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.

The properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows are explored both experimentally and theoretically. Available highquality data reveal a dynamically relevant four-layer description that is a departure from the mean profile four-layer description traditionally and nearly universally ascribed to turbulent wall flows. Each of the four layers is characterized by a predominance of two of the three terms in the governing equations, and thus the mean dynamics of these four layers are unambiguously defined. The inner normalized physical extent of three of the layers exhibits significant Reynolds-number dependence. The scaling properties of these layer thicknesses are determined. Particular significance is attached to the viscous/Reynolds-stress-gradient balance layer since its thickness defines a required length scale. Multiscale analysis (necessarily incomplete) substantiates the four-layer structure in developed turbulent channel flow. In particular, the analysis verifies the existence of at least one intermediate layer, with its own characteristic scaling, between the traditional inner and outer layers. Other information is obtained, such as (i) the widths (in order of magnitude) of the four layers, (ii) a flattening of the Reynolds stress profile near its maximum, and (iii) the asymptotic increase rate of the peak value of the Reynolds stress as the Reynolds number approaches infinity. Finally, on the basis of the experimental observation that the velocity increments over two of the four layers are unbounded with increasing Reynolds number and have the same order of magnitude, there is additional theoretical evidence (outside traditional arguments) for the asymptotically logarithmic character of the mean velocity profile in two of the layers; and (in order of magnitude) the mean velocity increments across each of the four layers are determined. All of these results follow from a systematic train of reasoning, using the averaged momentum balance equation together with other minimal assumptions, such as that the mean velocity increases monotonically from the wall.

Turbulent boundary layer measurements above a smooth wall and sandpaper roughness are presented across a wide range of friction Reynolds numbers, δ + 99 , and equivalent sand grain roughness Reynolds numbers, k + s (smooth wall: 2020 δ + 99 21 430, rough wall: 2890 δ + 99 29 900; 22 k + s 155; and 28 δ + 99 /k + s 199). For the rough-wall measurements, the mean wall shear stress is determined using a floating element drag balance. All smooth-and rough-wall data exhibit, over an inertial sublayer, regions of logarithmic dependence in the mean velocity and streamwise velocity variance. These logarithmic slopes are apparently the same between smooth and rough walls, indicating similar dynamics are present in this region. The streamwise mean velocity defect and skewness profiles each show convincing collapse in the outer region of the flow, suggesting that Townsend's (The Structure of Turbulent Shear Flow, vol. 1, 1956, Cambridge University Press.) wall-similarity hypothesis is a good approximation for these statistics even at these finite friction Reynolds numbers. Outer-layer collapse is also observed in the rough-wall streamwise velocity variance, but only for flows with δ + 99 14 000. At Reynolds numbers lower than this, profile invariance is only apparent when the flow is fully rough. In transitionally rough flows at low δ + 99 , the outer region of the inner-normalised streamwise velocity variance indicates a dependence on k + s for the present rough surface.

The present study explores the effects of Reynolds number, over three orders of magnitude, in the viscous wall region of a turbulent boundary layer. Complementary experiments were conducted both in the boundary layer wind tunnel at the University of Utah and in the atmospheric surface layer which flows over the salt flats of the Great Salt Lake Desert in western Utah. The Reynolds numbers, based on momentum deficit thickness, of the two flows were Rθ=2×103 and Rθ≈5×106, respectively. High-resolution velocity measurements were obtained from a five-element vertical rake of hot-wires spanning the buffer region. In both the low and high Rθ flows, the length of the hot-wires measured less than 6 viscous units. To facilitate reliable comparisons, both the laboratory and field experiments employed the same instrumentation and procedures. Data indicate that, even in the immediate vicinity of the surface, strong influences from low-frequency motions at high Rθ produce noticeable Reynolds number differences in the streamwise velocity and velocity gradient statistics. In particular, the peak value in the root mean square streamwise velocity profile, when normalized by viscous scales, was found to exhibit a logarithmic dependence on Reynolds number. The mean streamwise velocity profile, on the other hand, appears to be essentially independent of Reynolds number. Spectra and spatial correlation data suggest that low-frequency motions at high Reynolds number engender intensified local convection velocities which affect the structure of both the velocity and velocity gradient fields. Implications for turbulent production mechanisms and coherent motions in the buffer layer are discussed.