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The present work describes the processes of production, dissipation and transport of the Reynolds stress components in turbulent channel flow for three values of the Reynolds number, considering simultaneously the spaces of scales and positions. The tool used to perform the analysis is the Anisotropic Generalized Kolmogorov Equation (AGKE), a statistical budget equation for the second-order structure function.
For the computation of the AGKE terms, three DNS-generated databases for turbulent channel flow at friction Reynolds number Retau = 200, Retau = 500 and Retau = 1000 were considered. The analysis highlighted the presence of three peaks in the production of scale energy. The first, common to all the three Reynolds numbers, involves the structures of the near-wall cycle. The second, observed for Retau = 500 and Retau = 1000 but not for Retau = 200, was associated to the presence of attached eddies. The third, observed only for Retau = 1000, was linked to the so-called large- and very large-scale motions. In the region of the first peak, near to the wall, the presence of transport processes that do not scale in wall units highlighted the interaction with the outer scales. In the second peak, proportionality between the scale and the wall-normal distance of some transport processes and the inactivity at the wall of v2-transporting motions were observed.
Moreover, an observed transfer of energy related to spanwise fluctuations towards scales more and more spanwise-oriented for increasing wall-normal distances was associated to the presence of hairpin vortices in the flow. Finally, some features of this second peak were found to be visible also for Retau = 200, suggesting a continuous transition from low- to high-Reynolds number flows. The third peak of production was also characterized, together with the associated transport of energy.