Reynolds Stress Anisotropy in Open-Channel Flow

This paper reports the results of an experimental study characterizing turbulence and turbulence anisotropy in smooth and rough shallow open-channel flows. The rough bed consists of a train of two-dimensional transverse square ribs with a ratio of the roughness height (k) to the total depth of flow (d) equal to 0.10. Three rib separations (p/k) of 4.5, 9, and 18 were examined. Here, p is the pitch between consecutive roughness elements and was varied to reproduce the classical condition of d- and k-type roughness. For each case, two-component velocity measurements were obtained using a laser Doppler velocimetry system at two locations for p/k = 4.5 and 9: on the top of the rib and above the cavity, and an additional location for p/k = 18. The measurements allow examination of the local variations of the higher-order turbulent moments, stress ratios as well as turbulence anisotropy. Large variations of the turbulence intensities, Reynolds shear stress, turbulent kinetic energy and turbulence production are found for y1<3k. In this region, the flow is more directly influenced by the shear layers from the preceding ribs. The higher-order moments appear to be similar for all rough surfaces beyond y1 ≈ 7k. In the outer layer (y1>3k), all higher-order turbulent moments for the k-type roughness show a substantial increase due to the complex interactions between the roughness and the remnants overlying shear layers shed from succeeding ribs. Analysis of the components of the Reynolds stress anisotropy tensor shows that at p/k = 18, the flow at y1<5k tends to be more isotropic which implies that for this particular case, the effect of the roughness density could also be important. On the smooth bed, at the shallower depths, the correlation coefficient near the free surface increases and turbulence tends to become less anisotropic.     

Response of Velocity and Turbulence to Sudden Change of Bed Roughness in Open-Channel Flow

The experimental study shows how an open-channel flow would respond to a sudden change (from smooth to rough) in bed roughness. Using a two-dimensional acoustic Doppler velocimeter and a laser Doppler velocimeter, the velocity, turbulent intensities, and Reynolds stress profiles at different locations along a laboratory flume were measured. Additionally, the water surface profile was also measured using a capacitance-type wave height meter. The experimental data show the formation of an internal boundary layer as a result of the step change in bed roughness. The data show that this boundary layer grows much more rapidly than that formed in close-conduit flows. The results also show that the equivalent bed roughness, bed-shear stress, turbulent intensities, and Reynolds stress change gradually over a transitional region, although the bed roughness changes abruptly. The behavior is different from that observed in close-conduit flows, where an overshooting property—which describes the ability of the bed-shear stress to attain a high-peak value over the section with the larger roughness, was reported. A possible reason for the difference is the variation of the water surface profile when an open-channel flow is subjected to a sudden change in bed roughness.     

Characteristics of Turbulent Flow in Submerged Jumps on Rough Beds

The results of an experimental investigation on the flow field in submerged jumps on horizontal rough beds, detected by an acoustic Doppler velocimeter, are presented. Experiments were conducted for the conditions of submerged jumps, having submergence factors from 0.96 to 1.85 and jet Froude numbers from 2.58 to 4.87, over rough beds of Nikuradse’s equivalent sand roughness equaling 0.49, 0.8, 1.86, and 3?mm. The vertical distributions of time-averaged velocity components, turbulence intensity components, and Reynolds stress at different streamwise distances from the sluice opening and the horizontal distribution of bed-shear stress are plotted. Vector plots of the flow field show that the rate of decay of jet velocity in a submerged jump increases with increase in bed roughness. The flow characteristics on rough beds, being different from those on smooth bed, are discussed from the point of view of similarity, growth of the length scale, and decay of the velocity and turbulence characteristics scales. The most important observation is that the flow in the fully developed zone is found to be self-preserving.     

Distribution of Bed Shear Stress in Rotating Circular Flume

Distributions of bed shear stress across the width of a rotating circular flume with smooth and rough bed surfaces were obtained by measurement and model prediction. Results with flows over smooth beds showed that the flow in the central part may be considered to be two-dimensional and that effects of flow depth over the operating range of the flume are minor for flow depths not exceeding 0.14 m. For rough beds, the bed shear stress distributions were found to be skewed toward the inner wall. This can be corrected if a compensating roughness is added to the bottom of the ring. Such measures are also effective for flumes with smooth beds. Measured bed shear stress distributions agreed well with the predicted distributions for smooth beds and reasonably well for rough beds. The modified Preston tube, for measurement of bed shear stress in flows over rough beds, was found to give promising results. Further tests are required to completely define the uncertainty in bed shear stress measurements made with this instrument.     

Analyzing Turbulence Intensity in Gravel Bed Channels

In this paper, the results of an experimental investigation of the turbulence intensity in gravel bed channels are described. The runs were carried out by measuring, with an acoustic Doppler velocimeter, the turbulence intensity profile along six verticals of a given cross section in a laboratory flume. The analysis of the measured intensity distributions has shown the existence of two different regions, above and below the tops of the roughness elements, in which different intensity profiles occur. Furthermore, the measured profiles have shown a maximum of the turbulence intensity that decreases for increasing values of the roughness height, confirming that the turbulence damping efficiency increases when the roughness elements protrude inside the flow. The applicability of Nezu’s relationship (derived for a hydraulically smooth bed) for the experimental intensity profiles above the roughness elements is positively tested. Finally a new intensity distribution for a rough bed, applicable to the whole water depth, is proposed. In this profile, two coefficients having a known physical meaning (the maximum turbulence intensity and the depth at which this maximum is located) appear.     

Apparent Roughness in Wave–Current Flow: Implication for Coastal Studies

High turbulence intensities generated by waves in the wave bottom boundary layer affect the mean current velocity and should be taken into account for calculation of currents in the presence of waves. This influence of the wave-induced turbulence on the mean current can be schematized by introducing an “apparent” bed roughness, which is larger than the physical bottom roughness. Apparent bed roughness is defined here as roughness that provides the same depth-mean velocity for current alone configuration as for the wave–current flow. A one-dimensional vertical “k–l” turbulence closure model that allows detailed time dependent flow modeling has been applied for apparent roughness computations. The domain of variable parameters is chosen according to the Israeli near-shore conditions. An approximate expression for apparent bed roughness calculations as a function of wave and current parameters based on this turbulence closure model is derived. Simulation of flow patterns on the Tel Aviv coast using the three-dimensional Costal and Marine Engineering Research Institute flow model and implementing apparent roughness maps, calculated by the approximate expression, has been performed.     

Effects of Bed Roughness on Flow around Bed-Mounted Cylinders in Open Channels

This paper presents the results of an experimental study of flow around cylindrical objects on a rough bed in an open channel. This is an extension of a previous study of flow around cylinders on a smooth bed. The purpose of this study is to explore the effects of bed roughness on the characteristics of the deflected flow around cylindrical objects and the resulting bed-shear stress distributions. Similar to the previous study cylindrical objects of equal diameter and four heights were tested under similar flow conditions producing four different levels of submergence. Bed shear stress and deflected flow velocities were measured by a thin yaw-type Preston probe after a set of flow visualization tests. Flow visualization tests showed that the horse-shoe vortex systems on the rough bed occupy a relatively greater width compared to the smooth bed. Unlike smooth bed observations, the flow separation point upstream of the cylinder was not dependent on the level of submergence as the separation points were found to appear within a short range of x = ?1D to ?1.2D. Bed shear stress has been found to increase significantly near the shoulder of the cylinders, and its ratio with respect to the approach bed-shear stress was twice as large compared to the smooth bed case. Mean velocity profiles were analyzed in terms of three-dimensional turbulent boundary layer theories. Bed roughness was found to oppose the effect of the lateral pressure gradient that causes skewing in the boundary layer. Perry and Joubert’s model has been found to be equally accurate on smooth and rough beds for predicting the deflected velocity magnitudes around cylinders. The present study will enhance the knowledge of hydraulics of flow around bed-mounted objects (e.g. fish-rocks) in natural streams.     

Decay of Turbulence Downstream of a Stilling Basin

Turbulence must be modeled accurately to simulate river processes, particularly transport of aqueous oxygen and nitrogen. Spillway operations affect downstream turbulence, but there has been little research on turbulence intensities downstream of stilling basins. For this study, laboratory measurements were taken on a three-dimensional, physical model of McNary Dam, Columbia River, United States to determine how the turbulence, initially generated by spillway flow, decreases with distance downstream. The experiments also examined how flow rate, tailwater depth, and the presence of spillway deflectors affect turbulence. A mathematical analysis was used to predict turbulent kinetic energy with distance, and good agreement was found between laboratory measurements and numerical predictions. Turbulence production generated by channel bed roughness was found to be small compared to turbulent energy dissipation, and the effect of flow separation related to bed irregularities on turbulence production was found to be negligible.     

Plane Turbulent Wall Jets on Rough Boundaries with Limited Tailwater

Combining the results of a laboratory study of plane turbulent wall jets on rough boundaries with shallow tailwater, with the results of an earlier work of Rajaratnam on wall jets on rough boundaries with deep tailwater, this paper attempts to describe the effects of boundary roughness and tailwater depth on the characteristics of plane turbulent wall jets on rough beds, which are important in the field of hydraulic engineering. The time-averaged axial velocity profiles at different sections in the wall jet were found to be similar, with some difference from the profile of the classical plane wall jet. The normalized boundary layer thickness δ/b, where b is the length scale of the velocity profile, was equal to 0.35 for wall jets on rough boundaries compared to 0.16 for the classic wall jet. Two stages were seen to exist in the decay of the maximum velocity um as well as in the growth of the length scale, with the first stage corresponding to that of deep tailwater and the second stage to shallow tailwater. In the first stage, the decay of the maximum velocity um at any section in terms of the velocity u0 at the slot, with the longitudinal distance x in terms of L which is the distance where um = 0.5U0, was described by one general function, for smooth as well as rough boundaries. The length scale L in terms of slot width decreases as the relative roughness of the boundary increases. The onset of the second stage was not affected significantly by the bed roughness. The growth rate of the length scale b of the wall jet increased from 0.076 for a smooth boundary to about 0.125 for a relative roughness ks/b0 in the range of 0.25 to 0.50, where ks is the equivalent sand roughness and b0 is the thickness of the jet at the slot.     

Measurement of Fluctuating Pressures on Coarse Bed Material

Bed protections are usually characterized by low-mobility transport conditions and nonequilibrium turbulence profiles. As the present knowledge of the influence of turbulence on stability of cover layer units is minimal, an in-depth investigation was undertaken regarding the influence of turbulence on the stability of rough granular beds. Detailed measurements of (fluctuating) pressures on a bed element are used to evaluate certain concepts that are often used in modeling the entrainment of bed material from hydraulically rough beds. Three pressure transducers are placed in a cube that is part of a rough granular bed under open-channel flow, and velocities are measured using laser Doppler velocimetry. The measurements show that the magnitude of the fluctuating pressure at a certain point of the cube is a function of the exposure relative to the stones upstream of the cube. A quadrant analysis reveals that the drag force is not only directly dependent on the horizontal near-bed velocity, but on the vertical velocity as well. Further, the effect of small-scale eddies shedding from the stone during large-scale increases of longitudinal velocity is shown. The fact that large-scale velocity fluctuations create a large part of the pressure (or force) variance indicates that downstream of a roughness transition these fluctuations have to be taken into account in order to evaluate the stability of the bed.     

Bed-Load Effects on Hydrodynamics of Rough-Bed Open-Channel Flows

The extent to which turbulent structure is affected by bed-load transport is investigated experimentally using a nonporous fixed planar bed comprising mixed-sized granular sediment with a d50 of 1.95?mm. Three different sizes of sediment (d50 = 0.77, 1.99, and 3.96?mm) were fed into the flow at two different rates (0.003 and 0.006?kg/m/s), and subsequently transported as bed load. Particle image velocimetry (PIV) was used to determine the turbulence characteristics over the fixed bed during clear water and sediment feed cases. Mean longitudinal flow velocities at any given depth were lower than their clear water counterparts for all but one of the mobile sediment cases. The exception was with the transport of fine grains at the higher feed rate. In this case, longitudinal mean flow velocities increased compared to the clear water condition. The coarse grains tended to augment bed roughness, but fine grains saturated the troughs and interstices in the bed topography, effectively causing the influence of bed irregularities to be smoothed. The PIV technique permitted examination of both temporal and spatial fluctuations in flow variables: therefore many results are presented in terms of double-averaged quantities (in temporal and spatial domains). In particular, the form-induced stress, which arises from spatially averaging the Reynolds averaged Navier–Stokes equations and is analogous to the Reynolds turbulent stress, contributed between 15 and 35% of the total measured shear stress in the roughness layer. Flow around protrusive roughness elements produced a significant proportion of the turbulent kinetic energy shear production, suggesting that this process is highly intermittent near rough beds.     

Probability Density Function of Instantaneous Drag Forces and Shear Stresses on a Bed

A probability density function (PDF) of the instantaneous bed shear stress in a turbulent flow is derived in this paper. It is argued that the shape of the PDF is similar to the PDF of the instantaneous drag forces on bed roughness elements. The influence of the near-bed relative turbulence intensity is included in the PDF. The shape of the distribution compares well with our measurements of the instantaneous drag force on a protruding bed element for a range of turbulence intensities. However, deviations are apparent at high turbulence intensities. The PDF also compares well with measurements of shear stresses on a smooth wall.     

Spatially Averaged Open-Channel Flow over Rough Bed

In this paper it is suggested that the double-averaged (in temporal and in spatial domains) momentum equations should be used as a natural basis for the hydraulics of rough-bed open-channel flows, especially with small relative submergence. The relationships for the vertical distribution of the total stress for the simplest case of 2D, steady, uniform, spatially averaged flow over a rough bed with flat free surface are derived. These relationships explicitly include the form-induced stresses and form drag as components of the total stress. Using this approach, we define three types of rough-bed flows: (1) Flow with high relative submergence; (2) flow with small relative submergence; and (3) flow over a partially inundated rough bed. The relationships for the double-averaged velocity distribution and hydraulic resistance for all three flow types are derived and compared with measurements where possible. The double-averaged turbulent and form-induced intensities and stresses for the case of regular spherical-segment-type roughness show the dominant role of the double-averaged turbulence stresses and form drag in momentum transfer in the near-bed region.     

Turbulence Characteristics of Open-Channel Flow with Bed Suction

The influence of bed suction on the characteristics of turbulent open channel flow is studied in a laboratory flume using a two-component laser Doppler velocimeter. The experimental results show how bed suction significantly affects the mean flow properties, turbulence levels, and Reynolds stress distributions. The data reveal the presence of a more negative vertical (downward) velocity. The results also show how the horizontal and vertical turbulence intensities and Reynolds shear stresses respond to suction. All these properties are found to reduce with increasing relative suctions: decreasing more rapidly around the bed region than that near the free surface. In the downstream direction, the flow structure in the suction zone undergoes a process of rapid readjustment within a transitional region. Beyond this region, the turbulence flow structures asymptotes toward an “equilibrium” region.     

Rough Wall Boundary Layer on Plates in Open Channels

Experiments were performed to measure the characteristics of a turbulent boundary layer developing on a rough surface placed in an open channel flow at close proximity to the free surface. Streamwise velocity measurements were made with a one-component laser Doppler velocimeter system at the top of the spherical roughness elements. Measurements at three stations downstream of the plate leading edge show the growth of the boundary layer on the rough wall and its interaction with the exterior open-channel flow and the free surface. Resorting to the turbulence profile provides an alternative definition of the boundary layer thickness. The near-wall flow follows the well-known logarithmic law with a shift due to roughness. In the outer layer, there are two opposing effects: the free surface tends to decrease the wake component while the roughness tends to increase it. The streamwise turbulence intensity is affected by the shear and turbulence in the exterior flow, the effect of the free surface being greater than that of wall roughness.     

Numerical Simulation of Flow over a Rough Bed

This paper presents results of a direct numerical simulation (DNS) of turbulent flow over the rough bed of an open channel. We consider a hexagonal arrangement of spheres on the channel bed. The depth of flow has been taken as four times the diameter of the spheres and the Reynolds number has been chosen so that the roughness Reynolds number is greater than 70, thus ensuring a fully rough flow. A parallel code based on finite difference, domain decomposition, and multigrid methods has been used for the DNS. Computed results are compared with available experimental data. We report the first- and second-order statistics, variation of lift/drag and exchange coefficients. Good agreement with experimental results is seen for the mean velocity, turbulence intensities, and Reynolds stress. Further, the DNS results provide accurate quantitative statistics for rough bed flow. Detailed analysis of the DNS data confirms the streaky nature of the flow near the effective bed and the existence of a hierarchy of vortices aligned with the streamwise direction, and supports the wall similarity hypothesis. The computed exchange coefficients indicate a large degree of mixing between the fluid trapped below the midplane of the roughness elements and that above it.     

Modeling of a Rough-Wall Oscillatory Boundary Layer Using Two-Equation Turbulence Models

The standard k?ω turbulence model and two versions of blended k?ω/k?ε models have been used to study the characteristics of a one-dimensional oscillatory boundary layer on a rough surface. The wall boundary condition for the specific dissipation rate of turbulent kinetic energy at the wall is specified in terms of a function based on wall roughness. A detailed comparison has been made for mean velocity, turbulent kinetic energy, Reynolds stress, and wall shear stress with the available experimental data. The three models predict the above properties reasonably well. In particular, the prediction of turbulent kinetic energy for the rough case by the blended models is much better than that for smooth oscillatory boundary layers as reported in previous studies. As a result of the present study, the use of one of the blended models in calculating the sediment transport in coastal environments may be recommended.     

Surface Roughness Effects in Near-Bed Turbulence: Implications to Sediment Entrainment

In this study, the characteristics of near-bed turbulence were experimentally investigated for three distinct roughness regimes, namely (1) isolated; (2) wake interference; and (3) skimming. Spherical particles of the same size and density were placed upon a rough sediment bed to simulate the three regimes. Experimental runs for the aforementioned regimes were performed in a tilting water-recirculating flume. Flow measurements atop the spherical particles were performed by means of a 3D laser Doppler velocimeter. The aim of the tests was to provide further evidence that the structure of turbulence is affected throughout the boundary layer by the presence of roughness geometry. The measurements reported here include velocity profiles of the mean streamwise and vertical velocity components and of the Reynolds shear stress distribution. To further quantify the differences in turbulent structure under various surface roughnesses, a quadrant analysis was performed.     

Turbulence Characteristics in Gradual Channel Transition

A field study was conducted to determine the effects of a channel transition on turbulence characteristics. Detailed three-dimensional (3D) flow measurements were collected at a cross section that is located downstream of a gradual channel expansion. These measurements were obtained via an acoustic doppler velocimeter and include the 3D velocity field, the mean local velocities, the turbulent intensities, the frictional characteristics of the flow, the secondary velocity along the transverse plane, and the instantaneous shear stress components in the streamwise and transverse directions. Analysis of the 3D flow data indicates that the turbulent flow on the outer bank of the channel is anisotropic. Such anisotropy of turbulence, which is attributed to the gradual expansion in the channel and bed roughness, yields the development of a secondary flow of Prandtl’s second kind as reported in 1952. In particular, it was found that turbulent intensities in the vertical and transverse directions on the outer bank section are different in magnitude creating turbulence anisotropy in the cross-sectional plane and secondary flows of the second kind. Turbulent intensities increase toward the free surface indicating the transfer of a higher-momentum flux from the channel bed to the free surface, which contradicts common wisdom. Results for the normalized stress components in the streamwise and transverse direction show similar behavior to the intensities. Moreover, the nonlinear distribution of stresses is indicative of the oscillatory nature of the flow induced by the secondary flows of Prandtl’s second kind. A similar behavior was found for flows in straight rectangular channels over different roughness. Finally, a comparison between the secondary current velocity with the mainstream velocity indicates that secondary flow of Prandtl’s second kind is present within the right half of the measured cross section.