/pdf/evidence-of-very-long-meandering-features-in-the-logarithmic-2m2f4f0daq.pdf

Evidence of very long meandering features in the logarithmic region of turbulent boundary layers

Coherent structures in wall turbulence transport momentum and provide a means of producing turbulent kinetic energy. Above the viscous wall layer, the hairpin vortex paradigm of Theodorsen coupled with the quasistreamwise vortex paradigm have gained considerable support from multidimensional visualization using particle image velocimetry and direct numerical simulation experiments. Hairpins can autogenerate to form packets that populate a significant fraction of the boundary layer, even at very high Reynolds numbers. The dynamics of packet formation and the ramifications of organization of coherent structures (hairpins or packets) into larger-scale structures are discussed. Evidence for a large-scale mechanism in the outer layer suggests that further organization of packets may occur on scales equal to and larger than the boundary layer thickness.

Hairpin vortex organization in wall turbulencea)

It has been thought that sheets of cells move by traction forces exerted by the cells at the leading edge of the sheet. Using traction microscopy to create a map of physical forces, it is now shown that in fact it is cells many rows from the front that do most of the work. Fundamental biological processes including morphogenesis, tissue repair and tumour metastasis require collective cell motions1,2,3, and to drive these motions cells exert traction forces on their surroundings4. Current understanding emphasizes that these traction forces arise mainly in ‘leader cells’ at the front edge of the advancing cell sheet5,6,7,8,9. Our data are contrary to that assumption and show for the first time by direct measurement that traction forces driving collective cell migration arise predominately many cell rows behind the leading front edge and extend across enormous distances. Traction fluctuations are anomalous, moreover, exhibiting broad non-Gaussian distributions characterized by exponential tails10,11,12. Taken together, these unexpected findings demonstrate that although the leader cell may have a pivotal role in local cell guidance, physical forces that it generates are but a small part of a global tug-of-war involving cells well back from the leading edge.

/pdf/physical-forces-during-collective-cell-migration-3s53rslx6s.pdf

Physical forces during collective cell migration

The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.

/pdf/the-structure-of-turbulent-shear-flow-2yf3szhaqb.pdf

The Structure of Turbulent Shear Flow

A new numerical simulation of a turbulent channel in a large box at Reτ=2003 is described and briefly compared with simulations at lower Reynolds numbers and with experiments. Some of the fluctuation intensities, especially the streamwise velocity, do not scale well in wall units, both near and away from the wall. Spectral analysis traces the near-wall scaling failure to the interaction of the logarithmic layer with the wall. The present statistics can be downloaded from http://torroja.dmt.upm.es/ftp/channels. Further ones will be added to the site as they become available.

Scaling of the velocity fluctuations in turbulent channels up to Reτ=2003

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 at very large ones.

/pdf/scaling-of-the-energy-spectra-of-turbulent-channels-yaaftn9z8z.pdf

Scaling of the energy spectra of turbulent channels

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.

Spectra of the very large anisotropic scales in turbulent channels

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 τ = 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 Ay 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 Δ 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.

Self-similar vortex clusters in the turbulent logarithmic region

We study the temporal stability of the Orr-Sommerfeld and Squire equations in channels with turbulent mean velocity profiles and turbulent eddy viscosities. Friction Reynolds numbers up to Re τ =2×10 4 are considered. All the eigensolutions of the problem are damped, but initial perturbations with wavelengths λ x > λ z can grow temporarily before decaying. The most amplified solutions reproduce the organization of turbulent structures in actual channels, including their self-similar spreading in the logarithmic region. The typical widths of the near-wall streaks and of the large-scale structures of the outer layer, λ + z = 100 and λ z /h = 3, are predicted well. The dynamics of the most amplified solutions is roughly the same regardless of the wavelength of the perturbations and of the Reynolds number. They start with a wall-normal v event which does not grow but which forces streamwise velocity fluctuations by stirring the mean shear (uv < 0). The resulting u fluctuations grow significantly and last longer than the v ones, and contain nearly all the kinetic energy at the instant of maximum amplification.

Linear energy amplification in turbulent channels

A new method is introduced for estimating the convection velocity of individual modes in turbulent shear flows that, in contrast to most previous ones, only requires spectral information in the temporal or spatial direction over which a modal decomposition is desired, while only using local derivatives in other directions. If no spectral information is desired, the method provides a natural definition for the average convection velocity, as well as a way to estimate the accuracy of the frozen-turbulence approximation. Existing data from numerical turbulent channels at friction Reynolds numbers Reτ 1900 are used to validate the new method against classical ones, and to characterize the dependence of the convection velocity on the eddy wavelength and wall distance. The results indicate that the small scales in turbulent channels travel at the local mean velocity, while large ‘global’ modes travel at a more uniform speed proportional to the bulk velocity. To estimate the systematic deviations introduced in experimental spectra by the use of Taylor’s approximation with a wavelengthindependent convection velocity, a semi-empirical fit to the computed convection velocities is provided. It represents well the data throughout the Reynolds number range of the simulations. It is shown that Taylor’s approximation not only displaces the large scales near the wall to shorter apparent wavelengths but also modifies the shape of the spectrum, giving rise to spurious peaks similar to those observed in some experiments. To a lesser extent the opposite is true above the logarithmic layer. The effect increases with the Reynolds number, suggesting that some of the recent challenges to the k −1 x energy spectrum may have to be reconsidered.

Juan C. del Álamo

Papers

Scaling of the energy spectra of turbulent channels

Spectra of the very large anisotropic scales in turbulent channels

Self-similar vortex clusters in the turbulent logarithmic region

Linear energy amplification in turbulent channels

Estimation of turbulent convection velocities and corrections to Taylor's approximation