Scour Downstream of an Apron Due to Submerged Horizontal Jets

The results of an experimental investigation on scour of noncohesive sediment beds (uniform and nonuniform sediments) downstream of an apron due to a submerged horizontal jet issuing from a sluice opening are presented. Attempts are made to explain the similarity existing in the scour process and profiles (including dune in the downstream of the scour hole). The scour profiles at different times follow a particular geometrical similarity and can be expressed by the combination of two polynomials. Using experimental scour depth at different times, the time variation of scour depth is scaled by an exponential law, where time scale increases linearly with densimetric Froude number. The equilibrium scour depth, related to the sediment size relative to the sluice opening, decreases with increase in sediment size and sluice opening. On the other hand, the equilibrium scour depth increases with increase in densimetric Froude number. The variation of equilibrium scour depth with tailwater depth indicates a critical tailwater depth corresponding to a minimum equilibrium scour depth. The effect of sediment gradation on scour depth is pronounced for nonuniform sediments, which reduce scour depth significantly due to formation of an armor layer, and therefore prompted study of the reduction of scour depth by a launching apron placed downstream of the rigid apron. The results show that the average reduction of scour depth by placing a launching apron was 39%, having a maximum of 57.3% and a minimum of 16.2%. The characteristic parameters affecting maximum equilibrium scour depth are identified based on the physical reasoning and dimensional analysis. Equation of maximum equilibrium scour depth obtained empirically agrees well with the experimental data.     

Effect of Upward Seepage on Scour and Flow Downstream of an Apron due to Submerged Jets

The upward seepage through the bed sediment downstream of an apron of a sluice gate structure is a common occurrence due to afflux of the flow level between the upstream and downstream reaches of a sluice gate. The result of an experimental investigation on the characteristics of the scour hole and the flow-field downstream of an apron due to submerged jets under the influence of upward seepage through the bed sediment is presented. Experiments were run for the conditions of submerged jets, having submergence factors from 0.99 to 1.72 and jet Froude numbers from 3.15 to 4.87, over beds of sediments (median sizes = 0.8, 1.86, and 3?mm) downstream of an apron under upward seepage velocities. The characteristic lengths of the scour hole determined from the scour profiles are: the maximum equilibrium scour depth, the horizontal distance of the location of maximum scour depth from the edge of the apron, the horizontal extent of the scour hole from the edge of the apron, the dune height, and the horizontal distance of the dune crest from the edge of the apron, all of which were found to increase with an increase in the seepage velocity. Using experimental results, the time variation of the scour depth is scaled by an exponential law, where the nondimensional time scale decreases linearly with an increase in the ratio of the seepage velocity to the issuing jet velocity. The flow field in the submerged jets over both the apron and within the scour hole was detected using an acoustic Doppler velocimeter. The vertical distributions of time-averaged velocities, turbulence intensities and Reynolds stress at different streamwise distances, and the horizontal distribution of bed-shear stress are plotted for the conditions of scour holes with and without upward seepage. Vector plots of the flow field show that the rate of decay of the submerged jet decreases with an increase in the seepage velocity. The flow characteristics in the scour holes are analyzed in the context of the influence of upward seepage velocity on the decay of the velocity and turbulence intensities and the growth of the boundary layer.     

Influence of Cohesion on Scour under Submerged Circular Vertical Jets

The results of an experimental study on scour under submerged circular vertical jets of water in cohesionless and cohesive sediments are presented. The difference between scour patterns in cohesionless and cohesive sediments is identified. In cohesive sediments, the variations of maximum depth and volume of scour have been studied with respect to the percentage of clay content, dry density, antecedent moisture content, etc. Empirical relationships have been proposed for the maximum depth and volume of scour for both nonplastic and plastic cohesive sediments. The range of data for the applicability of the proposed relationships is specified.     

Scour at Submerged Cylindrical Obstacles under Steady Flow

Results of an experimental study on clear-water scour at submerged cylindrical obstacles (circular cylinders) in uniform bed sediments under steady flow are presented. The scour depths at submerged circular cylinders are compared with the scour depths at corresponding unsubmerged cylinders (extended above the free surface of flow) of the same diameters under similar flow and bed sediment conditions. The scour depth decreases with an increase in submergence ratio. A submergence factor is introduced to determine the scour depth at a submerged cylinder from the information of the scour depth at an unsubmerged cylinder of the same diameter. In addition, the flow fields along the upstream vertical plane of symmetry of unsubmerged and submerged cylinders are presented through vector plots, which reveal that the dimension and strength of the horseshoe vortex decreases with an increase in submergence ratio. The horseshoe vortex circulations, which decrease with an increase in submergence ratio, are computed from the vorticity contours by using the Stokes theorem.     

Local Scour Downstream of Positive-Step Stilling Basins

This note focuses on the temporal and spatial evolution of local scour below low-head spillways. Steady-flow experiments were carried out in a 1-m wide and 20-m long rectangular straight channel. The jet was generated by an ogee-crest spillway followed by a positive-step stilling basin. Nearly uniform sandy beds were generally tested, but additional tests were also performed with a special bed of lead spheres. To circumvent the combination of local and general scour phenomena, tailwater depths were set such that tailwater flow intensities were below the threshold of sediment motion. As a consequence, for each run a submerged hydraulic jump formed. Tests were of long durations (of order of days) mainly to achieve conditions of quasi-equilibrium. Based on the data collected, literature approaches are discussed. Then, empirical models are proposed to estimate: (1) the maximum scour depth at the quasi-equilibrium stage and its horizontal distance from edge of stilling basin; (2) the time variation of scour depth; and (3) the axial scour profiles. The proposed equations agree well with experimental data. Findings also highlight that affinity rather than similarity may be the typical property of low-angle eroding jets.     

Hydraulics of Submerged Jet Subject to Change in Cohesive Bed Geometry

The results of an experimental investigation of the time variation of scour hole and the flow characteristics of the quasi-equilibrium state of scour of a cohesive bed downstream of an apron due to a submerged horizontal jet issuing from a sluice opening are presented. Experiments were carried out with natural cohesive sediment for various sluice openings, jet velocities, and lengths of apron. Attempts are made to explain the similarity existing either in the process of scour or in the scour profiles that the scour holes follow downstream of an apron. The scour profiles at different times follow a particular geometrical similarity and can be expressed by a polynomial using relevant parameters. The characteristic parameters affecting the time variation of scour depth are identified based on the physical reasoning and dimensional analysis. An equation for time variation of maximum scour depth is obtained empirically. The diffusion characteristics of the submerged jet, growth of boundary layer thickness, velocity distribution within the boundary layer, and shear stress at the quasi-equilibrium state of scour are also investigated. The expression of shear stress is obtained from the solution of the von Kármán momentum integral equation.     

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.     

Clear-Water Scour at Abutments in Thinly Armored Beds

Experiments on local scour at short abutments (ratio of abutment length to approaching flow depth less than unity), namely vertical-wall, 45° wing-wall, and semicircular, embedded in a bed of relatively fine noncohesive sediment overlain by a thin armor-layer of coarser sediment, were conducted for different flow conditions, thickness of armor-layers, armor-layer, and bed sediments. The abutments were aligned with the approaching flow in a rectangular channel. The armor-layer and the bed underneath it were composed of different combinations of uniform sediments. In the experiments, the approaching flow velocities were restricted to the clear-water scour condition with respect to the armor-layer particles. Depending on the approaching flow conditions, three cases of scour at abutments in armored beds were identified. Effects of different parameters pertaining to scour at abutments are examined. The comparison of the experimental data shows that the scour depth at an abutment with an armor-layer in clear-water scour condition under limiting stability of the surface particles (approaching flow velocity nearly equaling critical velocity for the threshold motion of surface particles) is always greater than that without armor-layer for the same bed sediments. The characteristic parameters affecting the maximum equilibrium nondimensional scour depth (scour depth-abutment length ratio), identified based on the physical reasoning and dimensional analysis, are excess abutment Froude number, flow depth-abutment length ratio, armor-layer thickness-armor particle diameter ratio, and armor particle-bed sediment diameter ratio. The experimental data of clear-water scour condition in thinly armored beds under limiting stability of surface particles were used to determine the equation of maximum equilibrium scour depth through regression analysis. The estimated scour depths were in agreement with the experimental scour depths. Also, an equation of maximum equilibrium scour depth in uniform sediments was obtained.     

Characteristics of Horseshoe Vortex in Developing Scour Holes at Piers

The outcome of an experimental study on the turbulent horseshoe vortex flow within the developing (intermediate stages and equilibrium) scour holes at cylindrical piers measured by an acoustic Doppler velocimeter (ADV) are presented. Since the primary objective was to analyze the evolution of the turbulent flow characteristics of a horseshoe vortex within a developing scour hole, the flow zone downstream of the pier was beyond the scope of the investigation. Experiments were conducted for the approaching flow having undisturbed flow depth ( = 0.25?m) greater than twice the pier diameter and the depth-averaged approaching flow velocity ( = 0.357?m/s) about 95% of the critical velocity of the uniform bed sand that had a median diameter of 0.81?mm. The flow measurements by the ADV were taken within the intermediate (having depths of 0.25, 0.5, and 0.75 times the equilibrium scour depth) and equilibrium scour holes (frozen by spraying glue) at a circular pier of diameter 0.12?m. In order to have a comparative study, the ADV measurements within an equilibrium scour hole at a square pier (side facing the approaching flow) of sides equaling the diameter of the circular pier were also taken. The contours of the time-averaged velocities, turbulence intensities, and Reynolds stresses at different azimuthal planes (0, 45, and 90°) are presented. Vector plots of the flow field at azimuthal planes reveal the evolution of the characteristics of the horseshoe vortex flow associated with a downflow from intermediate stages to equilibrium condition of scour holes. The bed-shear stresses are determined from the Reynolds stress distributions. The flow characteristics of the horseshoe vortex are discussed from the point of view of the similarity with the velocity and turbulence characteristic scales. The imperative observation is that the flow and turbulence intensities in the horseshoe vortex flow in a developing scour hole are reasonably similar.     

Scour in Long Contractions

Experimental results on local scour in long contractions for uniform and nonuniform sediments (gravels and sands) under clear-water scour are presented. An emphasis was given to conduct the experiments on scour in long contractions for gravels. The findings of the experiments are used to describe the effects of various parameters (obtained from dimensional analysis) on equilibrium scour depth under clear-water scour. The equilibrium scour depth increases with decrease in opening ratio and with increase in sediment size for gravels. But the curves of scour depth versus sediment size have considerable sag at the transition of sand and gravel. The scour depth decreases with increase in densimetric Froude number, for larger opening ratios, and increases with increase in approaching flow depth at lower depths. However, it becomes independent of approaching flow depth at higher flow depths. The effect of sediment gradation on scour depth is pronounced for nonuniform sediments, which reduce scour depth significantly due to the formation of armor layer in the scour hole. Using the continuity and energy equations, a simple analytical model for the computation of clear-water scour depth in long contractions is developed with and without sidewall correction for contracted zone. The models agree satisfactorily with the present and other experimental data. Also, a new empirical equation of maximum equilibrium scour depth, which is based on the experimental data at the limiting stability of sediments in approaching channel under clear-water scour, is proposed. The potential predictors of the maximum equilibrium scour depth in long contractions are compared with the experimental data. The comparisons indicate that the equations given by Komura and Lim are the best predictors among those examined.     

Rapid Profiling of an Evolving Bed Form Using Planar Laser Sheet Illumination

Traditional methods of measuring the profile of a scour hole or bed form have poor temporal resolution and may require the temporary cessation of the flow in order to be executed. These are undesirable characteristics since many hydraulic flows have unsteady water-sediment interfaces that can display considerable differences between their “dynamic” (flow on) and “static” (flow off) states. The present technical note discusses the application of planar laser sheet illumination to the erosion of a cohesionless granular bed due to a planar turbulent wall jet. The measurements allow for the quantitative study of the evolution of the bed in its earliest stages. In some cases an ephemeral bed form is observed to form prior to the development of the main bed form. Additionally, the measurements illustrate the oscillatory nature of the bed form under certain conditions. The experiments therefore demonstrate the great potential of this experimental technique for gaining previously inaccessible information on scour processes.     

Clear-Water Scour below Underwater Pipelines under Steady Flow

Experiments on clear-water scour below underwater pipelines (initially laid on the sediment bed) in uniform and nonuniform sediments under steady flow were conducted. Equilibrium scour profiles were modeled by a cubic polynomial. The experimental results are examined to describe the influence of various parameters on equilibrium scour depth. The equilibrium scour depth ds increases with increase in approach flow depth h for shallow flow depths, becoming independent of higher flow depths when h/b>5, where b=pipe diameter. However, the curves of scour depth versus sediment size d and Froude number Fb have a maximum value of ds/b = 1.65 at b/d = 27 and Fb = 0.6. The influence of sediment gradation on scour depth is prominent for nonuniform sediments, which reduce scour depth to a large extent due to the formation of armor layer within the scour hole. The influence of different shaped cross sections of pipes on the scour depth was investigated, where the shape factors for circular, 45° (diagonal facing) and 90° (side facing) square pipes obtained as 1, 1.29, and 1.91, respectively. Using the data of scour depths at different times, the time variation of scour depth is scaled by an exponential law, where the nondimensional time scale increases sharply with increase in Froude number characterized by the pipe diameter. In addition, clear-water scour below circular pipelines laid on a thinly armored sand bed (the sand bed is overlain by a thin armor layer of gravels) was experimentally studied. Depending on the pipe diameter, armor gravel, and bed-sand sizes, three cases of scour holes were recognized. The comparison of the experimental data reveals that the scour depth below a pipeline with an armor layer under limiting stability of the surface particles (approach flow velocity nearly equaling critical velocity for surface particles) is greater than that without armor layer for the same sand bed, if the secondary armoring formed within the scour hole is scattered. In contrast, the scour depth with an armor layer is less than that without armor layer for the same sand bed, when the scour hole is shielded by the secondary armor layer.     

Scour below a High Vertical Drop

Experimental results on scour below a high vertical drop (drop height/critical depth >1) in uniform sands and gravels are presented. The experimental results are used to describe the effects of important parameters, identified from the dimensional analysis, on equilibrium scour depth. The important observations are that the equilibrium scour depth increases with increase in densimetric Froude number, whereas the scour depth decreases with increase in sediment size and tailwater depth. The time scale of scour depth that follows an exponential law is determined. The nondimensional time scale decreases with increase in densimetric Froude number.     

Erosion of Finite Thickness Sediment Beds by Single and Multiple Circular Jets

Sediment management in reservoirs with the help of water jets has motivated this work. Erosion caused by single and multiple submerged circular turbulent wall jets on a noncohesive sediment bed of finite thickness lying on a fixed boundary was studied with the help of laboratory experiments. Different combinations of jet diameter, jet separation, and sediment thickness to jet diameter ratio were tested. Results show a relation between dimensionless parameters characterizing the steady state bed profile and the densimetric particle Froude number F0 given by the velocity at the nozzle and the effective diameter and submerged specific density of the sediment. Evolution of scour with time confirms previous studies where the erosion was found to initially grow with the logarithm of time up to a certain reference time t*. This time, made dimensionless with a time scale tc involving the volume of sediment scoured and the rate of erosion, was also related to the densimetric Froude number. A comparison with studies regarding erosion of a semiinfinite layer of sediment is also presented.     

Temporal Scales for Live-Bed Scour at Abutments

Live-bed scour at a vertical-wall abutment is experimentally investigated with specific attention paid to the conceptual issues concerning the temporal development of local scour phenomenon. First explored are the time scales for the initial rising phase of the time variation of scour depth. An appropriate identification of such scales and of their normalizing parameters makes it possible to recognize a quantitative dependency of nondimensional time scales on flow intensity. Second, the time scales for the subsequent fluctuations around a mean equilibrium value are considered. Experimental results indicate that the quasiperiodical fluctuations of scour depths do not always correspond to those of bed forms. A conceptual model is outlined to explain this aspect.     

Time Variation of Scour at Abutments

A semiempirical model is presented to compute the time variation of scour depth in an evolving scour hole at short abutments (abutment length/flow depth ? 1), namely the vertical wall, 45° wing wall, and semicircular, in uniform and nonuniform sediments under a clear water scour condition. The methodology developed for computing the time variation of scour depth is based on the concept of the conservation of the mass of sediment, considering the primary vortex system as the main agent of scouring, and assuming a layer-by-layer scouring process. For an equilibrium scour hole, the characteristic parameters affecting the nondimensional equilibrium scour depth (scour depth/abutment length), identified based on the physical reasoning and dimensional analysis, are excess abutment Froude number, flow depth—abutment length ratio, and abutment length—sediment diameter ratio. Experiments were conducted for time variation and equilibrium scour depths at different sizes of vertical walls, 45° wing walls and semicircular abutments in uniform and nonuniform sediments under limiting clear water scour conditions (approaching flow velocity nearly equal to the critical velocity for bed sediments). The present model corresponds closely with the data of time variation of scour depth in uniform and nonuniform sediments obtained from the present experiments and reported by different investigators.     

Clear-Water Scour at Piers in Sand Beds with an Armor Layer of Gravels

Clear-water scour at circular and square piers, embedded in a sand bed overlain by a thin armor layer of gravels, was experimentally studied. Depending on the pier width, flow depth, armor gravel, and bed-sand sizes, three cases of scour holes at piers in armored beds were recognized. A comparison of the experimental data shows that the scour depth at a pier with an armor layer under limiting stability of the surface particles is greater than that without an armor layer for the same bed sediments, if the secondary armoring formed within the scour hole is scattered. The equations of maximum equilibrium scour depths at piers in armored beds for these cases are proposed. On the other hand, the scour depth with an armor layer is less than that without an armor layer for the same bed sediments, when the scour hole is shielded by the compact secondary armor layer.     

Two-Phase Analysis of Vertical Sediment-Laden Jets

In this study, we investigated a vertical dilute sediment-laden jet both experimentally and theoretically. First, an instantaneous whole-field velocimetry tool, particle image velocimetry, was applied to measure the sediment and fluid mean and fluctuating velocities of a downward sediment-laden jet at the same time. Subsequently, an analysis was performed based on two-phase conservation equations for both downward and upward jets. The analysis shows that the mean sediment velocity can be taken as the sum of fluid velocity and the settling velocity in both cases. For the downward jets, the decay rate of the centerline sediment concentration increases with the sediment settling velocity while decreases with the initial discharge velocity. The zone of flow establishment for the sediment velocity is found to be longer than that of the fluid. For the upward jets, the maximum rise of the sediment particles and their deposition distribution on the ground were derived theoretically. The predicted results compare well to the experimental data in the literature.     

Two-Dimensional Scour Hole Problem: Role of Fluid Structures

An experimental program was carried out to understand scour caused by a plane wall jet. A two-dimensional laser Doppler anemometer was used to characterize the velocity field at various locations in the scour hole region. Observations indicate that different types of flow structures influence scour at different time periods. Based on the present tests, the entire test duration is divided into five time zones. Following vigorous scour caused principally by jet shear forces and impingement at the start of the test and during early time periods, the flow was characterized by the presence of longitudinal axial vortices, turbulent bursts, and movement of the jet impingement point during the later stages. Attempts were made to distinguish the fluid structures at asymptotic conditions. The scour hole region was characterized by the presence of randomly forming and disappearing streaks, laterally located concave shaped depressions, rolling and ejection of the bed material. Through analysis of higher order moments and quadrant decomposition, sweep and ejection type events were observed, which can potentially contribute to scour.     

Characteristics of a Three-Dimensional Square Jet in the Vicinity of a Free Surface

The characteristics of a turbulent jet issuing from a square cross section nozzle in the vicinity of a free surface are presented. Two-component laser Doppler measurements were obtained at eight stations downstream of the nozzle exit, up to a distance of 27 nozzle widths. The Reynolds number based on the exit condition was 40,000. The proximity of the free surface influence the turbulence levels in the jet. Both confinement effects and axis switching influence the evolution of the velocity profiles downstream of the nozzle. The shear stress profiles indicate the formation of a wider mixing zone in the bottom portion of the jet in regions closer to the nozzle exit. Through quadrant decomposition, ejection, and entraining type events were identified. The magnitudes of the peak shear stress in the various quadrants indicate differences in the turbulence characteristics on the top and bottom portions of the jet. As distinguished in the extreme event plots, there are differences in the magnitudes of the peaks and also in their locations.