Emeritus Professor Robert Antonia

The th-order velocity structure function in homogeneous isotropic turbulence is usually represented by, where the spatial separation lies within the inertial range. The first prediction for (i.e.) was proposed by Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 30, 1941) using a dimensional argument. Subsequently, starting with Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82-85), models for the intermittency of the turbulent energy dissipation have predicted values of that, except for, differ from. In order to assess differences between predictions of, we use the Hölder inequality to derive exact relations, denoted plausibility constraints. We first derive the constraint between the exponents, where are any three positive numbers. It is further shown that this relation leads to. It is also shown that the relation, which complies with, can be derived from constraints imposed on using the Cauchy-Schwarz inequality, a special case of the Hölder inequality. These results show that while the intermittency of, which is not ignored in the present analysis, is not incompatible with the plausible relation, the prediction is not plausible, unless.

An equation that relates the principal derivative of the Reynolds shear stress and large-scale vorticity fluxes is developed and validated using experimental data in a cylinder near wake. When large-scale vortices prevail, the Reynolds shear stress associated with the coherent motion is a good approximation to the conventional Reynolds shear stress. The latter is essentially determined by the imbalance between the dynamic pressure arising from the streamwise non-homogeneity caused by large-scale vortical structures and the lateral coherent vorticity flux.

We analyse the approach towards local isotropy in statistically stationary turbulent shear flows using the transport equations for the fourth-order moments of the velocity derivative. It is found that terms of these equations representing the large-scale contribution associated with the uniform mean velocity gradient gradually decrease as the Taylor microscale Reynolds number Re¿ increases, and finally disappear when Re¿ is sufficiently large. This gradual weakening of the large-scale effect is accompanied by a gradual approach towards local isotropy of the small-scale motion. The rate at which local isotropy is approached depends on the weakening of the large-scale forcing, which is controlled by the magnitude of the non-dimensional velocity shear parameter S* (= u21¯ (¿ U1/¿x2)/¿¯iso, where ¿iso is the isotropic mean turbulent energy dissipation rate, u21¯ is the streamwise velocity variance, and ¿ U1/¿x2 is the uniform mean velocity gradient in the transverse direction). In particular, we show that the approach towards local isotropy can be recast in the form CRe-1¿, where C is the product of S* and a ratio of transverse-to-streamwise velocity derivative variances. This is consistent with the behaviour of the normalized third-order moments of transverse velocity derivatives. With the further use of the transport equations for the eighth- and twelfth-order velocity derivative moments, it is found that the even moments of transverse velocity derivatives can significantly affect the rate at which local isotropy is approached, especially for higher orders.

The dominant view in the theory of fluid turbulence assumes that, once the effect of the Reynolds number is negligible, moments of order n of the longitudinal velocity increment, (d u), can be described by a simple power-law r ¿ n, where the scaling exponent ¿n depends on n and, except for ¿ 3 (= 1), needs to be determined. In this Letter, we show that applying Hölder's inequality to the power-law form (d u) n ¯ ~ (r L) ¿ n (with r / L « 1; L is an integral length scale) leads to the following mathematical constraint: ¿ 2 p = p ¿ 2. When we further apply the Cauchy-Schwarz inequality, a particular case of Hölder's inequality, to | (d u) 3 ¯ | with ¿ 3 = 1, we obtain the following constraint: ¿ 2 = 2 / 3. Finally, when Hölder's inequality is also applied to the power-law form (| d u |) n ¯ ~ (r L) ¿ n (this form is often used in the extended self-similarity analysis) while assuming ¿ 3 = 1, it leads to ¿ 2 = 2 / 3. The present results show that the scaling exponents predicted by the 1941 theory of Kolmogorov in the limit of infinitely large Reynolds number comply with Hölder's inequality. On the other hand, scaling exponents, except for ¿3, predicted by current small-scale intermittency models do not comply with Hölder's inequality, most probably because they were estimated in finite Reynolds number turbulence. The results reported in this Letter should guide the development of new theoretical and modeling approaches so that they are consistent with the constraints imposed by Hölder's inequality.

Numerical calculations based on a recent version of the eddy-damped quasi-normal model (EDQNM-LMFA) are carried out for homogeneous isotropic turbulence (HIT) with the aim of investigating the dependency on the Reynolds number of second and third order velocity structure functions. The quantities investigated include the energy spectrum E, the non-linear energy transfer T as well as the second (S2) and third (S3) order moments of the longitudinal velocity increment. Both free decaying HIT and (steady state) forced HIT are considered. The analysis of the structure functions for Re¿¿[50,106] indicates that, regardless of whether one considers decaying or forced HIT, the large scales affect S2 and S3 in the scaling range. In that range, forcing affects S2 and S3 differently. For forced HIT, S2/(¿¯r)2/3 exhibits a distinct ¿bump¿ near the upper end of the scaling range while no such bump is seen for S3/(¿¯r). The latter quantity remains approximately constant for values of r which extend to the scale corresponding to the forcing. For decaying HIT, there is no discernible bump in either S2/(¿¯r)2/3 or S3/(¿¯r). The slope of S3 in the scaling range approaches the theoretical value of 1, when Re¿ is sufficiently large. However, at similar Re¿, the slope of S2 has not yet reached a constant for either decaying or forced HIT.

Self-preservation (SP) solutions on the axis of a turbulent round jet are derived for the transport equation of the second-order structure function of the turbulent kinetic energy , which may be interpreted as a scale-by-scale (s.b.s.) energy budget. The analysis shows that the mean turbulent energy dissipation rate, , evolves like ( is the streamwise direction). It is important to stress that this derivation does not use the constancy of the non-dimensional dissipation rate parameter ( and are the integral length scale and root mean square of the longitudinal velocity fluctuation respectively). We show, in fact, that the constancy of is simply a consequence of complete SP (i.e. SP at all scales of motion). The significance of the analysis relates to the fact that the SP requirements for the mean velocity and mean turbulent kinetic energy (i.e. and respectively) are derived without invoking the transport equations for and . Experimental hot-wire data along the axis of a turbulent round jet show that, after a transient downstream distance which increases with Reynolds number, the turbulence statistics comply with complete SP. For example, the measured agrees well with the SP prediction, i.e. , while the Taylor microscale Reynolds number remains constant. The analytical expression for the prefactor for (where is a virtual origin), first developed by Thiesset et al. (J. Fluid Mech., vol. 748, 2014, R2) and rederived here solely from the SP analysis of the s.b.s. energy budget, is validated and provides a relatively simple and accurate method for estimating along the axis of a turbulent round jet.

The transport equation for the mean scalar dissipation rate ¿¿ is derived by applyingthe limit at small separations to the generalized form of Yaglom's equation in twotypes of flows, those dominated mainly by a decay of energy in the streamwisedirection and those which are forced, through a continuous injection of energy atlarge scales. In grid turbulence, the imbalance between the production of ¿¿ dueto stretching of the temperature field and the destruction of ¿¿ by the thermaldiffusivity is governed by the streamwise advection of ¿¿ by the mean velocity.This imbalance is intrinsically different from that in stationary forced periodic boxturbulence (or SFPBT), which is virtually negligible. In essence, the different typesof imbalance represent different constraints imposed by the large-scale motion on therelation between the so-called mixed velocity-temperature derivative skewness STand the scalar enstrophy destruction coefficient G¿ in different flows, thus resultingin non-universal approaches of ST towards a constant value as Re¿ increases. Thedata for ST collected in grid turbulence and in SFPBT indicate that the magnitudeof ST is bounded, this limit being close to 0.5.

The transport of momentum and heat in the turbulent intermediate wake of a circular cylinder is inherently three-dimensional (3-D). This work aims to gain new insight into the 3-D vorticity structure, momentum and heat transport in this flow. All three components of the velocity and vorticity vectors, along with the fluctuating temperature, are measured simultaneously, at nominally the same point in the flow, with a probe consisting of four X-wires and four cold wires. Measurements are made in the ( , ) or mean shear plane at , 20 and 40 at a Reynolds number of based on the cylinder diameter and the free-stream velocity. A phase-averaging technique is developed to separate the large-scale coherent structures from the remainder of the flow. It is found that the effects of vorticity on heat transport at and are distinctly different. At , both spanwise and streamwise vorticity components account significantly for the heat flux. At and 40, the spanwise vortex rollers play a major role in inducing the coherent components of the heat flux vector, while the ribs are responsible for the small-scale heat diffusion out of the spanwise vortex rollers. The present data indicate that, if the spanwise-velocity-related terms are ignored, the estimated values of the production can have errors of approximately 22 % and 13 % respectively for the turbulent energy and temperature variance at , and the errors are expected to further increase downstream. A conceptual model summarizing the 3-D features of the heat and momentum transports at is proposed. Compared with the previous two-dimensional model of Matsumura & Antonia (J. Fluid Mech., vol. 250, 1993, pp. 651-668) or MA, the new model provides a more detailed description of the role the rib-like structures undertake in transporting heat and momentum, and also underlines the importance of the upstream half of the spanwise vortex rollers, instead of only one quadrant of these rollers, as in the MA model, in diffusing heat out of the vortex.

In this paper, the velocity-based POD and the vorticity-based POD have been systematically compared in three characteristic regions of the flow downstream of a two-dimensional circular cylinder, namely the near, intermediate and far wakes. The two-point space correlation function is used to determine which of the two methods is better suited for extracting the large-scale flow structures based on the repartition of energy among the different POD modes. It is found that the POD, based on the lateral velocity fluctuation v, leads to the most optimum extraction in all three flow regions, while the vorticity-based POD is only effective in the near and intermediate wakes. Based on two-point space correlation functions, a scenario is proposed for the application of POD to the present two-dimensional wake.

Hot-wire velocity measurements are carried out in a turbulent boundary layer over a rough wall consisting of transverse circular rods, with a ratio of 8 between the spacing (w) of two consecutive rods and the rod height (k). The pressure distribution around the roughness element is used to accurately measure the mean friction velocity (Ut) and the error in the origin. It is found that Ut remained practically constant in the streamwise direction suggesting that the boundary layer over this surface is evolving in a self-similar manner. This is further corroborated by the similarity observed at all scales of motion, in the region 0.2=y/d=0.6, as reflected in the constancy of Reynolds number (R¿) based on Taylor's microscale and the collapse of Kolmogorov normalized velocity spectra at all wavenumbers.A scale-by-scale budget for the second-order structure function <(du)2> (du=u(x+r)-u(x), where u is the fluctuating streamwise velocity component and r is the longitudinal separation) is carried out to investigate the energy distribution amongst different scales in the boundary layer. It is found that while the small scales are controlled by the viscosity, intermediate scales over which the transfer of energy (or <(du)3>) is important are affected by mechanisms induced by the large-scale inhomogeneities in the flow, such as production, advection and turbulent diffusion. For example, there are non-negligible contributions from the large-scale inhomogeneity to the budget at scales of the order of ¿, the Taylor microscale, in the region of the boundary layer extending from y/d=0.2 to 0.6 (d is the boundary layer thickness).

The transport equation for the isotropic turbulent energy dissipation rate along the centreline in the far-wake of a circular cylinder is derived by applying the limit at small separations to the two-point energy budget equation. It is found that the imbalance between the production and the destruction of eiso, respectively due to vortex stretching and viscosity, is governed by both the streamwise advection and the lateral turbulent diffusion (the former contributes more to the budget than the latter). This imbalance differs intrinsically from that in other flows, e.g. grid turbulence and the flow along the centreline of a fully developed channel, where either the streamwise advection or the lateral turbulent diffusion of eiso governs the imbalance. More importantly, the different types of imbalance represent different constraints on the relation between the skewness of the longitudinal velocity derivative and the destruction coefficient of enstrophy G. This results in a non-universal approach of towards a constant value as the Taylor microscale Reynolds number R¿ increases. For the present flow, the magnitude of S decreases initially before increasing (R¿ > 40) towards this constant value. The constancy of S at large R¿ violates the modified similarity hypothesis introduced by Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82-85) but is consistent with the original similarity hypotheses (Kolmogorov, Dokl. Akad. Nauk SSSR, vol. 30, 1941b, pp. 299-303 (see also 1991 Proc. R. Soc. Lond. A, vol. 434, pp. 9-13)) , and, more importantly, with the almost completely self-preserving nature of the plane far-wake.

Direct numerical simulations (DNS) are carried out to study the passive heat transport in a turbulent channel flow with either square bars or circular rods on one wall. Several values of the pitch to height ratio and two Reynolds numbers are considered. The roughness increases the heat transfer by inducing ejections at the leading edge of the roughness elements. The amounts of heat transfer and mixing depend on the separation between the roughness elements, an increase in heat transfer accompanying an increase in drag. The ratio of non-dimensional heat flux to the non-dimensional wall shear stress is higher for circular rods than square bars irrespectively of the pitch to height ratio. The turbulent heat flux varies within the cavities and is larger near the roughness elements. Both momentum and thermal eddy diffusivities increase relative to the smooth wall. For square cavities the turbulent Prandtl number is smaller than for a smooth channel near the wall. As increases, the turbulent Prandtl number increases up to a maximum of 2.5 at the crests plane of the square bars . With increasing distance from the wall, the differences with respect to the smooth wall vanish and at three roughness heights above the crests plane, the turbulent Prandtl number is essentially the same for smooth and rough walls.

The transport equation for the mean turbulent energy dissipation rate along the centreline of a fully developed channel flow is derived by applying the limit at small separations to the two-point budget equation. Since the ratio of the isotropic energy dissipation rate to the mean turbulent energy dissipation rate is sufficiently close to 1 on the centreline, our main focus is on the isotropic form of the transport equation. It is found that the imbalance between the production of due to vortex stretching and the destruction of caused by the action of viscosity is governed by the diffusion of by the wall-normal velocity fluctuation. This imbalance is intrinsically different from the advection-driven imbalance in decaying-type flows, such as grid turbulence, jets and wakes. In effect, the different types of imbalance represent different constraints on the relation between the skewness of the longitudinal velocity derivative and the destruction coefficient of enstrophy in different flows, thus resulting in non-universal approaches of towards a constant value as the Taylor microscale Reynolds number, , increases. For example, the approach is slower for the measured values of along either the channel or pipe centreline than along the axis in the self-preserving region of a round jet. The data for collected in different flows strongly suggest that, in each flow, the magnitude of is bounded, the value being slightly larger than 0.5.

A general framework of self-preservation (SP) is established, based on the transport equation of the second-order longitudinal velocity structure function in decaying homogeneous isotropic turbulence (HIT). The analysis introduces the skewness of the longitudinal velocity increment, S(r, t) (r and t are space increment and time), as an SP controlling parameter. The present SP framework allows a critical appraisal of the specific assumptions that have been made in previous SP analyses. It is shown that SP is achieved when S(r, t) varies in a self-similar manner, i.e. S=c(t)f(r/l) where l is a scaling length, and c(t) and f(r/l) are dimensionless functions of time and (r/l), respectively. When c(t) is constant, l can be identified with the Kolmogorov length scale ¿, even when the Reynolds number is relatively small. On the other hand, the Taylor microscale ¿ is a relevant SP length scale only when certain conditions are met. The decay law for the turbulent kinetic energy (k) ensuing from the present SP is a generalization of the existing laws and can be expressed as k ~ (t-t0)n+B, where B is a constant representing the energy of the motions whose scales are excluded from the SP range of scales. When B = 0, SP is achieved at all scales of motion and ¿ becomes a relevant scaling length together with ¿. The analysis underlines the relation between the initial conditions and the power-law exponent n and also provides a link between them. In particular, an expression relating n to the initial values of the scaling length and velocity is developed. Finally, the present SP analysis is consistent with both experimental grid turbulence data and the eddy-damped quasi-normal Markovian numerical simulation of decaying HIT by Meldi & Sagaut (J. Turbul., vol. 14, 2013, pp. 24-53).

The variation of S, the velocity derivative skewness, with the Taylor microscale Reynolds number Re¿ is examined for different turbulent flows by considering the locally isotropic form of the transport equation for the mean energy dissipation rate e¯iso. In each flow, the equation can be expressed in the form S C 2G=Re¿ D C=Re¿, where G is a non-dimensional rate of destruction of e¯iso and C is a flow-dependent constant. Since 2G=Re¿ is found to be very nearly constant for Re¿ = 70, S should approach a universal constant when Re¿ is sufficiently large, but the way this constant is approached is flow dependent. For example, the approach is slow in grid turbulence and rapid along the axis of a round jet. For all the flows considered, the approach is reasonably well supported by experimental and numerical data. The constancy of S at large Re¿ has obvious ramifications for small-scale turbulence research since it violates the modified similarity hypothesis introduced by Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82-85) but is consistent with the original similarity hypothesis (Kolmogorov, Dokl. Akad. Nauk SSSR, vol. 30, 1941, pp. 299-303).

For homogeneous isotropic turbulence approximated by grid turbulence, velocity and temperature fluctuations decay under the effects of viscosity and thermal diffusivity of the fluid. In the self-similar region of grid flow, there is no mean shear and no turbulence production, and the decay rate is well represented by a power law; this is supported by the present measurements in three different grid flows and by previously published data for passive-grid turbulence obtained over different ranges of streamwise distance and/or Reynolds number. The grid flow is slightly heated so that temperature acts as a passive scalar. From dimensional analysis and empirical power-law correlations, relations for basic flow parameters, such as the Kolmogorov, Taylor, and Corrsin microscales, and the Reynolds and Péclet numbers, are established as functions of the normalized streamwise distance downstream of the grid. With these relations, it is possible to determine the flow parameters for a specific passive-grid geometry or, more generally, a specific set of initial conditions. © 2014 Copyright Taylor & Francis Group, LLC.

A numerical simulation based on the lattice Boltzmann method is carried out in the wake of a square cylinder with the view to investigating possible surrogates for the instantaneous turbulent kinetic energy dissipation rate, Ie{cyrillic, ukrainian}, as well as its mean value, \documentclass[12pt]{minimal}\begin{document}$\overline{\epsilon }$\end{document}Ie{cyrillic, ukrainian}. Various surrogate approximations of Ie{cyrillic, ukrainian}, based on local isotropy (Ie{cyrillic, ukrainian}iso), local axisymmetry along the streamwise direction x (Ie{cyrillic, ukrainian}a, x) and the transverse direction y (Ie{cyrillic, ukrainian}a, y), local homogeneity (Ie{cyrillic,ukrainian}hom), and homogeneity in the transverse plane, (Ie{cyrillic,ukrainian}4x), are assessed. All the approximations are in agreement with \documentclass[12pt]{minimal}\begin{document}$\overline{\epsilon }$\end{document}Ie{cyrillic,ukrainian}when the distance downstream of the obstacle is larger than about 40 diameters. Closer to the obstacle, the agreement remains reasonable only for \documentclass[12pt]{minimal}\begin{document}$\overline{\epsilon }_{a,x}$\end{document}Ie{cyrillic, ukrainian}a,x, \documentclass[12pt]{minimal}\begin{document}$\overline{\epsilon }{hom}$\end{document}?hom and \documentclass[12pt]{minimal}\begin{document}$\overline{\epsilon }{4x}$\end{document}Ie{cyrillic, ukrainian}4x. The probability density functions (PDF) and joint PDFs of Ie{cyrillic, ukrainian} and its surrogates show that Ie{cyrillic, ukrainian}4x correlates best withIe{cyrillic, ukrainian}while ?iso and Ie{cyrillic, ukrainian}hom present the smallest correlation. The results indicate that Ie{cyrillic, ukrainian}4x is a very good surrogate for Ie{cyrillic, ukrainian}and can be used for correctly determining the behaviour of Ie{cyrillic, ukrainian}.

This article focuses on the effect that two different mesh grids have on the structure of the mixing layer of an axisymmetric jet. Detailed measurements of mean velocity and turbulent velocity fluctuations are made with an X hot-wire probe in the range 0.5 = x/d = 10, where x is the longitudinal distance from the nozzle exit plane and d is the nozzle diameter. The grids are introduced at two locations-one location just downstream of the nozzle exit plane and the other location upstream of the nozzle exit plane in order to perturb the nozzle exit boundary layer. One mesh completely covers the nozzle (full mesh or FM) and the other mesh covers the central, high-speed zone (disk mesh or DM). With reference to the undisturbed jet, FM yields a significant reduction in the turbulence intensity and width of the shear layer, whereas DM enhances the turbulence intensity and increases the width of the shear layer. Both grids suppress the formation of the Kelvin-Helmholtz instability in the mixing layer. Results are presented, mainly at x/d = 5 and 6 in both the spectral domain and physical space. In the latter context, second-and third-order structure functions associated with u (the longitudinal velocity fluctuation) and v (the lateral or radial velocity fluctuation) are presented only for the flow perturbed by placing the mesh outside the nozzle. All mesh geometries have a more significant effect on the second-order structure function of u than on that of v. The third-order energy transfer term is affected in such a way that, relative to the undisturbed jet, its peak location is shifted to a smaller scale when FM is used and to a larger scale with DM. This is consistent with our observations that FM reduces the turbulence in the shear layer while DM enhances it. It is suggested that the large-scale vortices that are formed at the edge of the grids play a significant role in the transfer of energy. © 2013 Taylor & Francis Group, LLC.

We investigate the effect of the hot wire resolution on measurements of the velocity derivative skewness in homogeneous isotropic turbulence. A single wire configuration (with different lengths and temporal sampling resolutions) is considered. Estimates of the attenuation, based on numerical data in box turbulence, are applied to experimental data taken in grid turbulence. It is found that the sampling resolution has a sizeable attenuation effect, while the length of the wire has a relatively minor impact. The corrected experimental values support the conclusion that the skewness is constantwith the Reynolds number, in agreement with Kolmogorov's 41 theory.

DNSs of turbulent channel flows with one rough wall and one smooth wall are presented to show how the vorticity field depends on the shape and orientation of the roughness elements. The passive scalar is also evaluated. The high correlation coefficients between vorticity and scalar gradients, in the wall layer, emphasize that in all cases flowvisualizations can be used in a laboratory to have a qualitative picture of the modifications of the high- and low-speed streaks. Joint probability density function between vorticity and scalar gradients show how the bursting events affect the scalar distribution. © 2006 Springer.

Direct Numerical Simulations of turbulent channel flow with square bars on the bottom wall are discussed have been carried out at different Reynolds numbers. The results tend to confirm the inappropriateness of the roughness function as an indication of the effect a particular roughness geometry exerts on the flow. Distributions of turbulent intensities support the improvement in global isotropy relative to a smooth-wall.

Objective: To analyse the microsatellite instability (MI) and loss of heterozygosity (LOH) in non-small cell lung cancer (NSCLC). Methods: MI and LOH at chromosome 17 were checked in 35 cases of NSCLC tumor-normal paired tissues using four microsatellite markers TP53 (17p13.1), THRA1 (17q11.2-12), D17S579 (17q12-21) and D17S855 (17q21) by PCR based analysis. Mutations of P53 exons 5-8 were also tested using PCR-single strand conformation polymorphism (PCR-SSCP) and PCR-denaturing gradient gel electrophoresis (PCR-DGGE) analysis. Results: 22 of 35 tumors (62.8%) displayed MI or LOH. 14 tumors (40.0%) exhibited MI, 11 tumors (31.4%) exhibited LOH, while 3 tumors (8.6%) exhibited MI and LOH concurrently. 23 tumors (8.6%) exhibited P53 gene mutations. The frequency of MI or LOH was obviously higher in the early-stage (stages I and II, 78.9%) than in the advanced-stage (stage III, 43.8%). However, the frequency of MI or LOH had no difference either between high-grade (75.0%) and low-grade (52.6%) differentiated NSCLC or between the tumors with P53 mutations (59.1%) and those without P53 mutations (69.2%). No relationship was observed between the presence of MI or LOH and the histologic subtype of NSCLC. Conclusion: The results suggest that MI and LOH at chromosome 17 may play a significant role in the development of NSCLC. The high frequency of MI or LOH in the early-stage tumors indicates that these genetic alterations could occur early during NSCLC development. Our data also show that the genetic alterations of microsatellite at chromosome 17 was not associated with P53 gene mutations.

The effects of large-scale intermittency and the mean shear rate on the various scaling range exponents in a turbulent jet were studied. Exponents studied were associated with second order structure functions and power spectra of both the longitudinal velocity fluctuations and the passive temperature fluctuations. All exponents were influenced by the intermittency and the mean shear rate. Scalar fluctuation exponents were more sensitive than the longitudinal velocity fluctuation exponents.

The classical treatment of rough wall turbulent boundary layers consists in determining the effect the roughness has on the mean velocity profile. This effect is usually described in terms of the roughness function ¿U+. The general implication is that different roughness geometries with the same ¿U+ will have similar turbulence characteristics, at least at a sufficient distance from the roughness elements. Measurements over two different surface geometries (a mesh roughness and spanwise circular rods regularly spaced in the streamwise direction) with nominally the same ¿U+ indicate significant differences in the Reynolds stresses, especially those involving the wall-normal velocity fluctuation, over the outer region. The differences are such that the Reynolds stress anisotropy is smaller over the mesh roughness than the rod roughness. The Reynolds stress anisotropy is largest for a smooth wall. The small-scale anisotropy and interniitency exhibit much smaller differences when the Taylor microscale Reynolds number and the Kolmogorov-normalized mean shear are nominally the same. There is nonetheless evidence that the small-scale structure over the three-dimensional mesh roughness conforms more closely with isotropy than that over the rod-roughened and smooth walls.