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Kolmogorov's 1941 theory is a mean field theory since it assumes that the relevant dynamical parameter is the mean energy dissipation rate. In fluid turbulence, the energy dissipation rate fluctuates in space and time, so it is possible to think of the microscales as quantities that also vary in space and time. However, standard practice is to ...
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.
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 ...
In fluid dynamics, the Taylor microscale, which is sometimes called the turbulence length scale, is a length scale used to characterize a turbulent fluid flow. [1] This microscale is named after Geoffrey Ingram Taylor .
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.