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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.
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 ...
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 ...
For homogeneous turbulence (i.e., statistically invariant under translations of the reference frame) this is usually done by means of the energy spectrum function E(k), where k is the modulus of the wavevector corresponding to some harmonics in a Fourier representation of the flow velocity field u(x):
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 ]
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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 quantum vortex dynamics can exhibit signatures of turbulence including a Kolmogorov −5/3 power law, [3] [4] [5] a quantum manifestation of the inertial transport of energy to large scales observed in classical fluids, known as an inverse energy cascade. [6] [7]