (or diameter) or the hydraulic diameter.
The Taylor microscale falls in between the large-scale eddies and the small-scale eddies, which can be seen by calculating the ratios between and the Kolmogorov microscale . Given the length scale of the larger eddies l ∝ k 3 / 2 ϵ {\displaystyle l\propto {\frac {k^{3/2}}{\epsilon }}} , and the turbulence Reynolds number Re l {\displaystyle ...
This means that the whole range of spatial and temporal scales of the turbulence must be resolved. All the spatial scales of the turbulence must be resolved in the computational mesh, from the smallest dissipative scales ( Kolmogorov microscales ), up to the integral scale L {\displaystyle L} , associated with the motions containing most of the ...
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ε is the rate of dissipation of turbulence kinetic energy per unit mass. Similar to the Kolmogorov microscales – which describe the smallest scales of turbulence before viscosity dominates – the Batchelor scale describes the smallest length scales of fluctuations in scalar concentration that can exist before being dominated by molecular ...