Smooth-wall Turbulent Boundary Layer Research Articles

Turbulent dispersion of a passive scalar in a smooth-wall turbulent boundary layer

The scalar dispersion of a ground-level point-source plume in a smooth-wall turbulent boundary layer is experimentally investigated using simultaneous particle image velocimetry and planar laser-induced fluorescence techniques. In the near-source region, the viscous sublayer is observed to trap dye, while in the far field, the half-width, vertical profiles and peak decay of the mean concentration and concentration variance exhibit self-similar behaviour and collapse with empirical relations. Full two-dimensional maps of the turbulent scalar fluxes show a net transport direction of upward and towards the incoming flow, with the vertical profiles collapsing well with Weibull-type exponential functions and the decay of peaks following power laws. Using the first-order gradient transport to model the turbulent scalar fluxes, maps of the anisotropic turbulent diffusivity tensor and an effective turbulent diffusivity coefficient are calculated. The streamwise and wall-normal turbulent scalar fluxes are driven dominantly by the wall-normal concentration gradient. The turbulent Schmidt number, relating the turbulent diffusivity and the turbulent (eddy) viscosity calculated using the Boussinesq hypothesis, varies with wall-normal position with values of the order of unity in the logarithmic layer.

Turbulence characteristics of the ship air-wake with two different topside arrangements and inflow conditions

We investigate the effect of the Atmospheric Boundary Layer (ABL) and vessel topside arrangement on ship air-wake flow. The investigation is performed by comparing experimental results with two inflow conditions: a simulated ABL and a smooth-wall flat-plate turbulent boundary layer; and two simplified ship models: Simplified Frigate Ship model 2 (SFS2) and NATO-Generic Destroyer (NATO-GD). Particle Image Velocimetry (PIV) and point measurements over the landing deck center-line show that the ABL inflow increases the flow fluctuations but reduces the length of the wake. Furthermore, we observed an enhancement of turbulence energy on the ship landing deck when the ABL is simulated. The data also show that the topside arrangement, especially at the hangar elevation upstream of the landing deck, plays an essential role in the air-wake over the ship center line. There are significant differences in the flow re-circulation regions, turbulence structure and energy content. Based on a turbulence structure and energy spectrum analysis, we highlight regions with a possible increased safety risk for both models. Over the SFS2 center line, regions with an increased safety risk are located directly above the landing deck. Meanwhile, on the NATO-GD center line, these regions are located above the hangar elevation.

Fluctuating Pressure Beneath Smooth Wall Boundary Layers in Nonequilibrium Pressure Gradients

An experimental investigation is made of smooth wall turbulent boundary layers under a family of continually varying streamwise pressure gradient distributions. In general, the effects of these pressure gradient cases on the boundary layer are found to be nonlocal and dependent on upstream history effects. However, the friction Reynolds number grows independent of applied pressure gradient and appears to be dependent only on the origin of the turbulent boundary layer. Special attention is paid to the statistics of the fluctuating pressure on the immersed surface, and it is found that there is a spectral-region-dependent relationship between pressure gradient and the fluctuating wall pressure, indicating the lack of a universal overlap region and providing insight into the impact of pressure gradient history on turbulence evolution. The classical viscous inner scaling of the pressure spectra appears universal as does a proposed mixed variable low-frequency scaling. The impact of the pressure gradients on the pressure space-time correlations and convection velocities is more locally dependent. The implications of these observations on our understanding of nonequilibrium flows are explored, and it is postulated that such flows may be describable as a three-dimensional space governing the mean growth, pressure gradient effect, and nonequilibrium effect, respectively.

Characteristics of fluctuating wall-shear stress in a turbulent boundary layer at low-to-moderate Reynolds number

Particle Image Velocimetry is used to measure the wall-shear stress (WSS) in a smooth-wall turbulent boundary layer at low-to-moderate Reynolds number. The fluctuating intensity of WSS is found to follow an empirical log-law with Re due to the effect of outer-layer large scale motions (LSMs) on the wall. A scale decomposition analysis suggests that the LSMs leave a mild footprint effect on the WSS in the present Re range. The amplitude modulation effect is inferred to play a more prominent role in affecting the characteristics of fluctuating WSS.

Characterization of the Spatio-Temporal Response of a Turbulent Boundary Layer to Dynamic Roughness

The spatio-temporal response of a smooth-wall turbulent boundary layer to two-dimensional dynamic roughness forcing was investigated using flow structure-resolved particle image velocimetry. While such a flow has been extensively studied through pointwise temporal measurements, we characterize the streamwise-spatial nature of the streamwise and wall-normal velocity components of the synthetic mode excited by the roughness, which had not been previously fully characterized. Investigation of the spanwise variation of the response confirms a broad extent of two-dimensional characteristics in the streamwise and spanwise directions. Spatial amplitude modulation is observed in the synthetic structure and investigated directly through the spatial spectra. A parametric study of the influences of forcing frequency (and roughness height) leads to an empirical relationship between input frequency and resultant streamwise spatial lengthscale, which is proposed to extend the usefulness of dynamic roughness as a well-characterized input by which to probe the structure and dynamics of wall turbulence. In turn, dynamic roughness forcing may be used to study the response of complex fluid systems to these deterministic structures and explore the efficacy of possible flow control strategies in a directed manner.

Wall-Normal Variation of Spanwise Streak Spacing in Turbulent Boundary Layer With Low-to-Moderate Reynolds Number.

Low-speed streaks in wall-bounded turbulence are the dominant structures in the near-wall turbulent self-sustaining cycle. Existing studies have well characterized their spanwise spacing in the buffer layer and below. Recent studies suggested the existence of these small-scale structures in the higher layer where large-scale structures usually receive more attention. The present study is thus devoted to extending the understanding of the streak spacing to the log layer. An analysis is taken on two-dimensional (2D) wall-parallel velocity fields in a smooth-wall turbulent boundary layer with = 440∼2400, obtained via either 2D Particle Image Velocimetry (PIV) measurement taken here or public Direct Numerical Simulation (DNS). Morphological-based streak identification analysis yields a -independent log-normal distribution of the streak spacing till the upper bound of the log layer, based on which an empirical model is proposed to account for its wall-normal growth. The small-scale part of the spanwise spectra of the streamwise fluctuating velocity below = 100 is reasonably restored by a synthetic simulation that distributes elementary streak units based on the proposed empirical streak spacing model, which highlights the physical significance of streaks in shaping the small-scale part of the velocity spectra beyond the buffer layer.

Buoyancy effects on large-scale motions in convective atmospheric boundary layers: implications for modulation of near-wall processes

A number of recent studies have demonstrated the existence of so-called large- and very-large-scale motions (LSM, VLSM) that occur in the logarithmic region of inertia-dominated wall-bounded turbulent flows. These regions exhibit significant streamwise coherence, and have been shown to modulate the amplitude and frequency of small-scale inner-layer fluctuations in smooth-wall turbulent boundary layers. In contrast, the extent to which analogous modulation occurs in inertia-dominated flows subjected to convective thermal stratification (low Richardson number) and Coriolis forcing (low Rossby number), has not been considered. And yet, these parameter values encompass a wide range of important environmental flows. In this article, we present evidence of amplitude modulation (AM) phenomena in the unstably stratified (i.e. convective) atmospheric boundary layer, and link changes in AM to changes in the topology of coherent structures with increasing instability. We perform a suite of large eddy simulations spanning weakly ($-z_{i}/L=3.1$) to highly convective ($-z_{i}/L=1082$) conditions (where $-z_{i}/L$ is the bulk stability parameter formed from the boundary-layer depth $z_{i}$ and the Obukhov length $L$) to investigate how AM is affected by buoyancy. Results demonstrate that as unstable stratification increases, the inclination angle of surface layer structures (as determined from the two-point correlation of streamwise velocity) increases from $\unicode[STIX]{x1D6FE}\approx 15^{\circ }$ for weakly convective conditions to nearly vertical for highly convective conditions. As $-z_{i}/L$ increases, LSMs in the streamwise velocity field transition from long, linear updrafts (or horizontal convective rolls) to open cellular patterns, analogous to turbulent Rayleigh–Bénard convection. These changes in the instantaneous velocity field are accompanied by a shift in the outer peak in the streamwise and vertical velocity spectra to smaller dimensionless wavelengths until the energy is concentrated at a single peak. The decoupling procedure proposed by Mathis et al. (J. Fluid Mech., vol. 628, 2009a, pp. 311–337) is used to investigate the extent to which amplitude modulation of small-scale turbulence occurs due to large-scale streamwise and vertical velocity fluctuations. As the spatial attributes of flow structures change from streamwise to vertically dominated, modulation by the large-scale streamwise velocity decreases monotonically. However, the modulating influence of the large-scale vertical velocity remains significant across the stability range considered. We report, finally, that amplitude modulation correlations are insensitive to the computational mesh resolution for flows forced by shear, buoyancy and Coriolis accelerations.

Effects of a Fence on Pollutant Dispersion in a Boundary Layer Exposed to a Rural-to-Urban Transition

Simultaneous particle-image velocimetry and laser-induced fluorescence combined with large-eddy simulations are used to investigate the flow and pollutant dispersion behaviour in a rural-to-urban roughness transition. The urban roughness is characterized by an array of cubical obstacles in an aligned arrangement. A plane fence is added one obstacle height h upstream of the urban roughness elements, with three different fence heights considered. A smooth-wall turbulent boundary layer with a depth of 10h is used as the approaching flow, and a passive tracer is released from a uniform line source 1h upstream of the fence. A shear layer is formed at the top of the fence, which increases in strength for the higher fence cases, resulting in a deeper internal boundary layer (IBL). It is found that the mean flow for the rural-to-urban transition can be described by means of a mixing-length model provided that the transitional effects are accounted for. The mixing-length formulation for sparse urban canopies, as found in the literature, is extended to take into account the blockage effect in dense canopies. Additionally, the average mean concentration field is found to scale with the IBL depth and the bulk velocity in the IBL.

Modulating the Near-Wall Velocity Fields in Wall-Bounded Turbulence via Discrete Surface Roughness

The present work investigates the effect of discrete surface roughness, which falls in the transitionally rough regime, on the near-wall velocity fields of a smooth-wall turbulent boundary layer with zero pressure gradient. A spanwise array of cylindrical elements, whose diameters were and heights were , were attached onto the wall with spanwise spacing of . Three roughness Reynolds numbers , 1000, and 1500 were studied, and the ratio between the roughness height and the boundary-layer thickness was . Two-dimensional velocity fields in multiple wall-parallel planes at were measured by two-dimensional particle image velocimetry. For each case, it is found that roughness elements always introduce -shaped low-speed regions in the near-wall mean velocity fields by direct wake interaction, in the downstream of which a phase shift occurs to form one high-speed mean streak with reduced streamwise velocity fluctuation intensity behind each roughness element, marking the onset of the modulation effect on the mean velocity fields. Further analysis on the swirling strength fields suggests that such a modulation effect can be attributed to the roughness-introduced streamwise vortex pairs, which compete with hairpin vortices shedding from the top of the roughness elements and promote the phase shift in a bottom-up way.

Turbulence investigation in the roughness sub-layer of a near wall flow

The turbulence behaviour along a wall roughened by pyramidal elements was analysed in the region extending from the apex of the roughness elements up to the external limit of the roughness sub-layer. The data used for the analysis were obtained by particle image velocimetry technique. The rough wall turbulent boundary layer flow is characterized by a relatively low Reynolds number. All the results on the rough wall were compared with data referring to the canonical flow on a smooth wall turbulent boundary layer. Mean values and turbulence quantities for the two flows collapse when approaching the external limit of the roughness sublayer. The quadrant analysis of the Reynolds shear stress, in the region near the surface, shows that the contribution of the sweep motions is about equivalent for the two flows (except for wall distances lower than 40 viscous units). The contribution of the ejection motions appears to be more important over the smooth wall than over the rough wall with increasing differences approaching the wall. The probability density functions of the streamwise fluctuating velocity field for the rough wall case appear to be positively skewed in the zone very close to the pyramid apex, in contrast with the behavior observed for the smooth wall case at corresponding distances from the wall. The integral and Taylor scales for the rough wall case appear to be strongly reduced by the presence of the roughness, while the Kolmogorov microscale shows higher values.

Pollutant Dispersion in Boundary Layers Exposed to Rural-to-Urban Transitions: Varying the Spanwise Length Scale of the Roughness

Both large-eddy simulations (LES) and water-tunnel experiments, using simultaneous stereoscopic particle image velocimetry and laser-induced fluorescence, have been used to investigate pollutant dispersion mechanisms in regions where the surface changes from rural to urban roughness. The urban roughness was characterized by an array of rectangular obstacles in an in-line arrangement. The streamwise length scale of the roughness was kept constant, while the spanwise length scale was varied by varying the obstacle aspect ratio l / h between 1 and 8, where l is the spanwise dimension of the obstacles and h is the height of the obstacles. Additionally, the case of two-dimensional roughness (riblets) was considered in LES. A smooth-wall turbulent boundary layer of depth 10h was used as the approaching flow, and a line source of passive tracer was placed 2h upstream of the urban canopy. The experimental and numerical results show good agreement, while minor discrepancies are readily explained. It is found that for l/h=2 the drag induced by the urban canopy is largest of all considered cases, and is caused by a large-scale secondary flow. In addition, due to the roughness transition the vertical advective pollutant flux is the main ventilation mechanism in the first three streets. Furthermore, by means of linear stochastic estimation the mean flow structure is identified that is responsible for street-canyon ventilation for the sixth street and onwards. Moreover, it is shown that the vertical length scale of this structure increases with increasing aspect ratio of the obstacles in the canopy, while the streamwise length scale does not show a similar trend.

Stable Stratification Effects on Flow and Pollutant Dispersion in Boundary Layers Entering a Generic Urban Environment

Large-eddy simulations (LES) are used to investigate the effect of stable stratification on rural-to-urban roughness transitions. Smooth-wall turbulent boundary layers are subjected to a generic urban roughness consisting of cubes in an in-line arrangement. Two line sources of pollutant are added to investigate the effect on pollutant dispersion. Firstly, the LES method is validated with data from wind-tunnel experiments on fully-developed flow over cubical roughness. Good agreement is found for the vertical profiles of the mean streamwise velocity component and mean Reynolds stress. Subsequently, roughness transition simulations are done for both neutral and stable conditions. Results are compared with fully-developed simulations with conventional double-periodic boundary conditions. In stable conditions, at the end of the domain the streamwise velocity component has not yet reached the fully-developed state even though the surface forces are nearly constant. Moreover, the internal boundary layer is shallower than in the neutral case. Furthermore, an investigation of the turbulence kinetic energy budget shows that the buoyancy destruction term is reduced in the internal boundary layer, above which it is equal to the undisturbed (smooth wall) value. In addition, in stable conditions pollutants emitted above the urban canopy enter the canopy farther downstream due to decreased vertical mixing. Pollutants emitted below the top of the urban canopy are 85 % higher in concentration in stable conditions mostly due to decreased advection. If this is taken into account concentrations remain 17 % greater in stable conditions due to less rapid internal boundary-layer growth. Finally, it is concluded that in the first seven streets the vertical advective pollutant flux is significant, in contrast to the fully-developed case.

Self-preservation in a zero pressure gradient rough-wall turbulent boundary layer

A self-preservation (SP) analysis is carried out for a zero pressure gradient (ZPG) rough-wall turbulent boundary layer with a view to establishing the requirements of complete SP (i.e. SP across the entire layer) and determining if these are achievable. The analysis shows that SP is achievable in certain rough-wall boundary layers (irrespectively of the Reynolds number$Re$), when the mean viscous stress is zero or negligible compared to the form drag across the entire boundary layer. In this case, the velocity scale$u^{\ast }$must be constant, the length scale$l$should vary linearly with the streamwise distance$x$and the roughness height$k$must be proportional to$l$. Although this result is consistent with that of Rotta (Prog. Aeronaut. Sci., vol. 2 (1), 1962, pp. 1–95), it is derived in a more rigorous manner than the method employed by Rotta. Further, it is noted that complete SP is not possible in a smooth-wall ZPG turbulent boundary layer. The SP conditions are tested against published experimental data on both a smooth wall (Kulandaivelu, 2012, PhD thesis, The University of Melbourne) and a rough wall, where the roughness height increases linearly with$x$(Kamedaet al.,J. Fluid Sci. Technol., vol. 3 (1), 2008, pp. 31–42). Complete SP in a ZPG rough-wall turbulent boundary layer seems indeed possible when$k\propto x$.

Drag of a turbulent boundary layer with transverse 2D circular rods on the wall

In this paper, we present the results of a turbulent boundary layer developing over a rod-roughened wall with a spacing of \(\lambda /k = 8\) (\(\lambda\) is the spacing between two adjacent roughness elements, and \(k\) is the rod diameter). Static pressure measurements are taken around a single roughness element to accurately determine the friction velocity, \(U_\tau\) and the error in the origin, \(d_0\), which are the two prominent issues that surround rough-wall boundary layers. In addition, velocity measurements are taken at several streamwise locations using hot-wire anemometry to obtain \(C_\mathrm{f}\) from the momentum integral equation. Results showed that both methods give consistent values for \(U_\tau\), indicating that the contribution of the viscous drag over this rough wall is negligible. This supports the results of Perry et al. (J Fluid Mech 177:437–466, 1969) and Antonia and Luxton (J Fluid Mech 48(04):721–761, 1971) in a boundary layer and of Leonardi et al. (2003) in a channel flow but does not agree with those of Furuya et al. (J Fluids Eng 98(4):635–643, 1976). The results show that both \(U_{\tau }\) and \(d_0\) can be unambiguously measured on this particular rough wall. This paves the way for a proper comparison between the boundary layer developing over this wall and the smooth-wall turbulent boundary layer.

On the homogenization of turbulent flow structures in the wake of a model wind turbine

The structure of flow turbulence, measured experimentally, in the wake of a model wind turbine is investigated here through higher order scale-dependent statistics of the velocity increments and compared to the smooth wall turbulent boundary layer (base flow) case. The wind turbine wake flow is observed to possess higher turbulent kinetic energy, when compared to the base flow, though it contains more homogenized scale-dependent velocity increments, as confirmed via magnitude cumulant analysis of the streamwise velocities. Along with a reduction in intermittency (a measure of inhomogeneity) in the wake of the wind turbine, the asymmetry of the probability density functions of the velocity increments is also observed to be reduced. This is interpreted in terms of scale decoupling mechanisms and attenuating interactions and non-local energy transfer. In other words, wind turbines reduce the intermittency and asymmetry in the wake flow by breaking and/or deflecting the large-scale flow structures of the incoming flow, thus rendering the structure of the velocity fluctuations more homogenized as compared to the base flow. Experiments were conducted in a large scale, boundary layer wind tunnel at the St. Anthony Falls Laboratory.

Large-eddy simulation of the zero-pressure-gradient turbulent boundary layer up to Reθ = O(1012)

AbstractA near-wall subgrid-scale (SGS) model is used to perform large-eddy simulation (LES) of the developing, smooth-wall, zero-pressure-gradient flat-plate turbulent boundary layer. In this model, the stretched-vortex, SGS closure is utilized in conjunction with a tailored, near-wall model designed to incorporate anisotropic vorticity scales in the presence of the wall. Large-eddy simulations of the turbulent boundary layer are reported at Reynolds numbers ${\mathit{Re}}_{\theta } $ based on the free-stream velocity and the momentum thickness in the range ${\mathit{Re}}_{\theta } = 1{0}^{3} \text{{\ndash}} 1{0}^{12} $. Results include the inverse square-root skin-friction coefficient, $ \sqrt{2/ {C}_{f} } $, velocity profiles, the shape factor $H$, the von Kármán ‘constant’ and the Coles wake factor as functions of ${\mathit{Re}}_{\theta } $. Comparisons with some direct numerical simulation (DNS) and experiment are made including turbulent intensity data from atmospheric-layer measurements at ${\mathit{Re}}_{\theta } = O(1{0}^{6} )$. At extremely large ${\mathit{Re}}_{\theta } $, the empirical Coles–Fernholz relation for skin-friction coefficient provides a reasonable representation of the LES predictions. While the present LES methodology cannot probe the structure of the near-wall region, the present results show turbulence intensities that scale on the wall-friction velocity and on the Clauser length scale over almost all of the outer boundary layer. It is argued that LES is suggestive of the asymptotic, infinite Reynolds number limit for the smooth-wall turbulent boundary layer and different ways in which this limit can be approached are discussed. The maximum ${\mathit{Re}}_{\theta } $ of the present simulations appears to be limited by machine precision and it is speculated, but not demonstrated, that even larger ${\mathit{Re}}_{\theta } $ could be achieved with quad- or higher-precision arithmetic.

Buffer layer structures associated with extreme wall stress events in a smooth wall turbulent boundary layer

Three-dimensional velocity distributions and corresponding wall stresses are measured concurrently in the inner part of a turbulent boundary layer over a smooth wall using digital holographic microscopy. The measurements are performed in a square duct channel flow atReδ= 50000 andReτ= 1470. A spatial resolution of 3–8 wall units (δυ= μm) in streamwise and spanwise directions and 1 wall unit in the wall-normal direction are sufficient for resolving buffer layer structures and for measuring the instantaneous wall shear stresses from velocity gradients in the viscous sublayer. Mean velocity and Reynolds stress profiles agree well with previous publications. Rudimentary observations classify the buffer layer three-dimensional flow into (i) a pair of counter-rotating inclined vortices, (ii) multiple streamwise vortices, some of them powerful, and (iii) no apparent buffer layer structures. Each appears in about one third of the realizations. Conditional sampling based on local wall shear stress maxima and minima reveals two types of three-dimensional buffer layer structures that generate extreme stress events. The first structure develops as spanwise vorticity lifts from the wall abruptly and within a short distance of about 10 wall units, creating initially a vertical arch. Its only precursors are a slight velocity deficit that does not involve an inflection point and low levels of vertical vorticity. This arch is subsequently stretched vertically and in the streamwise direction, culminating in formation of a pair of inclined, counter-rotating vortices with similar strength and inclination angle exceeding 45°. A wall stress minimum exists under the point of initial lifting. A pair of stress maxima develops 35δυdownstream, on the outer (downflow) sides of the vortex pair and is displaced laterally by 35–40δυfrom the minimum. This flow structure exists not only in the conditionally averaged field but in the instantaneous measurement as well and appears in 16.4% of the realizations. Most of the streamwise velocity deficit generated by this phenomenon develops during this initial lifting, but it persists between the pair of vortices. Distribution of velocity fluctuations shows that spanwise transport of streamwise momentum plays a dominant role and that vertical transport is small under the vortices. In other regions, e.g. during initial lifting, and between the vortices, vertical transport dominates. The characteristics of this structure are compared to early experimental findings, highlighting similarities and differences. Abundance of pairs of streamwise vortices with similar strength is inconsistent with conclusions of several studies based on analysis of direct numerical simulation (DNS) data. The second buffer layer structure generating high wall stresses is a single, predominantly streamwise vortex, with characteristic diameter of 20–40δυand inclination angle of 12°. It generates an elongated, strong stress maximum on one side and a weak minimum on the other and has been observed in 20.4% of the realizations. Except for a limited region of sweep above the high-stress region, this low-lying vortex mostly induces spanwise momentum transport. This structure appears to be similar to those observed in several numerical studies.

Realization of the Turbulent Boundary Layer over the Rough Wall Satisfied the Conditions of Complete Similarity and Its Mean Flow Quantities

Mean flow quantities have been investigated for the equilibrium boundary layer evolving over the rough wall with a roughness height that is proportional to streamwise distance. The wall shear stress measured by drag balance with a floating element device of a zero displacement mechanism. The local skin friction coefficient is independent of both streamwise distance and momentum thickness Reynolds number and has a value of 0.00826. The boundary layer thickness is proportional to the streamwise distance. The relative roughness height then maintains a constant value. The log-law profile has the same slope of that of the smooth wall turbulent boundary layer in the logarithmic liner part. The value of the roughness function increases in the streamwise direction. The wake parameter approaches to a constant value of approximately 0.70. In addition, the value is consistent with the result determined from the analytical method using the momentum integral equation and Coles's wake law. For the analytical result, the wake parameter decreases with increasing friction parameter.

Particle image velocimetry study of turbulent flow over transverse square ribs in an asymmetric diffuser

The objective of this paper is to study the combined effects of rib roughness and adverse pressure gradient produced in an asymmetric diffuser on turbulent flows. The two-dimensional asymmetric diffuser was comprised of a straight flat floor and a curved roof. The diffuser section was preceded and followed by straight parallel walls. The complete test conditions were comprised of a reference smooth floor and repeated arrays of transverse square ribs glued onto the floor to produce three pitch-to-height ratios, p∕k=3, 6, and 8. The curved roof was kept smooth in all the experiments. For each of the four test conditions, a particle image velocimetry was used to conduct detailed velocity measurements within the diverging section and also at locations upstream and downstream of the diverging section. From these measurements, the mean streamlines, mean velocities, turbulent intensities, Reynolds shear stress, and production terms in the transport equations for the turbulent kinetic energy and Reynolds stresses were obtained. The results obtained in the diverging section showed that the boundary layers that developed on the ribs thickened considerably at the expense of those adjacent to the roof opposite to the ribs. The streamlines and mean velocity profiles over the ribs showed that adverse pressure gradient increased the roughness sublayer substantially. Adverse pressure gradient and rib roughness also increased the drag and levels of the turbulent intensities, Reynolds shear stress and production terms compared to smooth-wall zero pressure gradient turbulent boundary layer. It appears, however, that adverse pressure gradient enhanced turbulence more effectively than it increased drag.

Realization of the Turbulent Boundary Layer over the Rough Surface Satisfied the Conditions of Complete Similarity and Its Mean Flow Quantities

Mean flow quantities have been investigated for the equilibrium boundary layer developing over the rough surface with roughness height proportional to streamwise distance. The wall shear stress was measured by direct measurement with a floating element device of zero displacement mechanism. Local skin friction coefficient is independent of two parameters both streamwise coordinate and Reynolds number based on momentum thickness and has a value of 0.0826. The boundary layer thickness is proportional to the streamwise distance. Then, the relative roughness height keeps a constant value. The log-law profile has same slope of that for the smooth wall turbulent boundary layer in the logarithmic linear part. The value of the roughness function increases in the streamwise direction. The wake parameter approaches to the constant value of about 0.7. Also, the value is consistent with the result deduced from the analytical method used both the momentum integral equation and Coles's wake law. Then, the wake parameter decreases with increasing the friction parameter.