Spatial variability of three‐dimensional Reynolds stresses in a developing channel bend

Experimental results of the mean flow field and turbulence characteristics for flow in a model channel bend with a mobile sand bed are presented. Acoustic Doppler velocimeters (ADVs) were used to measure the three components of instantaneous velocities at multiple cross sections in a 135° channel bend for two separate experiments at different stages of clear water scour conditions. With measurements at multiple cross sections through the bend it was possible to map the changes in both the spatial distribution of the mean velocity field and the three Reynolds shear stresses. Turbulent stresses are known to contribute to sediment transport and the three‐dimensionality inherent to flow in open channel bends presents a useful case for determining specific relations between three‐dimensional turbulence and sediment entrainment and transport. These measurements will also provide the necessary data for validating numerical simulations of turbulent flow and sediment transport. The results show that the magnitude and distribution of three‐dimensional Reynolds stresses increase through the bend, with streamwise‐cross stream and cross stream‐vertical components exceeding the maximum principal Reynolds stress through the bend. The most intriguing observation is that near‐bed maximum positive streamwise‐cross stream Reynolds stress coincides with the leading edge of the outer bank scour hole (or thalweg), while maximum cross stream‐vertical Reynolds stress (in combination with high negative streamwise‐cross stream Reynolds stress near the bend apex) coincides with the leading edge of the inner bank bar. Maximum Reynolds stress and average turbulent kinetic energy appear to be greater and more localized over the scour hole before final equilibrium scour is reached. This suggests that the turbulent energy in the flow is higher while the channel bed is developing, and both lower turbulent energy and a broader distribution of turbulent stresses near the bed are required for cessation of particle mobilization and transport. Copyright © 2010 John Wiley & Sons, Ltd.     

Shear velocity estimates in rough‐bed open‐channel flow

Shear velocity u_* is an important parameter in geophysical flows, in particular with respect to sediment transport dynamics. In this study, we investigate the feasibility of applying five standard methods [the logarithmic mean velocity profile, the Reynolds stress profile, the turbulent kinetic energy (TKE) profile, the wall similarity and spectral methods] that were initially developed to estimate shear velocity in smooth bed flow to turbulent flow over a loose bed of coarse gravel (D₅₀ = 1·5 cm) under sub‐threshold conditions. The analysis is based on quasi‐instantaneous three‐dimensional (3D) full depth velocity profiles with high spatial and temporal resolution that were measured with an Acoustic Doppler Velocity Profiler (ADVP) in an open channel. The results of the analysis confirm the importance of detailed velocity profile measurements for the determination of shear velocity in rough‐bed flows. Results from all methods fall into a range of ± 20% variability and no systematic trend between methods was observed. Local and temporal variation in the loose bed roughness may contribute to the variability of the logarithmic profile method results. Estimates obtained from the TKE and Reynolds stress methods reasonably agree. Most results from the wall similarity method are within 10% of those obtained by the TKE and Reynolds stress methods. The spectral method was difficult to use since the spectral energy of the vertical velocity component strongly increased with distance from the bed in the inner layer. This made the choice of the reference level problematic. Mean shear stress for all experiments follows a quadratic relationship with the mean velocity in the flow. The wall similarity method appears to be a promising tool for estimating shear velocity under rough‐bed flow conditions and in field studies where other methods may be difficult to apply. This method allows for the determination of u_* from a single point measurement at one level in the intermediate range (0·3 < h < 0·6). Copyright © 2013 John Wiley & Sons, Ltd.     

Effects of turbulence on the transport of individual particles as bedload in a gravel‐bed river

This study investigates the association between mean and turbulent flow variables and the movement of individual particles in a gravel‐bed river. The experimental design implemented in the Eaton‐North River (Québec, Canada) is based on the simultaneous observations at a high temporal resolution of both particle movements as bedload using an underwater video camera and of the streamwise and vertical flow velocity components using a vertical array of three electromagnetic current meters (ECMs). The frequency and distance of displacement of particles larger than 20 mm that were sliding or rolling on the bed were measured from a 10 minutes long film. Mean and turbulent flow properties obtained for periods without sediment transport are compared to those when particles were sliding and rolling. When particles are sliding, weak differences are present for the mean streamwise velocity and normal vertical stresses. Instantaneous Reynolds shear stresses are significantly lower for sliding events which was not expected but could be explained by the important dominance of Quadrant 3 events (inward interactions). When particles are rolling, only the vertical normal stresses show a weak difference from those observed in the absence of transport but they tend to occur when Quadrant 2 (ejections) dominate the flow field. For both sliding and rolling particles, vertical and/or streamwise fluid accelerations show high magnitude values when compared to periods without transport. For sliding particles, streamwise acceleration is mostly negative and combines most of the time with a positive vertical acceleration. For rolling particles, streamwise and vertical acceleration are predominantly of opposite sign. These results suggest that fluid acceleration or deceleration in the streamwise and vertical directions is affecting the pressure field around particles. In this study, fluid acceleration seems to play a more important role than Reynolds shear stress or normal stresses for bedload movements. Copyright © 2010 John Wiley & Sons, Ltd.     

Turbulent flow structures in alluvial channels with curved cross‐sections under conditions of downward seepage

Experimental investigations have been done to analyze turbulent structures in curved sand bed channels with and without seepage. Measures of turbulent statistics such as time‐averaged near‐bed velocities, Reynolds stresses, thickness of roughness sublayer and shear velocities were found to increase with application of downward seepage. Turbulent kinetic energy and Reynolds normal stresses are increased in the streamwise direction under the action of downward seepage, causing bed particles to move rapidly. Analysis of bursting events shows that the relative contributions of all events (ejections, sweeps and interactions) increase throughout the boundary layer, and the thickness of the zone of dominance of sweep events, which are responsible for the bed material movement, increases in the case of downward seepage. The increased sediment transport rate due to downward seepage deforms the cross‐sectional geometry of the channel made of erodible boundaries, which is caused by an increase in flow turbulence and an associated decrease in turbulent kinetic energy dissipation and turbulent diffusion.     

An analysis of the characteristics of rough bed turbulent shear stresses in an open channel

Entrainment of sediment particles from channel beds into the channel flow is influenced by the characteristics of the flow turbulence which produces stochastic shear stress fluctuations at the bed. Recent studies of the structure of turbulent flow has recognized the importance of bursting processes as important mechanisms for the transfer of momentum into the laminar boundary layer. Of these processes, the sweep event has been recognized as the most important bursting event for entrainment of sediment particles as it imposes forces in the direction of the flow resulting in movement of particles by rolling, sliding and occasionally saltating. Similarly, the ejection event has been recognized as important for sediment transport since these events maintain the sediment particles in suspension. In this study, the characteristics of bursting processes and, in particular, the sweep event were investigated in a flume with a rough bed. The instantaneous velocity fluctuations of the flow were measured in two-dimensions using a small electromagnetic velocity meter and the turbulent shear stresses were determined from these velocity fluctuations. It was found that the shear stress applied to the sediment particles on the bed resulting from sweep events depends on the magnitude of the turbulent shear stress and its probability distribution. A statistical analysis of the experimental data was undertaken and it was found necessary to apply a Box-Cox transformation to transform the data into a normally distributed sample. This enabled determination of the mean shear stress, angle of action and standard error of estimate for sweep and ejection events. These instantaneous shear stresses were found to be greater than the mean flow shear stress and for the sweep event to be approximately 40 percent greater near the channel bed. Results from this analysis suggest that the critical shear stress determined from Shield's diagram is not sufficient to predict the initiation of motion due to its use of the temporal mean shear stress. It is suggested that initiation of particle motion, but not continuous motion, can occur earlier than suggested by Shield's diagram due to the higher shear stresses imposed on the particles by the stochastic shear stresses resulting from turbulence within the flow.     

Turbulent kinetic energy budget in a gravel-bed channel flow

The present experimental investigation focuses on the characteristics of near bed turbulence in a fully rough, uniform open-channel flow over a gravel-type bed. Due to bed topography small scale heterogeneity, the flow is not uniform locally in the near bed region and a double averaging methodology is applied over a length scale much larger than the gravel size. The double-averaged Turbulent Kinetic Energy (TKE) budget derived in the context of the present flow over a gravel bed differs from the TKE budget written for flow over a vegetation canopy. The non-constant shape of the roughness function measured in our gravel bed leads to an additional bed-induced production term which is null for vertical roughness elements, such as simplified vegetation elements. The experimental estimation of the terms of the TKE budget reveals that the maximum turbulent activity takes place away from the reference plane, near the roughness crests. However, within the interface sublayer the work of the bed induced velocity fluctuations against the Reynolds stress is of the same magnitude as the main turbulence production term. Consequently, the characteristics of the TKE budget have similarities with uniform flows over canopies and strongly differ from uniform flows over smooth and transitionally rough flows over sedimentlike beds.     

Variable and conflicting shear stress estimates inside a boundary layer with sediment transport

This paper presents a comparison between two methods for estimating shear stress in an atmospheric internal boundary layer over a beach surface under optimum conditions, using wind velocities measured synchronously at 13 heights over a 1.7 m vertical array using ultrasonic anemometry. The Reynolds decomposition technique determines at‐a‐point shear stresses at each measurement height, while the Law‐of‐the‐Wall yields a single boundary layer estimate based on fitting a logarithmic velocity profile through the array data. Analysis reveals significant inconsistencies between estimates derived from the two methods, on both a whole‐event basis and as time‐series. Despite a near‐perfect fit of the Law‐of‐the‐Wall, the point estimates of Reynolds shear stress vary greatly between heights, calling into question the assumed presence of a constant stress layer. A comparison with simultaneously measured sediment transport finds no relationship between transport activity and the discrepancies in shear stress estimates. Results do show, however, that Reynolds shear stress measured nearer the bed exhibits slightly better correlation with sand transport rate. The findings serve as a major cautionary message to the interpretation and application of single‐height measurements of Reynolds shear stress and their equivalence to Law‐of‐the‐Wall derived estimates, and these concerns apply widely to boundary layer flows in general. © 2015 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.     

Effect of non‐uniformity of flow on velocity and turbulence intensities over a cobble‐bed

Non‐uniform flows encompassing both accelerating and decelerating flows over a cobble‐bed flume have been experimentally investigated in a flume at a scale of intermediate relative submergence. Measurements of mean longitudinal flow velocity u, and determinations of turbulence intensities u′, v′, w′, and Reynolds shear stress ?u_fw_f have been made. The longitudinal velocity distribution was divided into the inner zone close to the bed and the outer zone far from the bed. In the inner zone of the boundary layer (near the bed) the velocity profile closely followed the ‘Log Law’; however, in the outer zone the velocity distribution deviated from the Log Law consistently for both accelerating and decelerating flows and the changes in bed slopes ranging from ?2% to + 2% had no considerable effect on the outer zone. For a constant bed slope (S = ±0·015), the larger the flow rate, the smaller the turbulence intensities. However, no detectable pattern has been observed for u′, v′ and w′ distributions near the bed. Likewise, for a constant flow rate (Q = 0·040 m³/s), with variation in bed slope the longitudinal turbulent intensity profile in the longitudinal direction remained concave for both accelerating and decelerating flows; whereas vertical turbulent intensity (w′) profile presented no specific form. The results reveal that the positions of maximum values of turbulence intensities and the Reynolds shear stress depend not only on the flow structure (accelerating or decelerating) but also on the intermediate relative submergence scale. Copyright © 2009 John Wiley & Sons, Ltd.     

ON THE NECESSITY OF APPLYING A ROTATION TO INSTANTANEOUS VELOCITY MEASUREMENTS IN RIVER FLOWS

In studies on river channel flow turbulence, it is often the case that the measured mean vertical velocity is different from zero, indicating that the frame of reference of the current meter is not parallel to the flow streamline. This situation affects the estimate of Reynolds shear stress in the streamwise and vertical planes and consequently the analysis of the flow turbulent structure. One way to solve this problem is to correct data by applying a rotation and this is reviewed in the first part of the paper. However, in fluvial geomorphology, the studied flow is often complex and streamlines may exhibit significant changes from one point of measurement to the other. In this context, applying a rotation complicates the situation more than it simplifies it. The second part of this paper examines the question of velocity data correction in complex flows using a field example of the turbulent boundary layer over a very rough gravel bed and a laboratory example taken from flow at a river channel confluence. In both cases, velocity vectors are spatially variable. In the first case, errors in the Reynolds shear stress estimates are relatively low (ranging from −13 to 7 per cent/deg) while in the second case, they are much larger (−200 to 164 per cent/deg). The significance of these errors on the interpretation of turbulence statistics in river channel flows is discussed. We propose that corrections should be applied in all clear cases of sensor misalignment and when the frame of reference changes spatially and temporally. However, no corrections should be used where different flow velocity vector orientations, not sensor misalignment, are responsible for the mean vertical velocity differing from zero.     

Comparison of bed shear stress in plane and curvilinear bed channel using multiple criteria

Experimental investigation on fluvial hydraulics needs a correct and accurate estimation of bed shear stress, which governs the hydrodynamics of the sediment transport. Present work compares bed shear stress estimated from the reach-averaged bed shear stress, Log profile, Quadratic stress law, Prandtl’s seventh power law, Reynolds shear stress, turbulent kinetic energy and graphical method approaches by doing experimentation on plane bed and curvilinear bed channel. On plane bed condition, the bed shear estimated from Reynolds stresses and Graphical methods are comparable to the reach-averaged bed shear stress (the difference is within 10%). However, all approaches estimate approximately less than 10% from reach-averaged bed shear stress in curvilinear bed channel.     

Turbulence characteristics of flows passing through a tetrahedron frame in a smooth open-channel

The turbulence characteristics of flows passing through a tetrahedron frame were investigated by using a 2-dimensional fiber-optic laser Doppler velocimeter (2-D FLDV). Experiments for uniform flows with different bed slopes under both submerged and un-submerged conditions were carried out in a re-circulating flume with glass side walls. The experimental bed was a smooth fixed bed. It was observed that with the tetrahedron frame the mean longitudinal velocity decrease in the retardation zone. However, both the longitudinal and the vertical turbulence intensities are larger than those for the undisturbed approach flow. The tetrahedron frame may reduce the probability of sediment entrainment by retarding the flow and reducing the boundary shear stress. In addition, it may induce sediment deposition in a sediment laden flow by changing the flow direction and increasing the energy dissipation.     

Turbulence characteristics of flow past submerged vanes

Submerged vanes are hydrofoils utilized to manage the sediment transport through the river by generating the turbulence in the flow in the form of helical currents.The vanes are placed in the flow with respect to its direction at angle of 10°to 40°.In the current study,an attempt has been made to study the effect of the introduction of vanes in form of rows on parameters like turbulence intensities,Reynolds stresses,turbulent kinetic energy,anisotropy index,and the velocity profile of the flow.It is observed that the profile of variation of turbulence intensities,turbulent kinetic energy,vertical Reynolds stress and velocity over three different marked verticals on a transect are nearly identical whereas a large scatter is observed in the variation of transverse Reynolds stress over the vertical of the aforementioned vertical locations.This observation suggests that flow turbulence is homogeneous over the vertical while scattering in the variation of the transverse Reynolds stress component may be attributed to the presence of secondary currents in the flow.After introducing rows of submerged vanes,the bed turbulence is reduced,hence,helping reduce many scour related phenomenon.It is also observed that a vortex occurred at 0.85 times the height of the vane and the variation of turbulence quantities in the presence of vanes shows the existence of a peak in these quantities.It is observed that as flow moves away from the vane rows,due to the interaction of vortices and the action of vorticity,vortices dampens down and the flow regains homogeneity.After the introduction of submerged vane rows,bed shear stress reduces as fluid from the surface replaces the slow-moving fluid near the bed due to the secondary currents generated by the vanes leading to reduction in the magnitude of turbulence intensities,Reynolds stresses,and turbulent kinetic energy near the bed.The anisotropy index is observed to increase near the bed as induced secondary currents enhanced the turbulence production in the near bed region.All the profiles of parameters obtained in the current study show the existence of a peak or inflexions at a height of 0.85 H from bed(Where,H is the height of the submerged vane).Profiles of parameters obtained in the current study suggest that as the vorticity dampens the vane-generated secondary currents,the scattering in the profiles along the vertical reduces and profiles are observed to regain the variation which they had before the introduction of vane rows,suggesting that flow turbulence has regained its homogeneity.     

Velocity distribution in a gradually accelerating free surface flow

This study investigates the interaction of the vertical velocity v and the streamwise velocity u in a gradually accelerating flow. The analytical result shows that the momentum of uv driven by the mean velocities in a non-uniform flow is not negligible. This additional momentum directly results in the concave profiles of Reynolds shear stress in gradually accelerating flows, a departure from the expected linear profile. Consequently, this momentum causes the maximum velocity to be located below the free surface, i.e., the dip-phenomenon. This paper investigated the interactions of the Reynolds shear stress, non-zero vertical velocity and dip-phenomenon, it is found that the non-zero vertical velocity causes the dip-phenomenon. The approach is tested using the experimental data of Song and others, and good agreements between the predicted and measured velocity profiles have been achieved.     

Reduction of bend scour with an air-bubble screen-morphology and flow patterns

The interplay between streamwise flow,curvature-induced secondary flow,sediment transport and bed morphology leads to the formation of a typical bar-pool bed morphology in open-channel bends.The associated scour at the outer bank and deposition at the inner bank may endanger the outer bank’s stability or reduce the navigable width of the channel.Previous preliminary laboratory experiments in a sharply curved flume with a fixed horizontal bed have shown that a bubble screen located near the outer bank can generate an additional secondary flow located between the outer bank and the curvature-induced secondary flow and with a sense of rotation opposite to the latter.This bubble-induced secondary flow redistributes velocities and bed shear stresses.The reported study investigates the implications of a bubble screen on the flow and the morphology in configurations with mobile bed.Velocity measurements show that the bubble-induced secondary flow shifts the curvature-induced secondary flow in inwards direction and reduces its strength.The bubble screen considerably reduces morphological gradients.Maximum bend scour is reduced by about 50%and occurs further away from the outer bank where it does not endanger the bank stability anymore.The location of maximum scour coincides with the junction of the curvature-induced and bubble-induced secondary flows.At this same location,the maximum streamwise velocities and maximum vertical velocities impinging on the bed also occur,which indicates their importance with respect to the formation of bend scour.The bubble screen also substantially reduced deposition at the inner bank.These preliminary experiments show the potential of a bubble screen to influence and modify the bed morphology.     

NONUNIFORMOPEN CHANNEL FLOW WITH UPWARD SEEPAGE THROUGH LOOSE BEDS

The Reynolds stress and bed shear stress are important parameters in fluvial hydraulics. Steady-nonuniform flow in open channels with streamwise sloping beds having upward seepage through loose beds is theoretically analyzed to estimate the Reynolds stress and bed shear stress. Equations of the Reynolds stress and bed shear stress are developed, assuming a modified logarithmic velocity distribution law due to upward seepage, and using the Reynolds and continuity equations of two-dimensional flow in open channels.     

Mean and turbulent flow fields in a simulated ice‐covered channel with a gravel bed: some laboratory observations

Northern rivers experience freeze‐up over the winter, creating asymmetric under‐ice flows. Field and laboratory measurements of under‐ice flows typically exhibit flow asymmetry and its characteristics depend on the presence of roughness elements on the ice cover underside. In this study, flume experiments of flows under a simulated ice cover are presented. Open water conditions and simulated rough ice‐covered flows are discussed. Mean flow and turbulent flow statistics were obtained from an Acoustic Doppler Velocimeter (ADV) above a gravel‐bed surface. A central region of faster flow develops in the middle portion of the flow with the addition of a rough cover. The turbulent flow characteristics are unambiguously different when simulated ice covered conditions are used. Two distinct boundary layers (near the bed and in the vicinity of the ice cover, near the water surface) are clearly identified, each being characterized by high turbulent intensity levels. Detailed profile measurements of Reynolds stresses and turbulent kinetic energy indicate that the turbulence structure is strongly influenced by the presence of an ice cover and its roughness characteristics. In general, for y/d > 0·4 (where y is height above bed and d is local flow depth), the addition of cover and its roughening tends to generate higher turbulent kinetic energy values in comparison to open water flows and Reynolds stresses become increasingly negative due to increased turbulence levels in the vicinity of the rough ice cover. The high negative Reynolds stresses not only indicate high turbulence levels created by the rough ice cover but also coherent flow structures where quadrants one and three dominate. Copyright © 2012 John Wiley & Sons, Ltd.     

Influence of bank vegetation and gravel bed on velocity and Reynolds stress distributions

This paper presents the results of a laboratory flume experimental study on the interaction of bank vegetation and gravel bed on the flow velocity （primarily on the location of the maximum velocity, Umax） and the Reynolds stress distributions. The results reveal that the dip of the maximum velocity below the water surface is up to 35% of flow depth and the difference between Umax and the velocity at the water surface is considerable in the presence of vegetation on the walls. The zone of the log-law varies from y/h=2 up to 15 percent of flow depth and it does not depend on distance from the wall. Deviation of the velocity profile in the outer layer over a gravel bed with vegetation cover on the walls is much larger than the case of flow over a gravel bed without vegetation cover on the walls. The presence of vegetation on the walls changes uniform flow to non-uniform flow. This fact can be explained by considering the nonlinear Reynolds stress distribution and location of maximum velocity in each profile at different distances across the flume. The Reynolds stress distributions at the distance 0.02 m from the wall have negative values and away from the wall, they change the sign taking positive values with specific convex form with apex in higher location. Average of von Karman constant κ for this study is equal to 0.16. Based on to=0.16, the methods of Clauser and the Reynolds stress are compatible for determination of shear velocity.     

Space time evolution of sand bed topography and associated flow turbulence: experiments with statistical analysis

A series of flume experiments were conducted with varying the flow discharges at the Fluvial Mechanics Laboratory of Indian Statistical Institute (Kolkata) to understand the co-evolution patterns of generating bed forms and the corresponding flow turbulence. Instantaneous bed elevations and velocity components were recorded continuously for sufficient time using high resolution instruments, such as, Ultrasonic Ranging System and acoustic Doppler velocimeter, at some spatial location over the deformed bed for each flow discharge. Increase in mean bed elevations and bed-slopes was found to be increased in discharge. Heavy-tailed nature of the probability density functions of magnitude of bed elevation increments, magnitude of single continuous bed elevation increments and instantaneous Reynolds shear stresses along three planes were analyzed using Pareto and truncated Pareto distributions. The spectral analysis of bed elevations revealed that the slope of log–log linearity increased with increase in flow discharge. Wavelet cross-correlations depicted strong dependence of bed form evolution on the corresponding instantaneous Reynolds shear stress along xz-plane. A Gram–Charlier type of distribution was used to estimate the probability density function of fluctuating velocity components, instantaneous Reynolds shear stresses along three planes and the joint probability density functions of the fluctuating velocity components, which showed good fit with the experimental data.