Models for the viscous and buffer layers over smooth walls are reviewed. It is shown that there i... more Models for the viscous and buffer layers over smooth walls are reviewed. It is shown that there is a family of numerically-exact nonlinear structures which account for about half of the energy production and dissipation in the wall layer. The other half can be modelled by the unsteady bursting of those structures. Many of the best-known characteristics of the wall layer, such as the lateral spacing among the streaks, are well predicted by these models. The limitations of minimal models are then discussed, and it is noted that a better approximation is to represent the velocity streaks as ‘semi-infinite’ wakes of the wall-normal velocity structures, both in the buffer and in the logarithmic layer. The consequences of this characterization on the causal relation between bursting structures are also briefly discussed.
The spectra of numerically simulated channels at Reτ=180 and Reτ=550 in very large boxes are desc... more The spectra of numerically simulated channels at Reτ=180 and Reτ=550 in very large boxes are described and analyzed. They support a model in which the u-structures can be decomposed in two components. The first one is formed by structures of size λx>~5 h, λz~2 h, which span most of the channel height, and penetrate into the buffer layer. The second one has maximum intensity in the near-wall region, where it is highly anisotropic and scales in inner units. It widens, lengthens, and becomes more isotropic in the outer layer, where it scales with h. The cospectrum exhibits an analogous quasi-isotropic range, whose width grows linearly with wall distance. At the present Reynolds numbers, nothing can be said about a possible streamwise similarity, due to limited scale separation. An extensive set of statistics from the simulations is downloadable from ftp://torroja.dmt.upm.es/channels.
The organization of vortex clusters above the buffer layer of turbulent channels is analysed usin... more The organization of vortex clusters above the buffer layer of turbulent channels is analysed using direct numerical simulations at friction Reynolds numbers up to Re_{tau} {=} 1900. Especial attention is paid to a family of clusters that reach from the logarithmic layer to the near-wall region below y(+ {=} 20) . These tall attached clusters are markers of structures of the turbulent fluctuating velocity that are more intense than their background. Their lengths and widths are proportional to their heights Delta_y and grow self-similarly with time after originating at different wall-normal positions in the logarithmic layer. Their influence on the outer region is measured by the variation of their volume density with Delta_y. That influence depends on the vortex identification threshold, and becomes independent of the Reynolds number if the threshold is low enough. The clusters are parts of larger structures of the streamwise velocity fluctuations whose average geometry is consistent with a cone tangent to the wall along the streamwise axis. They form groups of a few members within each cone, with the larger individuals in front of the smaller ones. This behaviour is explained considering that the streamwise velocity cones are ‘wakes’ left behind by the clusters, while the clusters themselves are triggered by the wakes left by yet larger clusters in front of them. The whole process repeats self-similarly in a disorganized version of the vortex-streak regeneration cycle of the buffer layer, in which the clusters and the wakes spread linearly under the effect of the background turbulence. These results characterize for the first time the structural organization of the self-similar range of the turbulent logarithmic region.
The spectra and correlations of the velocity fluctuations in turbulent channels, especially above... more The spectra and correlations of the velocity fluctuations in turbulent channels, especially above the buffer layer, are analysed using new direct numerical simulations with friction Reynolds numbers up to Re_{tau} {=} 1900. It is found, and explained, that their scaling is anomalous in several respects, including a square-root behaviour of their width with respect to their length, and a velocity scaling of the largest modes with the centreline velocity U_c. It is shown that this implies a logarithmic correction to the k(-1) energy spectrum, and that it leads to a scaling of the total fluctuation intensities away from the wall which agrees well with the mixed scaling of de Graaff & Eaton (2000) at intermediate Reynolds numbers, but which tends to a pure scaling with U_c at very large ones.
Models for the viscous and buffer layers over smooth walls are reviewed. It is shown that there i... more Models for the viscous and buffer layers over smooth walls are reviewed. It is shown that there is a family of numerically-exact nonlinear structures which account for about half of the energy production and dissipation in the wall layer. The other half can be modelled by the unsteady bursting of those structures. Many of the best-known characteristics of the wall layer, such as the lateral spacing among the streaks, are well predicted by these models. The limitations of minimal models are then discussed, and it is noted that a better approximation is to represent the velocity streaks as ‘semi-infinite’ wakes of the wall-normal velocity structures, both in the buffer and in the logarithmic layer. The consequences of this characterization on the causal relation between bursting structures are also briefly discussed.
The spectra of numerically simulated channels at Reτ=180 and Reτ=550 in very large boxes are desc... more The spectra of numerically simulated channels at Reτ=180 and Reτ=550 in very large boxes are described and analyzed. They support a model in which the u-structures can be decomposed in two components. The first one is formed by structures of size λx>~5 h, λz~2 h, which span most of the channel height, and penetrate into the buffer layer. The second one has maximum intensity in the near-wall region, where it is highly anisotropic and scales in inner units. It widens, lengthens, and becomes more isotropic in the outer layer, where it scales with h. The cospectrum exhibits an analogous quasi-isotropic range, whose width grows linearly with wall distance. At the present Reynolds numbers, nothing can be said about a possible streamwise similarity, due to limited scale separation. An extensive set of statistics from the simulations is downloadable from ftp://torroja.dmt.upm.es/channels.
The organization of vortex clusters above the buffer layer of turbulent channels is analysed usin... more The organization of vortex clusters above the buffer layer of turbulent channels is analysed using direct numerical simulations at friction Reynolds numbers up to Re_{tau} {=} 1900. Especial attention is paid to a family of clusters that reach from the logarithmic layer to the near-wall region below y(+ {=} 20) . These tall attached clusters are markers of structures of the turbulent fluctuating velocity that are more intense than their background. Their lengths and widths are proportional to their heights Delta_y and grow self-similarly with time after originating at different wall-normal positions in the logarithmic layer. Their influence on the outer region is measured by the variation of their volume density with Delta_y. That influence depends on the vortex identification threshold, and becomes independent of the Reynolds number if the threshold is low enough. The clusters are parts of larger structures of the streamwise velocity fluctuations whose average geometry is consistent with a cone tangent to the wall along the streamwise axis. They form groups of a few members within each cone, with the larger individuals in front of the smaller ones. This behaviour is explained considering that the streamwise velocity cones are ‘wakes’ left behind by the clusters, while the clusters themselves are triggered by the wakes left by yet larger clusters in front of them. The whole process repeats self-similarly in a disorganized version of the vortex-streak regeneration cycle of the buffer layer, in which the clusters and the wakes spread linearly under the effect of the background turbulence. These results characterize for the first time the structural organization of the self-similar range of the turbulent logarithmic region.
The spectra and correlations of the velocity fluctuations in turbulent channels, especially above... more The spectra and correlations of the velocity fluctuations in turbulent channels, especially above the buffer layer, are analysed using new direct numerical simulations with friction Reynolds numbers up to Re_{tau} {=} 1900. It is found, and explained, that their scaling is anomalous in several respects, including a square-root behaviour of their width with respect to their length, and a velocity scaling of the largest modes with the centreline velocity U_c. It is shown that this implies a logarithmic correction to the k(-1) energy spectrum, and that it leads to a scaling of the total fluctuation intensities away from the wall which agrees well with the mixed scaling of de Graaff & Eaton (2000) at intermediate Reynolds numbers, but which tends to a pure scaling with U_c at very large ones.
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