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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.
The dynamics at these scales is described by use of self-similarity, or by assumptions – for turbulence closure – on the statistical properties of the flow in the inertial subrange. A pioneering work was the deduction by Andrey Kolmogorov in the 1940s of the expected wavenumber spectrum in the turbulence inertial subrange.
Thus the "Kolmogorov − 5 / 3 spectrum" is generally observed in turbulence. However, for high order structure functions, the difference with the Kolmogorov scaling is significant, and the breakdown of the statistical self-similarity is clear.
Turbulence kinetic energy is then transferred down the turbulence energy cascade, and is dissipated by viscous forces at the Kolmogorov scale. This process of production, transport and dissipation can be expressed as: D k D t + ∇ ⋅ T ′ = P − ε , {\displaystyle {\frac {Dk}{Dt}}+\nabla \cdot T'=P-\varepsilon ,} where: [ 1 ]
Also, direct numerical simulations are useful in the development of turbulence models for practical applications, such as sub-grid scale models for large eddy simulation (LES) and models for methods that solve the Reynolds-averaged Navier–Stokes equations (RANS). This is done by means of "a priori" tests, in which the input data for the model ...
The statistical theory of turbulence in viscous liquids describes the fluid flow by a scale-invariant distribution of the velocity field, which means that the typical size of the velocity as a function of wavenumber is a power-law. In steady state, larger scale eddies at long wavelengths disintegrate into smaller ones, dissipating their energy ...
For large length scales the quantum turbulence manifests as a Kolmogorov energy cascade (numerical simulations using the Gross-Pitaevskii equation [12] and the vortex-filament model confirmed this effect [13] [14]), with the energy spectrum following /. Lacking thermal dissipation, it is intuitive to assume that quantum turbulence in the low ...
SST (Menter's shear stress transport) turbulence model [11] is a widely used and robust two-equation eddy-viscosity turbulence model used in computational fluid dynamics. The model combines the k-omega turbulence model and K-epsilon turbulence model such that the k-omega is used in the inner region of the boundary layer and switches to the k ...