Considerable discussion over the past few years has been devoted to the question of whether the logarithmic region in wall turbulence is indeed universal. Here, we analyse recent experimental data in the Reynolds number range of nominally $2\times 1{0}^{4} \lt {\mathit{Re}}_{\tau } \lt 6\times 1{0}^{5} $ for boundary layers, pipe flow and the atmospheric surface layer, and show that, within experimental uncertainty, the data support the existence of a universal logarithmic region. The results support the theory of Townsend (The Structure of Turbulent Shear Flow, Vol. 2, 1976) where, in the interior part of the inertial region, both the mean velocities and streamwise turbulence intensities follow logarithmic functions of distance from the wall.

In recent years there has been significant progress made towards understanding the large-scale structure of wall-bounded shear flows. Most of this work has been conducted with turbulent boundary layers, leaving scope for further work in pipes and channels. In this article the structure of fully developed turbulent pipe and channel flow has been studied using custom-made arrays of hot-wire probes. Results reveal long meandering structures of length up to 25 pipe radii or channel half-heights. These appear to be qualitatively similar to those reported in the log region of a turbulent boundary layer. However, for the channel case, large-scale coherence persists further from the wall than in boundary layers. This is expected since these large-scale features are a property of the logarithmic region of the mean velocity profile in boundary layers and it is well-known that the mean velocity in a channel remains very close to the log law much further from the wall. Further comparison of the three turbulent flows shows that the characteristic structure width in the logarithmic region of a boundary layer is at least 1.6 times smaller than that in a pipe or channel.

The extent or existence of similarities between fully developed turbulent pipes and channels, and in zero-pressure-gradient turbulent boundary layers has come into question in recent years. This is in contrast to the traditionally accepted view that, upon appropriate normalization, all three flows can be regarded as the same in the near-wall region. In this paper, the authors aim to provide clarification of this issue through streamwise velocity measurements in these three flows with carefully matched Reynolds number and measurement resolution. Results show that mean statistics in the near-wall region collapse well. However, the premultiplied energy spectra of streamwise velocity fluctuations show marked structural differences that cannot be explained by scaling arguments. It is concluded that, while similarities exist at these Reynolds numbers, one should exercise caution when drawing comparisons between the three shear flows, even near the wall.

A collaborative experimental effort employing the minimally perturbed atmospheric surface-layer flow over the salt playa of western Utah has enabled us to map coherence in turbulent boundary layers at very high Reynolds numbers, Re τ ∼ O(10 6 ). It is found that the large-scale coherence noted in the logarithmic region of laboratory-scale boundary layers are also present in the very high Reynolds number atmospheric surface layer (ASL). In the ASL these features tend to scale on outer variables (approaching the kilometre scale in the streamwise direction for the present study). The mean statistics and two-point correlation map show that the surface layer under neutrally buoyant conditions behaves similarly to the canonical boundary layer. Linear stochastic estimation of the three-dimensional correlation map indicates that the low momentum fluid in the streamwise direction is accompanied by counter-rotating roll modes across the span of the flow. Instantaneous flow fields confirm the inferences made from the linear stochastic estimations. It is further shown that vortical structures aligned in the streamwise direction are present in the surface layer, and bear attributes that resemble the hairpin vortex features found in laboratory flows. Ramp-like high shear zones that contribute significantly to the Reynolds shear-stress are also present in the ASL in a form nearly identical to that found in laboratory flows. Overall, the present findings serve to draw useful connections between the vast number of observations made in the laboratory and in the atmosphere.

Modeling wall turbulence remains a major challenge, as a sufficient physical understanding of these flows is still lacking. In an effort to move toward a physics-based model, A.A. Townsend introduced the hypothesis that the dominant energy-containing motions in wall turbulence are due to large eddies attached to the wall. From this simple hypothesis, the attached eddy model evolved, which has proven to be highly effective in predicting velocity statistics and providing a framework for interpreting the energy-containing flow physics at high Reynolds numbers. This review summarizes the hypothesis itself and the modeling attempts made thereafter, with a focus on the validity of the model's assumptions and its limitations. Here, we review studies on this topic, which have markedly increased in recent years, highlighting refinements, extensions, and promising future directions for attached eddy modeling.

Compact metal probes: A solution for atomic force microscopy based tip-enhanced Raman spectroscopy Rev. Sci. Instrum. 83, 123708 (2012) Note: Radiofrequency scanning probe microscopy using vertically oriented cantilevers Rev. Sci. Instrum. 83, 126103 (2012) Switching spectroscopic measurement of surface potentials on ferroelectric surfaces via an open-loop Kelvin probe force microscopy method Appl. Phys. Lett. 101, 242906 (2012) Enhanced quality factors and force sensitivity by attaching magnetic beads to cantilevers for atomic force microscopy in liquid J. Appl. Phys. 112, 114324 (2012) Invited Review Article: High-speed flexure-guided nanopositioning: Mechanical design and control issues Rev. Sci. Instrum. 83, 121101 (2012) Additional information on Rev. Sci. Instrum. The spring constant of an atomic force microscope cantilever is often needed for quantitative measurements. The calibration method of Sader et al. [Rev. Sci. Instrum. 70, 3967 (1999)] for a rectangular cantilever requires measurement of the resonant frequency and quality factor in fluid (typically air), and knowledge of its plan view dimensions. This intrinsically uses the hydrodynamic function for a cantilever of rectangular plan view geometry. Here, we present hydrodynamic functions for a series of irregular and non-rectangular atomic force microscope cantilevers that are commonly used in practice. Cantilever geometries of arrow shape, small aspect ratio rectangular, quasi-rectangular, irregular rectangular, non-ideal trapezoidal cross sections, and V-shape are all studied. This enables the spring constants of all these cantilevers to be accurately and routinely determined through measurement of their resonant frequency and quality factor in fluid (such as air). An approximate formulation of the hydrodynamic function for microcantilevers of arbitrary geometry is also proposed. Implementation of the method and its performance in the presence of uncertainties and non-idealities is discussed, together with conversion factors for the static and dynamic spring constants of these cantilevers. These results are expected to be of particular value to the design and application of micro-and nanomechanical systems in general.

In this study we examine the impact of the strength of the large-scale motions on the amplitude and frequency of the small scales in high-Reynolds-number turbulent boundary layers. Time series of hot-wire data are decomposed into large- and small-scale components, and the impact of the large scale on the amplitude and frequency of the small scales is considered. The amplitude modulation effect is examined by conditionally averaging the small-scale intensity (${ u}_{S}^{2} $) for various values of the large-scale fluctuation (${u}_{L} $). It is shown that ${ u}_{S}^{2} $ increases with increasing value of ${u}_{L} $ in the near-wall region, whereas, farther away from the wall, ${ u}_{S}^{2} $ decreases with increasing ${u}_{L} $. The rate of increase in small-scale intensity with the strength of the large-scale signal is neither symmetric (about ${u}_{L} = 0$) nor linear. The extent of the frequency modulation is examined by counting the number of occurrences of local maxima or minima in the small-scale signal. It is shown that the frequency modulation effect is confined to the near-wall region and its extent diminishes rapidly beyond ${y}^{+ } = 100$. A phase lag between the large- and small-scale fluctuations, in terms of amplitude modulation, has also been identified, which is in agreement with previous studies. The phase lag between large- and small-scale fluctuations for frequency modulation is comparable to that of amplitude modulation in the near-wall region. The combined effect of both amplitude and frequency modulation is also examined by computing conditional spectra of the small-scale signal conditioned on the large scales. In the near-wall region, the results indicate that the peak value of pre-multiplied spectra increases with increasing value of ${u}_{L} $, indicating amplitude modulation, while the frequency at which this peak occurs also increases with increasing value of ${u}_{L} $, revealing frequency modulation. The overall trends observed from the conditional spectra are consistent with the results obtained through statistical analyses. Finally, a physical mechanism that can capture most of the above observations is also presented.

An array of surface hot-film shear-stress sensors together with a traversing hot-wire probe is used to identify the conditional structure associated with a large-scale skin-friction event in a high-Reynolds-number turbulent boundary layer. It is found that the large-scale skin-friction events convect at a velocity that is much faster than the local mean in the near-wall region (the convection velocity for large-scale skin-friction fluctuations is found to be close to the local mean at the midpoint of the logarithmic region). Instantaneous shear-stress data indicate the presence of large-scale structures at the wall that are comparable in scale and arrangement to the superstructure events that have been previously observed to populate the logarithmic regions of turbulent boundary layers. Conditional averages of streamwise velocity computed based on a low skin-friction footprint at the wall offer a wider three-dimensional view of the average superstructure event. These events consist of highly elongated forward-leaning low-speed structures, flanked on either side by high-speed events of similar general form. An analysis of small-scale energy associated with these large-scale events reveals that the small-scale velocity fluctuations are attenuated near the wall and upstream of a low skin-friction event, while downstream and above the low skin-friction event, the fluctuations are significantly amplified. In general, it is observed that the attenuation and amplification of the small-scale energy seems to approximately align with large-scale regions of streamwise acceleration and deceleration, respectively. Further conditional averaging based on streamwise skin-friction gradients confirms this observation. A conditioning scheme to detect the presence of meandering large-scale structures is also proposed. The large-scale meandering events are shown to be a possible source of the strong streamwise velocity gradients, and as such play a significant role in modulating the small-scale motions.