Townsend (J. Fluid Mech., vol. 11, issue 1, 1961, pp. 97–120) introduced the concept of active and inactive motions for wall-bounded turbulent flows, where the active motions are solely responsible for producing the Reynolds shear stress, the key momentum transport term in these flows. While the wall-normal component of velocity is associated exclusively with the active motions, the wall-parallel components of velocity are associated with both active and inactive motions. In this paper, we propose a method to segregate the active and inactive components of the two-dimensional (2-D) energy spectrum of the streamwise velocity, thereby allowing us to test the self-similarity characteristics of the former which are central to theoretical models for wall turbulence. The approach is based on analysing datasets comprising two-point streamwise velocity signals coupled with a spectral linear stochastic estimation based procedure. The data considered span a friction Reynolds number range $Re_{\tau }\sim {{O}}$($10^3$) – ${{O}}$($10^4$). The procedure linearly decomposes the full 2-D spectrum (${\varPhi }$) into two components, ${\varPhi }_{ia}$ and ${\varPhi }_{a}$, comprising contributions predominantly from the inactive and active motions, respectively. This is confirmed by ${\varPhi }_{a}$ exhibiting wall scaling, for both streamwise and spanwise wavelengths, corresponding well with the Reynolds shear stress cospectra reported in the literature. Both ${\varPhi }_{a}$ and ${\varPhi }_{ia}$ are found to depict prominent self-similar characteristics in the inertially dominated region close to the wall, suggestive of contributions from Townsend's attached eddies. Inactive contributions from the attached eddies reveal pure $k^{-1}$-scaling for the associated one-dimensional spectra (where $k$ is the streamwise/spanwise wavenumber), lending empirical support to the attached eddy model of Perry & Chong (J. Fluid Mech., vol. 119, 1982, pp. 173–217).

A surface roughness from a recently cleaned and painted ship's hull was scanned, scaled and replicated for laboratory testing to systematically investigate the influence of the ratio of in-plane roughness wavelength, $\lambda$, with respect to the boundary layer thickness $\delta$. The experiments were performed by geometrically scaling the surface which maintains a constant effective slope $ES_x$ and solidity $\varLambda$, while the ratio of $\lambda /\delta$ is varied. Here we scale the scanned roughness topography by a factor of 2.5 and 15, and measure the mean velocity profiles in the turbulent boundary layers developing over these surfaces at a range of free stream velocities and streamwise measurement locations. The results show that the $2.5\times$ scaled roughness, which has $\lambda /\delta \ll 1$, behaves in the expected $k$-type manner, with a roughness function ${\rm \Delta} U^+$ that is proportional to the viscous-scaled roughness height. The $15\times$ surface, however, which has $\lambda /\delta \approx 1$, exhibits very different non-$k$-type behaviour. This larger surface does not approach the fully rough asymptote and also exhibits a drag penalty that is comparable to the $2.5\times$ case despite the sixfold increase in the roughness height. Measurements on a spanwise–wall-normal plane reveal that the $15\times$ surface has introduced a large-scale spanwise variation in mean streamwise velocity (dispersive stresses) that extend far beyond the logarithmic region. Together this evidence suggests that a demarcation between $k$-type and non-$k$-type behaviour can occur in situations where the in-plane roughness wavelength approaches the boundary layer thickness. This finding has important implications to how we scale small-scale roughness from high Reynolds number (Re) large-scale applications for testing in low Re small-scale laboratory facilities or simulations.

The turbulent boundary layer developing under a turbulence-laden free stream is numerically investigated using the temporal boundary layer framework. This study focuses on the interaction between the fully turbulent boundary layer and decaying free-stream turbulence. Previous experiments and simulations of this physical problem have considered a spatially evolving boundary layer beset by free-stream turbulence. The state of the boundary layer at any given downstream position in fact reflects the accumulated history of the co-evolution of boundary layer and free-stream turbulence. The central aim of the present work is to isolate the effect of local free-stream disturbances existing at the same time as the ‘downstream’ boundary layer. The temporal framework used here helps expose when and how disturbances directly above the boundary layer actively impart change upon it. The bulk of our simulations were completed by seeding the free stream above boundary layers that were ‘pre-grown’ to a desired thickness with homogeneous isotropic turbulence from a precursor simulation. Moreover, this strategy allowed us to test various combinations of the turbulence intensity and large-eddy length scale of the free-stream turbulence with respect to the corresponding scales of the boundary layer. The relative large-eddy turnover time scale between the free-stream turbulence and the boundary layer emerges as an important parameter in predicting if the free-stream turbulence and boundary layer interaction will be ‘strong’ or ‘weak’ before the free-stream turbulence eventually fades to a negligible level. If the large-eddy turnover time scale of the free-stream turbulence is much smaller than that of the boundary layer, the interaction will be ‘weak’, as the free-stream disturbances will markedly decay before the boundary layer is able be altered significantly as a result of the free-stream disturbances. For a ‘strong’ interaction, the injected free-stream turbulence causes increased spreading of the boundary layer away from the wall, permitting large incursions of free-stream fluid deep within it.

Pulsatile rough-wall turbulent pipe flow is compared against its non-pulsatile counterpart using data obtained from direct numerical simulation. Results are presented at a mean friction Reynolds number of 540 for a set of three geometrically scaled roughness topographies at a single forcing condition, which, based on existing classifications, falls into the current-dominated very-high-frequency regime. By comparing the pulsatile data against an equivalent non-pulsatile dataset (Chan et al., J. Fluid Mech., vol. 854, 2018, pp. 5–33), the key differences (and similarities) between the forced and unforced configurations are identified. A major finding of this study is that the flow in the outer region retains its self-similar functional form under pulsatile rough-wall conditions, and, as a result, Townsend’s outer-layer similarity hypothesis holds for the roughness-forcing combinations considered here. On the other hand, the unsteady cases exhibit a rich array of flow physics in the region beneath the roughness crests not observed in the steady case. These differences are examined using a Moody chart, which encapsulates how the hydraulic properties of pulsatile rough-wall pipe flow differ from their non-pulsatile counterpart.

In this paper, we present the two-dimensional (2-D) energy cross-spectrum of the streamwise velocity ($u$) component and use it to test the notion of self-similarity in turbulent boundary layers. The primary focus is on the cross-spectrum ($\unicode[STIX]{x1D6F7}_{cross}^{w}$) measured across the logarithmic ($z_{o}$) and near-wall ($z_{r}$) wall-normal locations, providing the energy distribution across the range of streamwise ($\unicode[STIX]{x1D706}_{x}$) and spanwise ($\unicode[STIX]{x1D706}_{y}$) wavelengths (or length scales) that are coherent across the wall-normal distance. $\unicode[STIX]{x1D6F7}_{cross}^{w}$ may thus be interpreted as a wall-filtered subset of the full 2-D $u$-spectrum ($\unicode[STIX]{x1D6F7}$), the latter providing information on all coexisting eddies at $z_{o}$. To this end, datasets comprising synchronized two-point $u$-signals at $z_{o}$ and $z_{r}$, across the friction Reynolds number range $Re_{\unicode[STIX]{x1D70F}}\sim O(10^{3}){-}O(10^{4})$, are analysed. The published direct numerical simulation (DNS) dataset of Sillero et al. (Phys. Fluids, vol. 26 (10), 2014, 105109) is considered for low-$Re_{\unicode[STIX]{x1D70F}}$ analysis, while the high-$Re_{\unicode[STIX]{x1D70F}}$ dataset is obtained by conducting synchronous multipoint hot-wire measurements. High-$Re_{\unicode[STIX]{x1D70F}}$ cross-spectra reveal that the wall-attached large scales follow a $\unicode[STIX]{x1D706}_{y}/z_{o}\sim \unicode[STIX]{x1D706}_{x}/z_{o}$ relationship more closely than seen for $\unicode[STIX]{x1D6F7}$, where this self-similar trend is obscured by coexisting scales. The present analysis reaffirms that a self-similar structure, conforming to Townsend’s attached eddy hypothesis, is ingrained in the flow.

A statistical description of flow regions with negative streamwise velocity is provided based on simulations of turbulent plane channels in the Reynolds number range $547\leqslant Re_{\unicode[STIX]{x1D70F}}\leqslant 2003$. It is found that regions of backflow are attached and their density per surface area – in wall units – is an increasing function of $Re_{\unicode[STIX]{x1D70F}}$. Their size distribution along the three coordinates reveals that, even though in the mean they appear to be circular in the wall-parallel plane, they tend to become more elongated in the spanwise direction after reaching a certain height. Time-tracking of backflow regions in a $Re_{\unicode[STIX]{x1D70F}}=934$ simulation showed they convect downstream at the mean velocity corresponding to $y^{+}\approx 12$, they seldom interact with other backflow events, their statistical signature extends in the streamwise direction for at least $300$ wall units, and they result from a complex interaction between regions of high and low spanwise vorticity far beyond the viscous sublayer. This could explain why some statistical aspects of these near-wall events do not scale in viscous units; they are dependent on the $Re_{\unicode[STIX]{x1D70F}}$-dependent dynamics further away from the wall.

The streamwise inclination angle of large wall-attached structures, in the log region of a canonical turbulent boundary layer, is estimated via spectral coherence analysis, and is found to be approximately $45^{\circ }$. This is consistent with assumptions used in prior attached eddy model-based simulations. Given that the inclination angle obtained via standard two-point correlations is influenced by the range of scales in the turbulent flow (Marusic, Phys. Fluids, vol. 13 (3), 2001, pp. 735–743), the present result is obtained by isolating the large wall-attached structures from the rest of the turbulence. This is achieved by introducing a spanwise offset between two hot-wire probes, synchronously measuring the streamwise velocity at a near-wall and log-region reference location, to assess the wall coherence. The methodology is shown to be effective by applying it to data sets across Reynolds numbers, $Re_{\unicode[STIX]{x1D70F}}\sim O(10^{3})$–$O(10^{6})$.

Streamwise velocity and wall-shear stress are acquired simultaneously with a hot-wire and an array of azimuthal/spanwise-spaced skin friction sensors in large-scale pipe and boundary layer flow facilities at high Reynolds numbers. These allow for a correlation analysis on a per-scale basis between the velocity and reference skin friction signals to reveal which velocity-based turbulent motions are stochastically coherent with turbulent skin friction. In the logarithmic region, the wall-attached structures in both the pipe and boundary layers show evidence of self-similarity, and the range of scales over which the self-similarity is observed decreases with an increasing azimuthal/spanwise offset between the velocity and the reference skin friction signals. The present empirical observations support the existence of a self-similar range of wall-attached turbulence, which in turn are used to extend the model of Baars et al. (J. Fluid Mech., vol. 823, p. R2) to include the azimuthal/spanwise trends. Furthermore, the region where the self-similarity is observed correspond with the wall height where the mean momentum equation formally admits a self-similar invariant form, and simultaneously where the mean and variance profiles of the streamwise velocity exhibit logarithmic dependence. The experimental observations suggest that the self-similar wall-attached structures follow an aspect ratio of $7:1:1$ in the streamwise, spanwise and wall-normal directions, respectively.

Streamwise velocity profiles and their wall-normal derivatives were used to investigate the properties of turbulent channel flow in the low polymer drag reduction $(DR)$ regime ($DR=6.5\,\%$ to $26\,\%$), as realized via polymer injection at the channel surface. Streamwise velocity data were obtained over a friction Reynolds number ranging from $650$ to $1800$ using the single-velocity-component version of molecular tagging velocimetry (1c-MTV). This adaptation of the MTV technique has the ability to accurately capture instantaneous profiles at very high spatial resolution (${\gtrsim}850$ data points per wall-normal profile), and thus generate well-resolved derivative information as well. Owing to this ability, the present study is able to build upon and extend the recent numerical simulation analysis of White et al. (J. Fluid Mech., vol. 834, 2018, pp. 409–433) that examined the mean dynamical structure of polymer drag-reduced channel flow at friction Reynolds numbers up to $1000$. Consistently, the present mean velocity profiles indicate that the extent of the logarithmic region diminishes with increasing polymer concentration, while statistically significant increases in the logarithmic profile slope begin to occur for drag reductions less than $15\,\%$. Profiles of the r.m.s. streamwise velocity indicate that the maximum moves farther from the wall and increases in magnitude with reductions in drag. Similarly, with increasing drag reduction, the profile of the combined Reynolds and polymer shear stress exhibits a decrease in its maximum value that also moves farther from the wall. Correlations are presented that estimate the location and value of the maximum r.m.s. streamwise velocity and combined Reynolds and polymer shear stress. Over the range of $DR$ investigated, these effects consistently exhibit approximately linear trends as a function of $DR$. The present measurements allow reconstruction of the mean momentum balance (MMB) for channel flow, which provides further insights regarding the physics described in the study by White et al. In particular, the present findings support a physical scenario in which the self-similar properties on the inertial domain identified from the leading-order structure of the MMB begin to detectably and continuously vary for drag reductions less than $10\,\%$.

Wall-bounded turbulence, where it occurs in engineering or nature, is commonly subjected to spatial variations in wall shear stress. A prime example is spatially varying roughness. Here, we investigate the configuration where the wall shear stress varies only in the lateral direction. The investigation is idealised in order to focus on one aspect, namely, the similarity and structure of turbulent inertial motion over an imposed scale of stress variation. To this end, we analyse data from direct numerical simulation (DNS) of pressure-driven turbulent flow through a channel bounded by walls of laterally alternating patches of high and low wall shear stress. The wall shear stress is imposed as a Neumann boundary condition such that the wall shear stress ratio is fixed at 3 while the lateral spacing $s$ of the uniform-stress patches is varied from 0.39 to 6.28 of the half-channel height $\unicode[STIX]{x1D6FF}$. We find that global outer-layer similarity is maintained when $s$ is less than approximately $0.39\unicode[STIX]{x1D6FF}$ while local outer-layer similarity is recovered when $s$ is greater than approximately $6.28\unicode[STIX]{x1D6FF}$. However, the transition between the two regimes through $s\approx \unicode[STIX]{x1D6FF}$ is not monotonic owing to the presence of secondary roll motions that extend across the whole cross-section of the flow. Importantly, these secondary roll motions are associated with an amplified skin-friction coefficient relative to both the small- and large-$s/\unicode[STIX]{x1D6FF}$ limits. It is found that the relationship between the secondary roll motions and the mean isovels is reversed through this transition from low longitudinal velocity over low stress at small $s/\unicode[STIX]{x1D6FF}$ to high longitudinal velocity over low stress at large $s/\unicode[STIX]{x1D6FF}$.

A dynamical systems approach is used to devise a linear estimation tool for channel flow at a friction Reynolds number of $Re_{\unicode[STIX]{x1D70F}}=1000$. The estimator uses time-resolved velocity measurements at a single wall-normal location to estimate the velocity field at other wall-normal locations (the data coming from direct numerical simulations). The estimation tool builds on the work of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) by using a Navier–Stokes-based linear model and treating any nonlinear terms as unknown forcings to an otherwise linear system. In this way nonlinearities are not ignored, but instead treated as an unknown model input. It is shown that, while the linear estimator qualitatively reproduces large-scale flow features, it tends to overpredict the amplitude of velocity fluctuations – particularly for structures that are long in the streamwise direction and thin in the spanwise direction. An alternative linear model is therefore formed in which a simple eddy viscosity is used to model the influence of the small-scale turbulent fluctuations on the large scales of interest. This modification improves the estimator performance significantly. Importantly, as well as improving the performance of the estimator, the linear model with eddy viscosity is also able to predict with reasonable accuracy the range of wavenumber pairs and the range of wall-normal heights over which the estimator will perform well.

Here, we report the measurements of two-dimensional (2-D) spectra of the streamwise velocity ($u$) in a high-Reynolds-number turbulent boundary layer. A novel experiment employing multiple hot-wire probes was carried out at friction Reynolds numbers ranging from 2400 to 26 000. Taylor’s frozen turbulence hypothesis is used to convert temporal-spanwise information into a 2-D spatial spectrum which shows the contribution of streamwise ($\unicode[STIX]{x1D706}_{x}$) and spanwise ($\unicode[STIX]{x1D706}_{y}$) length scales to the streamwise variance at a given wall height ($z$). At low Reynolds numbers, the shape of the 2-D spectra at a constant energy level shows $\unicode[STIX]{x1D706}_{y}/z\sim (\unicode[STIX]{x1D706}_{x}/z)^{1/2}$ behaviour at larger scales, which is in agreement with the existing literature at a matched Reynolds number obtained from direct numerical simulations. However, at high Reynolds numbers, it is observed that the square-root relationship tends towards a linear relationship ($\unicode[STIX]{x1D706}_{y}\sim \unicode[STIX]{x1D706}_{x}$), as required for self-similarity and predicted by the attached eddy hypothesis.

Physical dormancy of Robinia pseudoacacia seeds makes it a challenge for scientists and forest managers to obtain a homogeneous germination for larger seed samples. Water imbibition of the seeds can be achieved through manual piercing of the seed coat, but this method remains time consuming and heterogeneous. We tested several ecologically friendly methods to break seed dormancy, including manual pin puncture, water soaking, oven dry-heating (two temperatures) and sanding. Sanding was performed using an automatic grinder to control shaking duration (three durations) and get a homogeneous scraping of the coat. All methods, except dry-heating, resulted in successful dormancy breaking; water soaking was the least efficient method, attaining 57% germination. Sanding proved to be as efficient as puncturing (97%) but long duration sanding (10 or 15 min) could damage cotyledons, which would impede further development of the plant. Short-time sanding (5 min) proved to be the best method to reach high total germination and healthy (undamaged cotyledon) seedlings, and was successfully applied to 500 seeds. The reference puncture method and the automatic sanding were also tested on seeds of nine Fabaceae species and proved to be efficient for some species. Automated sanding can thus be used as a standard to break physical dormancy of black locust or other Fabaceae seeds to allow further comparative studies of plant populations or genotypes.

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.

Vegetative filter strips (VFS) potentially reduce herbicide transport from agricultural fields by increasing herbicide mass infiltrated (Minf) and herbicide mass adsorbed (Mas) compared with bare field soil. However, there are conflicting reports in the literature concerning the contribution of Mas to herbicide trapping efficiency (TE). Moreover, no study has evaluated TE among metolachlor and metolachlor metabolites in a VFS. This experiment was conducted to compare TE, Minf, and Mas among metolachlor, metolachlor oxanilic acid (OA), and metolachlor ethanesulfonic acid (ESA) in buffalograss filter strips. Runoff was applied as a point source upslope of a 1- × 3-m microwatershed at a rate of 750 L h−1. The point source was fortified with metolachlor, metolachlor OA, and metolachlor ESA, each at 0.12 μg ml−1. After moving through the plot, water samples were collected at 5-min intervals and stored at 5 C until analysis. Water samples were extracted using solid-phase extraction and analyzed by high-performance liquid chromatography–photodiode array detection. TE was significantly greater for metolachlor (25.3%) as compared with the OA (15.5%) and ESA metabolites (14.2%). The average Minf was 8.5% and was not significantly different among compounds. Significantly more metolachlor (17.3%) was retained as Mas compared with either metolachlor OA (7.0%) or metolachlor ESA (5.5%). Moreover, Mas accounted for 68 and 42% of the total TE for metolachlor and metolachlor metabolites, respectively. These results demonstrate that adsorption to the VFS grass, grass thatch, or soil surface (or all) is an important retention mechanism for metolachlor and metolachlor metabolites, especially under saturated conditions. Moreover, the Mas data indicate that metolachlor is preferentially retained by the VFS grass, grass thatch, or soil surface (or all) compared with the OA and ESA metabolites. Greater metolachlor retention in VFS compared with the OA and ESA metabolites may partially explain why metolachlor metabolites are frequently measured at higher concentrations than metolachlor is in surface water.

We perform a direct numerical simulation (DNS) investigation of the incompressible temporally developing turbulent boundary layer. The approach is inspired by temporal simulations of flows which are generally thought of as developing in space, such as wakes and mixing layers. Compressible boundary layers have previously been studied in this manner yet the temporal approach appears to be under-exploited in the literature concerning incompressible boundary layers. The flow is the turbulent counterpart to the laminar Rayleigh problem or Stokes’ first problem, in which a fluid at rest is set into motion by a wall moving at constant velocity. An initial profile that models the effect of a wall-mounted trip wire is implemented and allows the characterisation of initial conditions by a trip Reynolds number. For the current set-up, a trip Reynolds number of 500 based on the trip-wire diameter successfully triggers transition yet only mildly perturbs the flow so it assumes a natural development at the lowest possible Reynolds number based on momentum thickness. A systematic trip study reveals that as the ratio of momentum thickness to trip-wire diameter approaches unity, our flow approaches a state free from the effects of its starting trip Reynolds number. The transport of a passive scalar by this flow is also simulated. The role played by domain size is investigated with two boxes, sized to accommodate two chosen final Reynolds numbers. Comparisons of the skin friction coefficient, velocity and scalar statistics demonstrate that the temporally developing boundary layer is a good model for the spatially developing boundary layer once initial conditions can be neglected. Analysis of similarity solutions suggests such a rapprochement of the spatial and temporal boundary layers may be expected at high Reynolds numbers given that the only terms that asymptotically persist are those common to both cases. If one seeks statistics for the turbulent boundary layer, the temporal boundary layer is therefore a viable method if modest convergence is sufficient. We suggest that such a temporal set-up could prove useful in the study of turbulence dynamics.

In the analysis of velocity fields in turbulent boundary layers, the traditional Reynolds decomposition is universally employed to calculate the fluctuating component of streamwise velocity. Here, we demonstrate the perils of such a determination of the fluctuating velocity in the context of structural analysis of turbulence when applied in the outer region where the flow is intermittently turbulent at a given wall distance. A new decomposition is postulated that ensures non-turbulent regions in the flow do not contaminate the fluctuating velocity components in the turbulent regions. Through this new decomposition, some of the typical statistics concerning the scale and structure of turbulent boundary layers are revisited.

The identification of uniform momentum zones in wall-turbulence, introduced by Adrian, Meinhart & Tomkins (J. Fluid Mech., vol. 422, 2000, pp. 1–54) has been applied to turbulent channel flow, revealing a large ‘core’ region having high and uniform velocity magnitude. Examination of the core reveals that it is a region of relatively weak turbulence levels. For channel flow in the range $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}Re_{\tau } = 1000\text {--}4000$, it was found that the ‘core’ is identifiable by regions bounded by the continuous isocontour lines of the streamwise velocity at $0.95U_{CL}$ (95 % of the centreline velocity). A detailed investigation into the properties of the core has revealed it has a large-scale oscillation which is predominantly anti-symmetric with respect to the channel centreline as it moves through the channel, and there is a distinct jump in turbulence statistics as the core boundary is crossed. It is concluded that the edge of the core demarcates a shear layer of relatively intense vorticity such that the interior of the core contains weakly varying, very low-level turbulence (relative to the flow closer to the wall). Although channel flows are generally referred to as ‘fully turbulent’, these findings suggest there exists a relatively large and ‘quiescent’ core region with a boundary qualitatively similar to the turbulent/non-turbulent interface of boundary layers, jets and wakes.

Direct numerical simulations of turbulent channel flow at the matched friction Reynolds number of 590, comparing the effect of no-slip versus shear-stress boundary conditions, reveal that the outer flow of wall turbulence, in accord with Townsend’s outer-layer similarity hypothesis, remains largely independent of the viscous sublayer. First- and second-order statistics, including spectra, agree closely from the buffer region out to the centre of the channel. Higher-order statistics also appear to obey the hypothesised similarity, although the influence of boundary conditions is more pronounced than in the lower-order statistics. The statistical agreement in the outer layer, in spite of the structural differences in the viscous sublayer, support Townsend’s idea that the primary effect of the wall is not the no-slip condition, but the impermeability condition imposed by a solid wall.