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

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The Structure of Turbulent Shear Flow

A theoretical decomposition of mean skin friction generation into physical phenomena across the whole profile of the incompressible zero-pressure-gradient smooth-flat-plate boundary layer is derived from a mean streamwise kinetic-energy budget in an absolute reference frame (in which the undisturbed fluid is not moving). The Reynolds-number dependences in the laminar and turbulent cases are investigated from direct numerical simulation datasets and Reynolds-averaged Navier–Stokes simulations, and the asymptotic trends are consistently predicted by theory. The generation of the difference between the mean friction in the turbulent and laminar cases is identified with the total production of turbulent kinetic energy (TKE) in the boundary layer, represented by the second term of the proposed decomposition of the mean skin friction coefficient. In contrast, the analysis introduced by Fukagata et al. (Phys. Fluids, vol. 14 (11), 2002, pp. 73–76), based on a streamwise momentum budget in the wall reference frame, relates the turbulence-induced excess friction to the Reynolds shear stress weighted by a linear function of the wall distance. The wall-normal distribution of the linearly-weighted Reynolds shear stress differs from the distribution of TKE production involved in the present discussion, which consequently draws different conclusions on the contribution of each layer to the mean skin friction coefficient. At low Reynolds numbers, the importance of the buffer-layer dynamics is confirmed. At high Reynolds numbers, the present decomposition quantitatively shows for the first time that the generation of the turbulence-induced excess friction is dominated by the logarithmic layer. This is caused by the well-known decay of the relative contributions of the buffer layer and wake region to TKE production with increasing Reynolds numbers. This result on mean skin friction, with a physical interpretation relying on an energy budget, is consistent with the well-established general importance of the logarithmic layer at high Reynolds numbers, contrary to the friction breakdown obtained from the approach of Fukagata et al. (Phys. Fluids, vol. 14 (11), 2002, pp. 73–76), essentially based on a momentum budget. The new decomposition suggests that it may be worth investigating new drag reduction strategies focusing on TKE production and on the nature of the logarithmic layer dynamics. The decomposition is finally extended to the pressure-gradient case and to channel and pipe flows.

A theoretical decomposition of mean skin friction generation into physical phenomena across the boundary layer

This study deals with turbulent boundary layers under adverse-pressure gradients. Well-resolved large-eddy simulations (LES) were performed to assess the influence of the streamwise pressure develo ...

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/39C38082C380F396D004B65F438C296A/S0022112017002361a.pdf/div-class-title-history-effects-and-near-equilibrium-in-adverse-pressure-gradient-turbulent-boundary-layers-div.pdf

History effects and near equilibrium in adverse-pressure-gradient turbulent boundary layers

In the present study, the physical meaning of vorticity is revisited based on the Liutex-Shear (RS) decomposition proposed by Liu et al. in the framework of Liutex (previously called Rortex), a vortex vector field with information of both rotation axis and swirling strength (Liu et al. 2018). It is demonstrated that the vorticity in the direction of rotational axis is twice the spatial mean angular velocity in the small neighborhood around the considered point while the imaginary part of the complex eigenvalue (λci) of the velocity gradient tensor (if exist) is the pseudo-time average angular velocity of a trajectory moving circularly or spirally around the axis. In addition, an explicit expression of the Liutex vector in terms of the eigenvalues and eigenvectors of velocity gradient is obtained for the first time from above understanding, which can further, though mildly, accelerate the calculation and give more physical comprehension of the Liutex vector.

Explicit formula for the Liutex vector and physical meaning of vorticity based on the Liutex-Shear decomposition

Effect of uniform blowing/suction in a turbulent boundary layer at moderate Reynolds number

Simulation and validation of a spatially evolving turbulent boundary layer up to Reθ = 8300

The present work presents a number of parallel and spatially developing simulations of boundary layers to address the question of whether hairpin vortices are a dominant feature of near-wall turbul ...

Hairpin vortices in turbulent boundary layers

The present work addresses the question whether hairpin vortices are a dominant feature of near-wall turbulence and which role they play during transition. First, the parent-offspring mechanism is investigated in temporal simulations of a single hairpin vortex introduced in a mean shear flow corresponding to turbulent channels and boundary layers up to Reτ = 590. Using an eddy viscosity computed from resolved simulations, the effect of a turbulent background is also considered. Tracking the vortical structure downstream, it is found that secondary hairpins are created shortly after initialization. Thereafter, all rotational structures decay, whereas this effect is enforced in the presence of an eddy viscosity. In a second approach, a laminar boundary layer is tripped to transition by insertion of a regular pattern of hairpins by means of defined volumetric forces representing an ejection event. The idea is to create a synthetic turbulent boundary layer dominated by hairpin-like vortices. The flow for Reτ < 250 is analysed with respect to the lifetime of individual hairpin-like vortices. Both the temporal and spatial simulations demonstrate that the regeneration process is rather short-lived and may not sustain once a turbulent background has formed. From the transitional flow simulations, it is conjectured that the forest of hairpins reported in former DNS studies is an outer layer phenomenon not being connected to the onset of near-wall turbulence.

https://iopscience.iop.org/article/10.1088/1742-6596/506/1/012008/pdf

The elementary question whether hairpin vortices constitute an inherent, universal structure of wall turbulence at moderate and high Reynolds numbers (Re) is addressed in this study. The downstream evolution of a single, artificial hairpin vortex is first studied in a mean shear flow to investigate possible decay and package-creation processes under high Re conditions. In a second step, hairpin-dominated flow in a transitional turbulent boundary layer is considered, whereas the lifetime of individual vortices and possible connection mechanisms are evaluated. The statistics obtained from this flow regime will be compared with reference data from turbulent-boundary-layer studies employing different transition mechanisms. Vortex eduction will be applied to comprehend the evolution from a well organized to a more chaotic state. The results could explain discrepancies in boundary-layer data close to transition and will contribute to the discussion about the relevance of hairpin-like structures in fully developed wall turbulence. Besides the statistical description of turbulent shear flows, models for inherent vortical motions and coherent structures have become very important. In this context, wall-attached, hairpin-shaped vortices have been suggested to be the main sustaining flow pattern in turbulent boundary layers (TBL) (7, 10). Models using superpositions of attached eddies succeed in explaining several features of wall turbulence like mean velocity profile, distribution of Reynolds stresses, and energy spectra. The existence of large-scale coherent structures is comprised by considering packets of hairpin vortices aligned in streamwise direction, whereas every hairpin above a certain size generates new loop-shaped vortices upstream and downstream of its own position (6, 13). These formations have been observed in experiments and numerical simulations of a single hairpin in laminar shear flow and in low Reynolds number (Re) turbulent channel flow (1, 13) being consistent with some forms of experimental data from channel and flat-plate boundary layer flows (2, 3, 4). However, actual evidence for such universal structures "in the wild" is still limited - especially at moderate to high Re - and spatial and evolutionary details as well as statistical relevance remain controversial. Definitely, hairpin structures are evident in turbulent flow close to transition, as shown by the early visualizations by Head and Bandyopadhya (4), and the simulations by Wu and Moin who even report a "forest of hairpins" in their TBL direct numerical simulations

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The significance of hairpin vortices in turbulent boundary layers

A new highly resolved large-eddy simulation is presented for a spatially developing turbulent boundary layer, covering in one single domain the range of Reynolds number Re θ = 180 to 8300. Turbulence statistics are in close agreement with experiments and other simulations. The evolution of the large outer-layer structures is examined using spectra. It is found that the near-wall region is very intermittent, and at high Re θ dominated by strong modulation of the turbulence intensity through the outer structures. The corrugated appearance of the boundary-layer edge is thus directly linked to the turbulence regeneration in the immediate wall vicinity.

Georg Eitel-Amor

Papers

Simulation and validation of a spatially evolving turbulent boundary layer up to Reθ = 8300

Hairpin vortices in turbulent boundary layers

Hairpin vortices in turbulent boundary layers

The significance of hairpin vortices in turbulent boundary layers

Turbulent Boundary Layers in Long Computational Domains