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A new scaling is derived that yields a Reynolds-number-independent profile for all components of the Reynolds stress in the near-wall region of wall-bounded flows, including channel, pipe and boundary layer flows. The scaling demonstrates the important role played by the wall shear stress fluctuations and how the large eddies determine the Reynolds number dependence of the near-wall turbulence behaviour.

An assessment of the turbulent boundary layer flow structure, which is coherent with the near-wall region, is carried out through a spectral coherence analysis. This spectral method is applied to datasets comprising synchronized two-point streamwise velocity signals at a near-wall reference position and a range of wall-normal positions spanning a Reynolds-number range $Re_{\\unicode[STIX]{x1D70F}}\\sim O(10^{3}){-}O(10^{6})$ . Within each dataset, a self-similar structure is identified from the coherence between the turbulence in the logarithmic region and at the near-wall reference position. This self-similarity is described by a streamwise/wall-normal aspect ratio of $\\unicode[STIX]{x1D706}_{x}/z\\approx 14$ , where $\\unicode[STIX]{x1D706}_{x}$ and $z$ are the streamwise wavelength and wall-normal distance respectively.

Trip-resolved large-eddy simulations of the DARPA SUBOFF are performed to investigate the development of turbulent boundary layers (TBLs) in model-scale studies. The primary consideration of the study is the extent to which the details of tripping affect statistics in large-eddy simulations of complex geometries, which are presently limited to moderate Reynolds number TBLs. Two trip wire configurations are considered, along with a simple numerical trip (wall-normal blowing), which serves as an exemplar of artificial computational tripping methods often used in practice. When the trip wire height exceeds the laminar boundary layer thickness, shedding from the trip wire initiates transition, and the near field is characterized by an elevation of the wall-normal Reynolds stress and a modification of the turbulence anisotropy and mean momentum balance. This trip wire also induces a large jump in the boundary layer thickness, which affects the way in which the TBL responds to the pressure gradients and streamwise curvature of the hull. The trip-induced turbulence decays along the edge of the TBL as a wake component that sits on top of the underlying TBL structure, which dictates the evolution of the momentum and displacement thicknesses. In contrast, for a trip wire height shorter than the laminar boundary layer thickness, transition is initiated at the reattachment point of the trip-induced recirculation bubble, and the artificial trip reasonably replicates the resolved trip wire behaviour relatively shortly downstream of the trip location. For each case, the inner layer collapses rapidly in terms of the mean profile, Reynolds stresses and mean momentum balance, which is followed by the collapse of the Reynolds stresses in coordinates normalized by the local momentum thickness, and finally against the 99 % thickness. By this point, the lasting impact of the trip is the offset in boundary layer thickness due to the trip itself, which becomes a diminishing fraction of the total boundary layer thickness as the TBL grows. The importance of tripping the model appendages is also highlighted due to their lower Reynolds numbers and susceptibility to laminar separations.

A turbulent boundary layer developed over a herringbone patterned riblet surface is investigated using stereoscopic particle image velocimetry in the cross-stream plane at $Re_{\\unicode[STIX]{x1D70F}}\\approx 3900$ . The three velocity components resulting from this experiment reveal a pronounced spanwise periodicity in all single-point velocity statistics. Consistent with previous hot-wire studies over similar-type riblets, we observe a weak time-average secondary flow in the form of $\\unicode[STIX]{x1D6FF}$ -filling streamwise vortices. The observed differences in the surface and secondary flow characteristics, compared to other heterogeneous-roughness studies, may suggest that different mechanisms are responsible for the flow modifications in this case. Observations of instantaneous velocity fields reveal modified and rearranged turbulence structures. The instantaneous snapshots also suggest that the time-average secondary flow may be an artefact arising from superpositions of much stronger instantaneous turbulent events enhanced by the surface texture. In addition, the observed instantaneous secondary motions seem to have promoted a free-stream-engulfing behaviour in the outer layer, which would indicate an increase turbulent/non-turbulent flow mixing. It is overall demonstrated that the presence of large-scale directionality in transitional surface roughness can cause a modification throughout the entire boundary layer, even when the roughness height is 0.5 % of the layer thickness.

Large-scale secondary flows can sometimes appear in turbulent boundary layers formed over rough surfaces, creating low- and high-momentum pathways along the surface (Barros & Christensen, J. Fluid Mech., vol. 748, 2014, R1). We investigate experimentally the dependence of these secondary flows on surface/flow conditions by measuring the flows over streamwise strips of roughness with systematically varied spanwise spacing. We find that the large-scale secondary flows are accentuated when the spacing of the roughness elements is roughly proportional to the boundary layer thickness ${\\it\\delta}$ , and do not appear for cases with finer spacing. Cases with coarser spacing also generate ${\\it\\delta}$ -scale secondary flows with tertiary flows in the spaces in between. These results show that the ratio of the spanwise length scale of roughness heterogeneity to the boundary layer thickness is a critical parameter for the occurrence of these secondary motions in turbulent boundary layers over rough walls.

A model-based description of the scaling and radial location of turbulent fluctuations in turbulent pipe flow is presented and used to illuminate the scaling behaviour of the very large scale motions. The model is derived by treating the nonlinearity in the perturbation equation (involving the Reynolds stress) as an unknown forcing, yielding a linear relationship between the velocity field response and this nonlinearity. We do not assume small perturbations. We examine propagating helical velocity response modes that are harmonic in the wall-parallel directions and in time, permitting comparison of our results to experimental data. The steady component of the velocity field that varies only in the wall-normal direction is identified as the turbulent mean profile. A singular value decomposition of the resolvent identifies the forcing shape that will lead to the largest velocity response at a given wavenumber–frequency combination. The hypothesis that these forcing shapes lead to response modes that will be dominant in turbulent pipe flow is tested by using physical arguments to constrain the range of wavenumbers and frequencies to those actually observed in experiments. An investigation of the most amplified velocity response at a given wavenumber–frequency combination reveals critical-layer-like behaviour reminiscent of the neutrally stable solutions of the Orr–Sommerfeld equation in linearly unstable flow. Two distinct regions in the flow where the influence of viscosity becomes important can be identified, namely wall layers that scale with R+1/2 and critical layers where the propagation velocity is equal to the local mean velocity, one of which scales with R+2/3 in pipe flow. This framework appears to be consistent with several scaling results in wall turbulence and reveals a mechanism by which the effects of viscosity can extend well beyond the immediate vicinity of the wall. The model reproduces inner scaling of the small scales near the wall and an approach to outer scaling in the flow interior. We use our analysis to make a first prediction that the appropriate scaling velocity for the very large scale motions is the centreline velocity, and show that this is in agreement with experimental results. Lastly, we interpret the wall modes as the motion required to meet the wall boundary condition, identifying the interaction between the critical and wall modes as a potential origin for an interaction between the large and small scales that has been observed in recent literature as an amplitude modulation of the near-wall turbulence by the very large scales.

Over the last 50 years the large-eddy simulation (LES) technique has developed into one of the most prominent numerical tools used to study transport processes in the atmospheric boundary layer (ABL). This review examines development of the technique as a tool for ABL research, integration with state-of-the-art scientific computing resources, and some key application areas. Analysis of the published literature indicates that LES research across a broad range of applications accelerated starting around 1990. From that point in time, robust research using LES developed in several different application areas and based on a review of the papers published in this journal, we identify seven major areas of intensive ABL–LES research: convective boundary layers, stable boundary layers, transitional boundary layers, plant canopy flows, urban meteorology and dispersion, surface heterogeneity, and the testing and development of subgrid-scale (SGS) models. We begin with a general overview of LES and then proceed to examine the SGS models developed for use in ABL–LES. After this overview of the technique itself, we review the specific model developments tailored to the identified application areas and the scientific advancements realized using the LES technique in each area. We conclude by examining the computational trends in published ABL–LES research and identify some resource underutilization. Future directions and research needs are identified from a synthesis of the reviewed literature.

Using super-large-scale particle image velocimetry (SLPIV), we investigate the spatial structure of the near-wall region in the fully rough atmospheric surface layer with Reynolds number $Re_{\\unicode[STIX]{x1D70F}}\\sim O(10^{6})$ . The field site consists of relatively flat, snow-covered farmland, allowing for the development of a fully rough turbulent boundary layer under near-neutral thermal stability conditions. The imaging field of view extends from 3 m to 19 m above the ground and captures the top of the roughness sublayer and the bottom of an extensive logarithmic region. The SLPIV technique uses natural snowfall as seeding particles for the flow imaging. We demonstrate that SLPIV provides reliable measurements of first- and second-order velocity statistics in the streamwise and wall-normal directions. Our results in the logarithmic region show that the structural features identified in laboratory studies are similarly present in the atmosphere. Using instantaneous vector fields and two-point correlation analysis, we identify vortex structures sharing the signature of hairpin vortex packets. We also evaluate the zonal structure of the boundary layer by tracking uniform momentum zones (UMZs) and the shear interfaces between UMZs in space and time. Statistics of the UMZs and shear interfaces reveal the role of the zonal structure in determining the mean and variance profiles. The velocity difference across the shear interfaces scales with the friction velocity, in agreement with previous studies, and the size of the UMZs scales with wall-normal distance, in agreement with the attached eddy framework.

We study the dynamics of turbulent boundary layer flow over a heterogeneous topography composed of roughness patches exhibiting relatively high and low correlation in the streamwise and spanwise directions, respectively (i.e. the roughness appears as streamwise-aligned ‘strips’). It has been reported that such roughness induces a spanwise-wall normal mean secondary flow in the form of mean streamwise vorticity associated with counter-rotating boundary-layer-scale circulations. Here, we demonstrate that this mean secondary flow is Prandtl’s secondary flow of the second kind, both driven and sustained by spatial gradients in the Reynolds-stress components, which cause a subsequent imbalance between production and dissipation of turbulent kinetic energy that necessitates secondary advective velocities. In reaching this conclusion, we study (i) secondary circulations due to spatial gradients of turbulent kinetic energy, and (ii) the production budgets of mean streamwise vorticity by gradients of the Reynolds stresses. We attribute the secondary flow phenomena to extreme peaks of surface stress on the relatively high-roughness regions and associated elevated turbulence production in the fluid immediately above. An optimized state is attained by entrainment of fluid exhibiting the lowest turbulent stresses – from above – and subsequent lateral ejection in order to preserve conservation of mass.

We employ global input–output analysis to quantify amplification of exogenous disturbances in compressible boundary layer flows. Using the spatial structure of the dominant response to time-periodic inputs, we explain the origin of steady reattachment streaks in a hypersonic flow over a compression ramp. Our analysis of the laminar shock–boundary layer interaction reveals that the streaks arise from a preferential amplification of upstream counter-rotating vortical perturbations with a specific spanwise wavelength. These streaks are associated with heat-flux striations at the wall near flow reattachment and they can trigger transition to turbulence. The streak wavelength predicted by our analysis compares favourably with observations from two different hypersonic compression ramp experiments. Furthermore, our analysis of inviscid transport equations demonstrates that base-flow deceleration contributes to the amplification of streamwise velocity and that the baroclinic effects are responsible for the production of streamwise vorticity. Finally, the appearance of the temperature streaks near reattachment is triggered by the growth of streamwise velocity and streamwise vorticity perturbations as well as by the amplification of upstream temperature perturbations by the reattachment shock.