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${session.getAttribute("locale")}5Relationship between temporal and spatial averages in grid turbulence
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Sat 24 Mar 2018 08:04:39 AEDT]]>Breakdown of Kolmogorov's first similarity hypothesis in grid turbulence
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λ drops below about 20, the Kolmogorov normalised spectra deviate from those at higher R_{λ}; the deviation increases with decreasing R_{λ}. It is shown that at R_{λ} ≃ 20, the contribution of the energy transfer in the scale-by-scale energy budget becomes smaller than the contributions from the viscous and (large-scale) non-homogeneous terms at all scales, but never vanishes, at least for the range of Reynolds investigated here. A phenomenological argument based on the ratio N between the energy-containing timescale and the dissipative range timescale leads to the condition [formula could not be replicated] for KSH1 to hold. The numerical data indicate that N = 5, yielding R_{λ} ≃ 20, thus confirming our numerical finding. The present results show that KSH1, unlike the second Kolmogorov similarity hypothesis (KSH2,) does not require the existence of an inertial range. While it may seem remarkable that KSH1 is validated at much lower Reynolds numbers than required for KSH2 in grid turbulence (R_{λ} ≥ 1000,), KSH1 applies to small scales which include both dissipative scales and inertial range (if it exists). One can expect that, as the Reynolds number increases, the dissipative scales should satisfy KSH1 first; then, as the Reynolds number attains very high values, the inertial range is established in conformity with KSH2.]]>Sat 24 Mar 2018 07:55:56 AEDT]]>On the anisotropy of a low-Reynolds-number grid turbulence
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ij) and Reynolds-stress dissipation-rate (d_{ij}) tensors and the approach taken is that using the invariant analysis introduced by Lumley & Newman (J. Fluid Mech., vol. 82, 1977, pp. 161-178). The grid is made up of thin square floating elements in an aligned configuration. The anisotropy is initially high behind the grid and decays quickly as the downstream distance increases. The anisotropy invariant map (AIM) analysis shows that the return-to-isotropic trend of both b_{ij} and d_{ij} is fast and follows a perfectly axisymmetic expansion, although just behind the grid there is an initial tendency toward a one-component state. It is found that the linear relation d_{ij} = Ab_{ij} with A = 0.21 is satisfied during the return-to-isotropy phase of the turbulence decay, although close to the grid a form d_{ij} = f(b_{ij}), where f is a nonlinear function of b_{ij}, is more appropriate. For large downstream distances, d_{ij} becomes almost independent of b_{ij}, suggesting that despite the absence of an inertial range, the (dissipative) small scales present a high degree of isotropy. It is argued that (i) the very small values of the mean strain rate and (ii) the weak anisotropy of the large scales are in fact responsible for this result.]]>Sat 24 Mar 2018 07:17:40 AEDT]]>