With the availability of new high-Reynolds-number (Re) databases of turbulent bound-ary layers (TBLs) it has been possible to identify in detail certain regions of the boundary layer with more complex behavior. In this study we consider a unique database at moderately-high Re, with a nearconstant adverse pressure gradient (APG) [Pozuelo et al., J. Fluid Mech. 939, A34 (2022)], and perform spectral analysis of the Reynolds stresses, focusing on the streamwise component. We assess different regions of the APG TBL, comparing this case with the zero-pressure-gradient (ZPG) TBL, and identify the relevant scaling parameters as well as the contribution of the scales of different sizes. The small scales in the near-wall region up to the near-wall spectral peak have been found to scale using viscous units. In APG TBLs, the largest scales close to the wall have a better scaling with the boundary-layer thickness (899), and they are significantly affected by the APG. In the overlap and wake regions of the boundary layer, the small energetic scales exhibit a good scaling with the displacement thickness (8*) while the larger scales and the outer spectral peak are better scaled with the boundary-layer thickness. Also, note that the wall-normal location of the spectral outer peak scales with the displacement thickness rather than the boundary layer thickness. The various scalings exhibited by the spectra in APG TBLs are reported here, and shed light on the complex phenomena present in these flows of great scientific and technological importance.

In this study, a new well-resolved large-eddy simulation of an incompressible near-equilibrium adverse-pressure-gradient (APG) turbulent boundary layer (TBL) over a flat plate is presented. In this simulation, we have established a near-equilibrium APG over a wide Reynolds-number range. In this so-called region of interest, the Rotta-Clauser pressure-gradient parameter beta exhibits an approximately constant value of around 1.4, and the Reynolds number based on momentum thickness reaches Re-theta = 8700. To the best of the authors' knowledge, this is to date the highest Re-theta achieved for a near-equilibrium APG TBL under an approximately constant moderate APG. We evaluated the self-similarity of the outer region using two scalings, namely the Zagarola-Smits and an alternative scaling based on edge velocity and displacement thickness. Our results reveal that outer-layer similarity is achieved, and the viscous scaling collapses the near-wall region of the mean flow in agreement with classical theory. Spectral analysis reveals that the APG displaces some small-scale energy from the near-wall to the outer region, an effect observed for all the components of the Reynolds-stress tensor, which becomes more evident at higher Reynolds numbers. In general, the effects of the APG are more noticeable at lower Reynolds numbers. For instance, the outer peak of turbulent-kinetic-energy (TKE) production is less prominent at higher Re. Although the scale separation increases with Re in zero-pressure-gradient TBLs, this effect becomes accentuated by the APG. Despite the reduction of the outer TKE production at higher Reynolds numbers, the mechanisms of energisation of large scales are still present.

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 Reθ = 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 Reθ 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.

Rare negative streamwise velocities and extreme wall-normal velocity fluctuations near the wall are investigated for turbulent channel flow at a series of Reynolds numbers based on friction velocity up to Re-tau = 1000. Probability density functions of the wall-shear stress and velocity components are presented as well as joint probability density functions of the velocity components and the pressure. Backflow occurs more often (0.06% at the wall at Re-tau = 1000) and further away (up to y(+) = 8.5) from the wall for increasing Reynolds number. The regions of backflow are circular with an average diameter, based on ensemble averages, of approximately 20 viscous units independent of Reynolds number. A strong oblique vortex outside the viscous sublayer is found to cause this backflow. Extreme wall-normal velocity events occur also more often for increasing Reynolds number. These extreme fluctuations cause high flatness values near the wall (F(v) = 43 at Re-tau = 1000). Positive and negative velocity spikes appear in pairs, located on the two edges of a strong streamwise vortex as documented by Xu et al. [Phys. Fluids 8, 1938 (1996)] for Re-tau = 180. The spikes are elliptical and orientated in streamwise direction with a typical length of 25 and a typical width of 7.5 viscous units at y(+) approximate to 1. The negative spike occurs in a high-speed streak indicating a sweeping motion, while the positive spike is located in between a high and low-speed streak. The joint probability density functions of negative streamwise and extreme wall-normal velocity events show that these events are largely uncorrelated. The majority of both type of events can be found lying underneath a large-scale structure in the outer region with positive sign, which can be understood by considering the more intense velocity fluctuations due to amplitude modulation of the inner layer by the outer layer. Simulations performed at different resolutions give only minor differences. Results from experiments and recent turbulent boundary layer simulations show similar results indicating that these rare events are universal for wall-bounded flows. In order to detect these rare events in experiments, measurement techniques have to be specifically tuned.

In this paper, the effect of subgrid-scale (SGS) modelling, grid resolution and anisotropy of the subgrid-scales on large eddy simulation (LES) is investigated. LES of turbulent channel flow is performed at Re=934, based on friction velocity and channel half width, for a wide range of resolutions. The dynamic Smagorinsky model (DS), the high-pass filtered dynamic Smagorinsky model (HPF) based on the variational multiscale method and the recent explicit algebraic model (EA), which accounts for the anisotropy of the SGS stresses are considered. The first part of the paper is focused on the resolution effects on LES, where the performances of the three SGS models at different resolutions are compared to direct numerical simulation (DNS) results. The results show that LES using eddy viscosity SGS models is very sensitive to resolution. At coarse resolutions, LES with the DS and the HPF models deviate considerably from DNS, whereas LES with the EA model still gives reasonable results. Further analysis shows that the two former models do not accurately predict the SGS dissipation near the wall, while the latter does, even at coarse resolutions. In the second part, the effect of SGS modelling on LES predictions of near-wall and outer-layer turbulent structures is discussed. It is found that different models predict near-wall turbulent structures of different sizes. Analysis of the spectra shows that although near-wall scales are not resolved at coarse resolutions, large-scale motions can be reasonably captured in LES using all the tested models.

Negative streamwise velocities, extreme wall-normal velocites and high flatness values for the wall-normal fluctuations near the wall are investigated for turbulent channel flow simulations at a series of Reynolds numbers up to Reτ = 1000 in this paper. Probability density functions of the wall-shear stress and velocity components are presented, as well as joint probability density functions of the velocity components and the pressure. Backflow occurs more often (0.06% at Reτ = 1000) and further away from the wall into the buffer layer for rising Reynolds number. An oblique vortex outside the viscous sublayer is found to cause this backflow. Extreme v events occur also more often for rising Rey nolds number. Positive and negative velocity spikes appear in pairs, located on the two edges of a strong streamwise vortex: the negative spike occurring in a high speed streak indicating a sweeping motion, while the positive spike is located between a high and low speed streak. These extreme v events cause high flatness values near the wall (F(v) = 43 at Reτ = 1000).

A recent data base from direct numerical simulation of a turbulent boundary layer up to Reθ = 4300 [Schlatter & Örlü, J. Fluid Mech. 659, 2010] has been analysed in an effort to educe the dominant flow structures populating the near-wall region. In particular, the question of whether hairpin vortices are indeed observable as a dominant building block of near-wall turbulence is addressed. It is shown that during the initial phase, dominanted by the specific laminar-turbulent transition induced via the tripping mechanism, hairpin vortices are very numerous, and can certainly be considered as the dominant structure. This is in agreement with previous experiments and low Reynolds number simulations such as Wu & Moin [J. Fluid Mech. 630, 2009]. At sufficient distance from transition, the flow is dominated by a staggered array of quasi-streamwise vortices which is the same situation as in previous channel flows. It turns out that even quantitatively, no major differences between boundary layers and channels can be detected; structures are about 200 viscous units in length, and inclined by about 9 degrees [Jeong et al., J. Fluid Mech. 332, 1997]. The present results clearly show that the regeneration process of turbulence does not involve the generation of (symmetric) hairpin vortices, and that their dominant appearance as instantaneous flow structures in the outer boundary-layer region is at least very unlikely.

Recent efforts in the simulation of turbulent boundary layers using direct and large-eddy simulations are described. The focus is naturally on a series of simulations performed at KTH Stockholm. These results have been used to examine various aspects of the boundary layer; starting from estimates of the extent of the transitional region, the detailed comparison to wind-tunnel experiments, the effect of ambient freestream turbulence on the boundary layer and to quantifications of the spectral composition of the turbulent signal. Furthermore, selected aspects of boundary layers with coupled scalar (e.g. heat) transport are summarised, including profiles of the turbulent Prandtl number.