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Mean-flow measurements of turbulent boundary layers over porous walls (permeable and rough) with varying pore size (s), permeability (K) and thickness (h) are presented across a wide range of friction Reynolds numbers (Reτ≈2000–18000) and permeability based Reynolds numbers (ReK≈1.5–60). The mean wall shear stress was determined using a floating element drag balance and the boundary layer profiles were acquired using hot-wire anemometry. Substrate permeability is shown to increase the magnitude of the mean velocity deficit. The use of a modified indicator function, assuming “universal” values for von Karman constant (κ=0.39) supports previous results where a strongly modified logarithmic region was observed. The indicator function was also used to estimate the zero-plane displacement (yd), the roughness function (ΔU+), and equivalent sandgrain roughness (ks). At high Reynolds numbers, the roughness function data collapses on to the Nikuradse's fully rough asymptote. However, at low roughness Reynolds numbers (ks+<100), we observe the flow to be transitionally rough, evolving with Nikuradse-type behavior. The equivalent sandgrain roughness ks for each substrate appears to include roughness and permeability contributions. These two contributions can be separated using data obtained from the same substrates with different thickness. This may allow us to model the porous wall as a combination of rough and permeable wall.

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The effects of bed roughness, isolated from that of bed permeability, on the vertical transport processes across the sediment-water interface (SWI) are not well understood. We compare the statistics and structure of the mean flow and turbulence in open-channel flows with a friction Reynolds number of 395 and a permeability Reynolds number of 2.6 over sediments with either regular or random grain packing at the SWI. The regular sediment interface is formed by cubic packing of spheres aligned with the mean-velocity direction. It is shown that, even in the absence of any bedform, the subtle details of the particle roughness alone can significantly affect the dynamics of turbulence and the time-mean flow. Such effects translate to large differences in penetration depths, apparent permeabilities, vertical mass fluxes and subsurface flow paths of passive scalars. The less organized distribution of mean recirculation regions near the interface with a random packing leads to a more isotropic form-induced stress tensor. The augmented wall-normal form-induced fluctuations play a significant role in increasing mixing and wall-normal mass and momentum exchange.

Indirect methods to estimate surface shear stress are commonly used to characterise rough-wall boundary-layer flows. The uncertainty is typically large and often insufficient to carry out quantitative analysis, especially for surface roughness where established scaling and similarity laws may not hold. It is, thus, preferable to rely instead on independent measurement techniques to accurately measure skin friction. The floating element was one of the first to be introduced, and still is the most popular for its features. Although its fundamental principle has remained unchanged, different arrangements have been suggested to overcome its inherent limitations. In this paper, we review some of these designs and further present an alternative that is able to correct for extraneous loads into the drag measurement. Its architecture is based on the parallel-shift linkage, and it features custom-built force transducers and a data acquisition system designed to achieve high signal-to-noise ratios. The smooth-wall boundary-layer flow is used as a benchmark to assess the accuracy of this balance. Values of skin-friction coefficient show an agreement with hot-wire anemometry to within \(2\%\) for \(Re_{\theta } = 4\times 10^3\) up to \(10^4\). A rough surface of staggered distributed cubes with large relative height, \(\delta /h\simeq 10\), is also investigated. Results indicate the flow reaches the fully rough regime, at the measurement location, for the entire range of Reynolds number. Furthermore, the values of skin friction agree with existing estimations from alternative methods.
Graphical abstract
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Drawings of the floating-element (FE) balance and skin-friction measurements for a smooth-wall boundary layer. On top: slice along the X-Y plane and top view (left) next to their corresponding pictures (right). Colors highlight distinct subsystems, namely, the floating frame for drag measurement (yellow), the pitching moment mechanism (red) and the acquisition system (blue). Bottom left: smooth-wall setup and calibration system. The FE is flush mounted with the wind tunnel floor and the pulley is attached to a linear traverse which allows setting its position at different wall-normal locations. During calibration, a lid is removed to make way for the pulley to move into the test section. A wire is then strung over to suspend the weights. Bottom right: Skin friction over a smooth wall. The inset indicates the relative discrepancy between the FE values (blue) and those inferred from hot-wire anemometry of the boundary-layer profile (red).

This paper reports turbulent boundary layer measurements made over open-cell reticulated foams with varying pore size and thickness, but constant porosity ($\epsilon \approx 0.97$). The foams were flush-mounted into a cutout on a flat plate. A Laser Doppler Velocimeter (LDV) was used to measure mean streamwise velocity and turbulence intensity immediately upstream of the porous section, and at multiple measurement stations along the porous substrate. The friction Reynolds number upstream of the porous section was $Re_\tau \approx 1690$. For all but the thickest foam tested, the internal boundary layer was fully developed by $<10 \delta$ downstream from the porous transition, where $\delta$ is the boundary layer thickness. Fully developed mean velocity profiles showed the presence of a substantial slip velocity at the porous interface ($>30\%$ of the free stream velocity) and a mean velocity deficit relative to the canonical smooth-wall profile further from the wall. While the magnitude of the mean velocity deficit increased with average pore size, the slip velocity remained approximately constant. Fits to the mean velocity profile suggest that the logarithmic region is shifted relative to a smooth wall, and that this shift increases with pore size until it becomes comparable to substrate thickness $h$. For all foams, the turbulence intensity was found to be elevated further into the boundary layer to $y/ \delta \approx 0.2$. An outer peak in intensity was also evident for the largest pore sizes. Velocity spectra indicate that this outer peak is associated with large-scale structures resembling Kelvin-Helmholtz vortices that have streamwise length scale $2\delta-4\delta$. Skewness profiles suggest that these large-scale structures may have an amplitude-modulating effect on the interfacial turbulence.

To understand turbulent transport mechanisms of interface turbulence over porous and rough walls, statistical analyses using direct numerical simulation (DNS) data are carried out at a bulk Reynolds number of 3000. The presently considered porous wall, whose porosity is 0.71, consists of interconnected staggered cube arrays and the rough wall has the same surface structure. Through quadrant and budget term analyses, the transport mechanisms of the plane averaged Reynolds stress are investigated and mutual dependency between turbulence and dispersion is elucidated. Moreover, the influence of the Kelvin-Helmholtz instability on turbulent transport is clarified.

To understand turbulence over porous media, a series of PIV measurements were carried out in porous-walled channel flows. The porous walls were made of three types of foamed ceramics which had the same porosity but different permeability. For turbulence inside porous media, LES studies of fully developed flows in three different model porous media were performed. Referring to these databases, a multi-scale k − ε four equation eddy viscosity model for turbulence around and/or inside porous media was developed. Through the comparison to the experimental results, the proposed model was validated with satisfactory accuracy.

We perform direct numerical simulations (DNS) of a turbulent channel flow over porous walls. In the fluid region the flow is governed by the incompressible Navier–Stokes (NS) equations, while in the porous layers the volume-averaged Navier–Stokes (VANS) equations are used, which are obtained by volume-averaging the microscopic flow field over a small volume that is larger than the typical dimensions of the pores. In this way the porous medium has a continuum description, and can be specified without the need of a detailed knowledge of the pore microstructure by independently assigning permeability and porosity. At the interface between the porous material and the fluid region, momentum-transfer conditions are applied, in which an available coefficient related to the unknown structure of the interface can be used as an error estimate. To set up the numerical problem, the velocity–vorticity formulation of the coupled NS and VANS equations is derived and implemented in a pseudo-spectral DNS solver. Most of the simulations are carried out at Re_tau=180 and consider low-permeability materials; a parameter study is used to describe the role played by permeability, porosity, thickness of the porous material, and the coefficient of the momentum-transfer interface conditions. Among them permeability, even when very small, is shown to play a major role in determining the response of the channel flow to the permeable wall. Turbulence statistics and instantaneous flow fields, in comparative form to the flow over a smooth impermeable wall, are used to understand the main changes introduced by the porous material. A simulation at higher Reynolds number is used to illustrate the main scaling quantities.

This paper outlines the authors' experimental research in rough-wall-bounded turbulent flows that has spanned the past 15 years. The results show that, in general, roughness effects are confined to the inner layer. In accordance with Townsend's Reynolds number similarity hypothesis, the outer layer is insensitive to surface condition except in the role it plays in setting the length and velocity scales for the outer flow. An exception to this can be two-dimensional roughness which has been observed in some cases to suffer roughness effects far from the wall. However, recent results indicate that similarity also holds for two-dimensional roughness provided the Reynolds number is large, and there is sufficient scale separation between the roughness length scale and the boundary layer thickness. The concept of similarity between smooth-and rough-wall flows is of great practical importance as most computational and analytical modeling tools rely on it either explicitly or implicitly in predicting flows over rough walls. Because of the observed similarity, the roughness function (Delta U+), or shift in the log layer, is a useful way of characterizing the roughness effect on the mean flow and the frictional drag. In the fully rough regime, it is shown that the hydraulic roughness length scale is related to the root-mean-square height (k(rms)) and skewness (s(k)) of the surface elevation probability density function. On the other hand, the onset of roughness effects is seen to be associated with the largest surface features which are typified by the peak-to-trough height (k(t)). Roughness function behavior in the transitionally rough regime varies significantly between roughness types. Since no "universal" roughness function exists, no single roughness length scale can characterize all roughness types in all the flow regimes. Despite this, research using roughness with a systematic variation in texture is ongoing in an effort to uncover surface parameters that lead to the variation in the frictional drag behavior witnessed in the transitionally rough regime.

Turbulent heat transfer in a channel partially filled by a porous medium is investigated using a direct numerical simulation of an incompressible flow. The porous medium consists of a three-dimensional Cartesian grid of cubes, which has a relatively high permeability. The energy equation is not solved in the cubes. Three different heating configurations are studied. The simulation is performed for a bulk Reynolds number Reb = 5500 and a Prandtl number Pr = 0.1. The turbulent flow quantities are compared with the results of Breugem and Boersma [“Direct numerical simulations of turbulent flow over a permeable wall using a direct and a continuum approach,” Phys. Fluids 17, 025103 (2005)] to validate the numerical approach and macroscopic turbulent quantities are analyzed. Regarding the temperature fields, original results are obtained. The temperature fields show an enhanced turbulent heat transfer just
above the porous region compared to the solid top wall, which can be related to the large vortical structures that develop in this region. Furthermore, these large structures induce pressure waves inside the porous domain which are responsible of large temperature fluctuations deep inside the porous region where the flow is laminar. Finally, macroscopic turbulent quantities are computed to get reference results for the
development of macroscopic turbulent heat transfer models in fluid-porous domain.

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 2×10 4 <Re τ <6×10 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 A. A. Townsend [The structure of turbulent shear flow. 2nd ed. Cambridge Monographs on Mechanics and Applied Mathematics. London etc.: Cambridge University Press. XI (1976; Zbl 0325.76063)], 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.

Results of an experimental investigation of the flow over a model roughness are presented. The series of roughness consists of close-packed pyramids in which both the height and the slope are systematically varied. The aim of this work is to gain insight into the physical roughness scales which contribute to drag. The mean velocity profiles for all nine rough surfaces collapse with smooth-wall results when presented in velocity-defect form. The Reynolds stresses also show good agreement with smooth-wall results outside the roughness sublayer when presented in outer variables. The results for the six steepest surfaces indicate that the roughness function, deltaU^+, scales almost entirely on the roughness height with only a weak dependence on the slope of the pyramids. However, deltaU^+ for the three surfaces with the smallest slope does not scale on the roughness height, indicating that these surfaces might not be thought of as surface `roughness' in a traditional sense but instead surface `waviness'.

This paper presents an experimental study devoted to investigating the effects of permeability on wall turbulence. Velocity measurements were performed by means of laser Doppler anemometry in open channel flows over walls characterized by a wide range of permeability. Previous studies proposed that the von Kármán coefficient associated with mean velocity profiles over permeable walls is significantly lower than the standard values reported for flows over smooth and rough walls. Furthermore, it was observed that turbulent flows over permeable walls do not fully respect the widely accepted paradigm of outer-layer similarity. Our data suggest that both anomalies can be explained as an effect of poor inner–outer scale separation if the depth of shear penetration within the permeable wall is considered as the representative length scale of the inner layer. We observed that with increasing permeability, the near-wall structure progressively evolves towards a more organized state until it reaches the condition of a perturbed mixing layer where the shear instability of the inflectional mean velocity profile dictates the scale of the dominant eddies. In our experiments such shear instability eddies were detected only over the wall with the highest permeability. In contrast attached eddies were present over all the other wall conditions. On the basis of these findings, we argue that the near-wall structure of turbulent flows over permeable walls is regulated by a competing mechanism between attached and shear instability eddies. We also argue that the ratio between the shear penetration depth and the boundary layer thickness quantifies the ratio between such eddy scales and, therefore, can be used as a diagnostic parameter to assess which eddy structure dominates the near-wall region for different wall permeability and flow conditions.

The behaviour of turbulent shear flow over a mass-neutral permeable wall is studied
numerically. The transpiration is assumed to be proportional to the local pressure
fluctuations. It is first shown that the friction coefficient increases by up to 40% over
passively porous walls, even for relatively small porosities. This is associated with
the presence of large spanwise rollers, originating from a linear instability which is
related both to the Kelvin–Helmholtz instability of shear layers, and to the neutral
inviscid shear waves of the mean turbulent profile. It is shown that the rollers can
be forced by patterned active transpiration through the wall, also leading to a large
increase in friction when the phase velocity of the forcing resonates with the linear
eigenfunctions mentioned above. Phase-lock averaging of the forced solutions is used
to further clarify the flow mechanism. This study is motivated by the control of
separation in boundary layers.

A review of predictive methods used to determine the frictional drag on a rough surface is presented. These methods utilize a wide range of roughness scales, including roughness height, pitch, density, and shape parameters. Most of these scales were developed for regular roughness, limiting their applicability to predict the drag for many engineering flows. A new correlation is proposed to estimate the frictional drag for a surface covered with three-dimensional, irregular roughness in the fully rough regime. The correlation relies solely on a measurement of the surface roughness profile and builds on previous work utilizing moments of the surface statistics. A relationship is given for the equivalent sandgrain roughness height as a function of the root-mean-square roughness height and the skewness of the roughness probability density function. Boundary layer similarity scaling then allows the overall frictional drag coefficient to be determined as a function of the ratio of the equivalent sandgrain roughness height to length of the surface.

The behavior of turbulent open channel flows over permeable surfaces is not well understood. In particular, it is not clear how the surface and the subsurface flow within the permeable bed interact and influence each other. In order to clarify this issue we carried out two sets of experiments, one involving velocity measurements in open channel flows over an impermeable bed composed of a single layer of spheres, and another one where velocities were measured over and within a permeable bed made of five such layers. Comparison of surface flow velocity statistics between the two sets of experiments confirmed that bed permeability can significantly affect flow resistance. It was also confirmed that even in the hydraulically rough regime, the friction factors for the permeable bed increase with increasing Reynolds number. Such an increase in flow resistance implies a different distribution of normal form-induced stress between the permeable and impermeable bed cases. Subsurface flow measurements performed within the permeable bed revealed that there is an intense transport of turbulent kinetic energy TKE occurring from the surface to the subsurface flow. We provide evidence that the transport of TKE toward the lower bed levels is driven mainly by pressure fluctuations, whereas TKE transport due to turbulent velocity fluctuations is limited to a thinner layer placed in the upper part of the bed. It was also confirmed that the turbulence imposed by the surface flow gradually dissipates while penetrating within the porous medium. Dissipation occurs faster for the small scales than for the large ones, which instead are persistent, although weak, even at the lowest bed levels. © 2009 American Institute of Physics.

A series of experiments have been made in a wind tunnel to investigate the ventilation of snow by shear. We argue that the
zero-plane displacement can be used as a convenient indicator of ventilation, and that this can be obtained from measurements
of mean velocity profiles in conditions of zero pressure gradient. Measurements made over a natural snow surface show a zero-plane
displacement depth of less than 5mm, but practical considerations preclude extensive use of snow for these measurements.
Instead, the influence of permeability is investigated using reticulated foams in place of snow. We demonstrate that the foam
and snow have similar structure and flow-relevant properties. Although the surface of the foam is flat, the roughness lengths
increase by two orders of magnitude as the permeability increases from 6 × 10−9 to 160 × 10−9 m2. The zero-plane displacement for the least permeable foams is effectively zero, but more than 15mm for the most permeable
foams. Our data compare well to the few studies available in the literature. By analogy to conditions over snow surfaces,
we suggest that shear-driven ventilation of snow is therefore limited to the upper few millimetres of snow surfaces.

A new model for turbulent flows in porous media is developed. The spatial- and time fluctuations in this new model are tied together and treated as a single quantity. This novel treatment of the fluctuations leads to a natural construction of the k and ε type equations for rigid and isotropic porous media in which all the kinetic energy filtered in the averaging process is modeled. The same terms as those found in the corresponding equations for clear flow, plus additional terms resulting from the interaction between solid walls in the porous media and the fluid characterize the model. These extra terms arise in a boundary integral form, facilitating their modeling. The model is closed by assuming the eddy viscosity approximation to be valid, and using simple models to represent the interaction between the walls in the porous media and the fluid.

Direct numerical simulations (DNS) have been performed of turbulent flow in a plane channel with a solid top wall and a permeable bottom wall. The permeable wall is a packed bed, which is characterized by the mean particle diameter and the porosity. The main objective is to study the influence of wall permeability on the structure and dynamics of turbulence. The flow inside the permeable wall is described by means of volume-averaged NavierHelmholtz type of instability. These structures are responsible for an exchange of momentum between the channel and the permeable wall. This process contributes strongly to the Reynolds-shear stress and thus to a large increase in the skin friction.

To understand the permeability effects on turbulent rib-roughened porous channel flows, particle image velocimetry measurements are performed at the bulk Reynolds number of 5000–20000. Solid impermeable and porous ribs are considered for the rib-roughness whose geometry is categorised in the k-type roughness whose pitch/rib-height is 10. Three isotropic porous media with nearly the same porosity: 0.8, and different permeabilities (0.004, 0.020, 0.033 mm²) are applied. It is observed that the recirculation between the ribs becomes weak and the recirculation vortex submerges into the porous wall as the wall permeability and Reynolds number increase for both solid and porous rib cases while the recirculation vanishes in high permeable cases. These phenomena result in characteristic difference in turbulence quantities. By fitting the mean velocity profiles to the log-law form, the permeability effects of both rib and bottom wall on the log-law parameters and the equivalent sand-grain roughness are discussed. It is concluded that the zero-plane displacement increases while the von Kármán constant and the equivalent sand-grain roughness decrease as the wall and rib permeability increases.

Experimental evidence of amplitude modulation in permeable-wall turbulence - Volume 887 - Taehoon Kim, Gianluca Blois, James L. Best, Kenneth T. Christensen

We explore the ability of anisotropic permeable substrates to reduce turbulent skin friction, studying the influence that these substrates have on the overlying turbulence. For this, we perform direct numerical simulations of channel flows bounded by permeable substrates. The results confirm theoretical predictions, and the resulting drag curves are similar to those of riblets. For small permeabilities, the drag reduction is proportional to the difference between the streamwise and spanwise permeabilities. This linear regime breaks down for a critical value of the wall-normal permeability, beyond which the performance begins to degrade. We observe that the degradation is associated with the appearance of spanwise-coherent structures, attributed to a Kelvin–Helmholtz-like instability of the mean flow. This feature is common to a variety of obstructed flows, and linear stability analysis can be used to predict it. For large permeabilities, these structures become prevalent in the flow, outweighing the drag-reducing effect of slip and eventually leading to an increase of drag. For the substrate configurations considered, the largest drag reduction observed is ${\approx}$ 20–25 % at a friction Reynolds number $\unicode[STIX]{x1D6FF}^{+}=180$ .

Turbulent flow overlying periodic arrays (cubic- and hexagonally-packed) of large hemispheres was examined experimentally. Flow in the vicinity of the individual roughness elements was successfully examined by conducting particle-image velocimetry measurements in a refractive-index matched flume where the refractive index of the working fluid matched that of the acrylic hemispheres. The spatial structure of flow in the roughness sublayer is spatially heterogeneous and significantly influenced by the topographic pattern of the hemispheres. However, structural coherence was observed outside the roughness sublayer, independent of the measurement location and packing arrangement. Consistent with previous studies, it appears that mean shear near the inflection point of the velocity profile plays an important role in generating high-intensity Reynolds shear stress events and the contribution of roughness-scale energy within the roughness sublayer was apparent in spatial spectra of velocity. In the outer layer, despite the small relative-submergence condition, first- and second- order velocity statistics in all rough-wall conditions showed outer-layer similarity.

Results of high-resolution particle-image velocimetry (PIV) measurements are presented to explore how turbulent flow overlying a permeable wall is linked to the underlying pore flow and how their interplay is controlled by the topography of the wall interface and wall thickness. Two permeable walls were constructed from uniform spherical elements (25.4 mm diameter) in a cubically packed arrangement (porosity ∼ 48%): one with two layers of spheres and the other with five layers. In addition, an impermeable rough wall with identical topography was considered as a baseline of comparison in order to explore the structural modifications imposed by permeability in the near-wall region. First- and second-order velocity statistics provide a quantitative assessment of such modifications of the local flow. A double-averaging approach allowed investigation of the global representation of the flow and assessment of conventional scaling parameters. A momentum deficit in the first pore layer and subsequent recovery beneath is observed, consistent with previous studies, as is a decay of the turbulent fluctuations. The transitional layer resides at the wall interface where free flow and pore flow interact, exchanging mass and momentum through intermittent turbulent events. Statistical investigation based on conditional averaging reveals that upwelling and down-welling flow events are associated with the passage of large-scale, low and high streamwise momentum free flow near the wall, respectively.

The turbulence characteristics within flows over water-worked gravel beds (WGBs) and screeded gravel beds (SGBs) were examined by measuring the instantaneous flow velocity field using a two-dimensional particle image velocimetry system. To compare the responses of a WGB and an SGB to velocity and various turbulence characteristics, the flow Froude number was kept identical for both the beds that remained immobile. The roughness structures of both the beds were measured using a laser scanner. The results showed that the bed surface roughness was higher in the WGB than in the SGB. However, the longest axis of the gravels of WGBs was oriented streamwise owing to the action of water work, but the gravels of SGBs were randomly poised. The distribution of bed roughness fluctuations was negatively skewed in the WGB and positively skewed in the SGB. Double averaging methodology was applied to analyze the flow parameters. In this paper, the vertical profiles of the double-averaged streamwise velocity and the turbulence parameters, specifically the spatially averaged (SA) Reynolds shear and normal stresses, form-induced shear and normal stresses, turbulent kinetic energy (TKE) and form-induced TKE fluxes, quadrant analysis of SA Reynolds shear stress, etc., are presented and analyzed critically by focusing on comparisons between a WGB and an SGB. A comparative study reveals that in the near-bed flow zone, the SGB underestimates the turbulence parameters compared to the WGB. Therefore, in order to represent the prototypical flow in laboratory, the experiments should be performed in a WGB.

In this study, macro-rough flows over beds with different permeability values are simulated using the large-eddy simulation, and the results are analysed by applying the double-averaging (DA) methodology. Spheres of different sizes and arrangements were used to form the beds, which are deemed to be permeable granular beds. The influence of bed permeability on the turbulence dynamics and structure is investigated. It was observed that the scales of the spanwise vortical structures over more permeable beds are larger than those over less permeable beds. This is attributed to large-scale spanwise-alternate strips of varying Reynolds shear stress (RSS), emerging from the surface of macro-rough elements for the permeable beds. The DA stress balance suggests that the time-averaged spanwise vortical structure leads to a damping in DA RSS and an unusual peak of the form-induced stress in the main flow. In the streamwise direction, both large turbulent structures that originate from the Kelvin–Helmholtz-type instability and small turbulent structures that are associated with the turbulent transport across the gaps of the roughness elements are more prevalent over highly permeable beds. Near the bed, the relative magnitude of turbulent events shows a transition from a ejections-dominating to sweeps-dominating zone with vertical distance. Further, several hydrodynamic characteristics normalized by inner scales (kinematic viscosity to shear velocity ratio) show a greater dependency on permeability Reynolds number than those normalized by sediment size. The study provides an insight into the mechanism of mass transfer near the fluid–particle interface, which is vital to benthic and aquatic ecology.

Understanding the mechanisms of solute transfer across the sediment-water interface plays a crucial role in water quality prediction and management. In this study, different arranged particles are used to form typical rough and permeable beds. Large Eddy Simulation (LES) is used to model the solute transfer from the overlying water to sediment beds. Three rough wall turbulence regimes, i.e., smooth, transitional and rough regime, are separately considered and the effects of bed roughness on solute transfer are quantitatively analyzed. Results show that the classic laws related to Schmidt numbers can well reflect the solute transfer under the smooth regime with small roughness Reynolds numbers. Under the transitional regime, the solute transfer coefficient (KL(+)) is enhanced and the effect of Schmidt number is weakened by increasing roughness Reynolds number. Under the rough regime, the solute transfer is suppressed by the transition layer (Brinkman layer) and controlled by the bed permeability. Moreover, it is found that water depth, friction velocity and bed permeability can be used to estimate the solute transfer velocity (KL) under the completely rough regime.

To investigate which component of the anisotropic permeability tensor of porous media influences turbulence over porous walls, direct numerical simulation of anisotropic porous-walled channel flows is performed by the D3Q27 multiple-relaxation-time lattice Boltzmann method. The presently considered anisotropic permeable walls have square pore arrays aligned with the Cartesian axes. Vertical, streamwise and spanwise pore arrays are systematically introduced to the walls to impose anisotropic permeability. Simulations are carried out at a friction Reynolds number of 111 and 230, which is based on the averaged friction velocity of the porous bottom and the smooth top walls. It is found that streamwise and spanwise permeabilities enhance turbulence whilst vertical permeability itself does not. In particular, the enhancement of turbulence is remarkable over porous walls with streamwise permeability. Over streamwise permeable walls, development of high- and low-speed streaks is prevented whilst large-scale intermittent patched patterns of ejection motions are induced. It is revealed by two-point correlation analysis that streamwise permeability allows the development of streamwise large-scale perturbations induced by Kelvin–Helmholtz instability. Spectral analysis reveals that this perturbation contributes to the enhancement of the Reynolds shear stress, leading to significant skin friction of the porous interface. Through the comparison between the two different Reynolds-number cases, it is found that, as the Reynolds number increases, the streamwise perturbation becomes larger and more organized. Consequently, owing to the enhancement of the large-scale perturbation, a significant Reynolds-number dependence of the skin friction of the porous interface can be observed over the streamwise permeable wall. It is also implied that the wavelength of the perturbation can be reasonably scaled by the outer-layer length scale.

To discuss the turbulent flow physics over porous walls, direct numerical simulation (DNS) of a porous-walled channel flow at the bulk Reynolds number of 3000 is performed by the D3Q27 multiple-relaxation time lattice Boltzmann method. The presently considered porous layer, whose porosity is 0.71, consists of interconnected staggered cube arrays. For understanding the influence of the wall permeability on turbulence, DNS of an impermeable rough walled channel flow is also conducted. By two-point autocorrelation, one-dimensional energy spectrum and proper orthogonal decomposition (POD) analyses, the existence and characteristics of the transverse pressure waves induced by the Kelvin-Helmholtz (K-H) instability over the porous and rough walls are elucidated. The structure, wave lengths and power spectra of the transverse waves are discussed in detail. The influence of the K-H instability on turbulence is also clarified.

A test coupon coated with light calcareous tubeworm fouling was scanned, scaled and reproduced for wind-tunnel testing to determine the equivalent sand grain roughness ks. It was found that this surface had a ks = 0.325 mm, substantially less than the previously reported values for light calcareous fouling. This result was used to predict the drag on a fouled full scale ship. To achieve this, a modified method for predicting the total drag of a spatially developing turbulent boundary layer (TBL), such as that on the hull of a ship, is presented. The method numerically integrates the skin friction over the length of the boundary layer, assuming an analytical form for the mean velocity profile of the TBL. The velocity profile contains the roughness (fouling) information, such that the prediction requires only an input of ks, the free-stream velocity (ship speed), the kinematic viscosity and the length of the boundary layer (the hull length). Using the equivalent sandgrain roughness height determined from experiments, a FFG-7 Oliver Perry class frigate is predicted to experience a 23% increase in total resistance at cruise, if its hull is coated in light calcareous tubeworm fouling. A similarly fouled very large crude carrier would experience a 34% increase in total resistance at cruise.

Tests were carried out to determine the velocity distribution and the hydraulic roughness in flows over 20 permeable beds made up of different sizes and gradings of spherical particles. Corresponding tests were carried out to determine the surface rugosity and the permeability of these beds. The investigation showed that the virtual zero of the velocity profile was depressed below the surface of the bed due to flow occurring in the permeable bed material. Despite this the hydraulic roughness of the permeable beds was higher than that for equivalent impermeable beds of the same surface rugosity. There was strong correlation between the hydraulic roughness of permeable beds and a simple parameter which included both a characteristic particle size of the bed material, and the permeability.

When the seepage flow in a highly permeable porous medium is accompanied by a turbulent free surface flow above it, an appreciable interaction between seepage flow and surface flow takes place. This interaction means mass and momentum exchanges between the surface flow and the seepage flow. The induced velocity fluctuation inside the porous medium contributes the momentum exchange and it plays an important role in determining the structure of the seepage flow. In this study, experiments are conducted to measure the velocity profile and the vertical mass transport in the porous medium beneath the free surface flow, and subsequently a macroscopic model is proposed to describe a seepage-flow velocity profile based on an eddy- viscosity assumption. (A)

Experimental researeli on flow over permeable surfaces is reported, in which flow over a permeable, rough surface is compared with flow over non-permeable, rough and smooth surfaces. The experiments were conducted in a wind tunnel using two permeable surfaces (Fig. 4) of relative thicknesses D/de = 2,73 and 9,67.Velocity profiles and their turbulent fluctuations (Fig. 2, Fig. 5 and Fig. 8) were measured with a constant-temperature hotfilm-anemometer. The universal velocity-defect law, eq. 2, was applied to obtain the shear velocity, u*.; and the law of the wall, eq. 1, was used to obtain the reference level (Fig. 3) and the roughness height, y', (Fig. 6); the impulse equation was used to check these results. The local resistance coefficient, e'f, versus the Reynolds number, Re, given in Fig. 7, may be considered as the resulting display of data. It is concluded that the boundary resistance of the tested permeable surface is higher than that of the non-permeable boundaries having identical roughness.

In order to understand the effects of the wall permeability on turbulence near a porous wall, flow field measurements are carried out for turbulent flows in a channel with a porous bottom wall by a two-component particle image velocimetry (PIV) system. The porous media used are three kinds of foamed ceramics which have almost the same porosity (∼0.8) but different permeability. It is confirmed that the flow becomes more turbulent over the porous wall and tends to be turbulent even at the bulk Reynolds number of Reb=1300 in the most permeable wall case tested. Corresponding to laminar to turbulent transition, the magnitude of the slip velocity on the porous wall is found to increase drastically in a narrow range of the Reynolds number. To discuss the effects of the wall roughness and the wall permeability, detailed discussions are made of zero-plane displacement and equivalent wall roughness for porous media. The results clearly indicate that the turbulence is induced by not only the wall roughness but the wall permeability. The measurements have also revealed that as Reb or the wall permeability increases, the wall normal fluctuating velocity near the porous wall is enhanced due to the effects of the wall permeability. This leads to the increase of the turbulent shear stress resulting in higher friction factors of turbulence over porous walls.

The main objectives of this study are to suggest a proper boundary condition at the
interface between a permeable block and turbulent channel flow and to investigate
the characteristics of turbulent channel flow with permeable walls. The boundary
condition suggested is an extended version of that applied to laminar channel flow
by Beavers & Joseph (1967) and describes the behaviour of slip velocities in the
streamwise and spanwise directions at the interface between the permeable block
and turbulent channel flow. With the proposed boundary condition, direct numerical
simulations of turbulent channel flow that is bounded by the permeable wall
are performed and significant skin-friction reductions at the permeable wall are
obtained with modification of overall flow structures. The viscous sublayer thickness
is decreased and the near-wall vortical structures are significantly weakened by the
permeable wall. The permeable wall also reduces the turbulence intensities, Reynolds
shear stress, and pressure and vorticity fluctuations throughout the channel except
very near the wall. The increase of some turbulence quantities there is due to the
slip-velocity fluctuations at the wall. The boundary condition proposed for the
permeable wall is validated by comparing solutions with those obtained from a separate
direct numerical simulation using both the Brinkman equation for the interior of a
permeable block and the Navier–Stokes equation for the main channel bounded by a
permeable block.

Careful reassessment of new and pre-existing data shows that recorded scatter in the hot-wire-measured near-wall peak in viscous-scaled streamwise turbulence intensity is due in large part to the simultaneous competing effects of the Reynolds number and viscous-scaled wire length l+. An empirical expression is given to account for these effects. These competing factors can explain much of the disparity in existing literature, in particular explaining how previous studies have incorrectly concluded that the inner-scaled near-wall peak is independent of the Reynolds number. We also investigate the appearance of the so-called outer peak in the broadband streamwise intensity, found by some researchers to occur within the log region of high-Reynolds-number boundary layers. We show that the ‘outer peak’ is consistent with the attenuation of small scales due to large l+. For turbulent boundary layers, in the absence of spatial resolution problems, there is no outer peak up to the Reynolds numbers investigated here (Reτ = 18830). Beyond these Reynolds numbers – and for internal geometries – the existence of such peaks remains open to debate. Fully mapped energy spectra, obtained with a range of l+, are used to demonstrate this phenomenon. We also establish the basis for a ‘maximum flow frequency’, a minimum time scale that the full experimental system must be capable of resolving, in order to ensure that the energetic scales are not attenuated. It is shown that where this criterion is not met (in this instance due to insufficient anemometer/probe response), an outer peak can be reproduced in the streamwise intensity even in the absence of spatial resolution problems. It is also shown that attenuation due to wire length can erode the region of the streamwise energy spectra in which we would normally expect to see kx−1 scaling. In doing so, we are able to rationalize much of the disparity in pre-existing literature over the kx−1 region of self-similarity. Not surprisingly, the attenuated spectra also indicate that Kolmogorov-scaled spectra are subject to substantial errors due to wire spatial resolution issues. These errors persist to wavelengths far beyond those which we might otherwise assume from simple isotropic assumptions of small-scale motions. The effects of hot-wire length-to-diameter ratio (l/d) are also briefly investigated. For the moderate wire Reynolds numbers investigated here, reducing l/d from 200 to 100 has a detrimental effect on measured turbulent fluctuations at a wide range of energetic scales, affecting both the broadband intensity and the energy spectra.

We review the experimental evidence on turbulent flows over rough walls. Two parameters are important: the roughness Reynolds number k + s , which mea-sures the effect of the roughness on the buffer layer, and the ratio of the boundary layer thickness to the roughness height, which determines whether a logarithmic layer survives. The behavior of transitionally rough surfaces with low k + s depends a lot on their geometry. Riblets and other drag-reducing cases belong to this regime. In flows with δ/k 50, the effect of the roughness extends across the boundary layer, and is also variable. There is little left of the original wall-flow dynamics in these flows, which can perhaps be better described as flows over obstacles. We also review the evidence for the phenomenon of d-roughness. The theoretical arguments are sound, but the experimental evidence is inconclusive. Finally, we discuss some ideas on how rough walls can be modeled without the detailed computation of the flow around the roughness elements themselves.

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