Journal of Hydraulic Engineering

The step aerator for stepped chutes was recently introduced. Its purpose is to preaerate the zone between the spillway crest and the point of incipient bottom aeration to counter cavitation damage for relatively large unit discharges. The shape of the step aerator is optimized herein by hydraulic modeling to design the air supply and to indicate the aerator blockage characteristics. The shape and the performance of the improved step aerator are described in terms of air supply and the development of air-water flow on the stepped chute. Further, step insets are considered to reduce the spray formation on stepped chutes for small unit discharges, in combination with the step aerator. The performance of the step insets was investigated and their effect on the spray formation analyzed. The step aerator generally increases the maximum spray height at smallest discharges as compared to the standard stepped chute without step aerator. Insets over the first five steps significantly reduce spray relative to standard stepped chutes.

Spurs are river engineering elements used to protect river banks from erosion and to concentrate flow to the river axis. Today, spurs are also employed for promoting environmental conditions along a river bank. These elements are characterized by a large variety of geometrical parameters, of which none is definitely fixed. Based on a preliminary study that identified optimum spur arrangements in a straight river reach the present research project adds to the protection of spurs by riprap. The first two spurs are demonstrated to require a suitable riprap for promoting nearly uniform scour conditions along the entire spur reach. This research investigated the effects of a variety of parameters on spur flow, notably spur length, spur spacing, spur height plus the diameter and the number of riprap rows, along with the main hydraulic and granulometric parameters. Design equations were established based on a large experimental campaign to predict riprap failure in terms of the previous set of variables. The failure modes are described along with a novel failure mechanism. The paper ends with a set of limitations allowing for the application of these results in river engineering.

This paper presents the results of a clear-water scour experiment where the sediment kinematics around a rectangular abutment was measured at various evolution stages of the erosion process. Sediment activity was quantified by measuring the instantaneous concentration and velocity of the moving grains by image processing. The analysis was mainly focused on the region upstream of the abutment, where the maximum scour depth is measured. Experimental results on the kinematics of the grains were discussed and interpreted on the basis of the typical literature descriptions of the water flow field. The suitability of averaged quantities to describe the grain mechanics was evaluated by analyzing the instantaneous values of sediment concentration and velocity. We found that the grain kinematics can be effectively interpreted by means of the mean sediment pattern only at some locations and evolution stages: Typically the sediment activity becomes progressively more intermittent in the upstream part of the scour hole, reducing the similarity between the instantaneous and the average sediment patterns. The findings may have important implications for both the phenomenological depiction and the numerical modeling of local scour processes.

The flow hydrodynamics in a straight open channel containing a multiple-embayment groyne field on one of its sides is investigated numerically using large eddy simulation. The vertical groynes are fully emerged. The mean flow depth in the groyne region is about half that of the main channel and the length and width of the embayments are much larger than the mean depth in the embayment region. The model is validated using mean velocity and turbulent fluctuations data collected at the free surface in a previous experimental study. It is found that despite the fact that the flow inside the main recirculation eddy in the embayments can be characterized as being quasi-two dimensional, the flow inside the mixing layer region between the embayments and the channel is strongly nonuniform over the depth. As this region controls the mass exchange processes between the groyne field and the main channel, a three-dimensional description of the flow in this area is essential. The large-scale eddies that populate the mixing layer can penetrate the embayment region over lateral distances of the order of the channel depth. These eddies advect with them channel fluid inside the embayment. Eventually, the channel fluid is mixed with the embayment fluid by the small scales. The other main mixing mechanism is due to the injection of patches of high-vorticity mixing-layer fluid near the tip of the downstream groyne and their subsequent convection in the form of a wall-attached jet-like flow into the embayment, first parallel to the downstream groyne face and then to the sidewall. It is shown that on average, most of the fluid leaves the embayment region via the top layer of the embayment-channel interface (upstream half) and enters the embayment region at levels situated around the middepth (practically over the whole length of the embayment) of the interface surface. This explains why the mass exchange coefficients are overestimated when predicted using methods that employ floating particles as a tracer. The instantaneous bed shear stress inside the cavity is found to peak close to the downstream groyne face of each embayment and to show a high variability around the mean values due to the interaction of the mixing layer eddies with the tip of the groynes and the formation of the jet-like flow parallel to the droyne face.

Laboratory experiments are presented that model the exchange processes between a river and dead-water zones created by groin fields. The measurement methods include particle image velocimetry (PIV) at the water surface to capture the dynamics of the flow field as well as planar concentration analysis (PCA) to determine the depth integrated mass fluxes of dissolved tracer. Idealized groins with variable length-to-width ratios and inclination angles relative to the flow direction are investigated. Two-dimensional large coherent structures (2DLCS) are found in the mixing layer between the groin field and the river, and these flow structures control the majority of mixing with the main stream. The PIV data allow quantification of the turbulence intensity distribution in these structures throughout the groin field and mixing region. The PCA data provide measurements of the exchange rate between the groin field and the main stream. Both methods give comparable measures of the entrainment coefficient for the exchange flow. The entrainment coefficient is found to depend on the groin field hydraulic radius (a measure of the average size of 2DLCS in the mixing layer) and the water depth (a parameter controlling the stability of the shallow water flow). These data provide a link between the exchange parameter in groin field dead zones and the river properties that can be used to efficiently develop river alarm models to predict contaminant transport without requiring a large amount of field dye studies for calibration.

Open-channel beds show variations in the transverse direction due to the interaction between downstream flow, cross-stream flow, and bed topography, which may reduce the navigable width or endanger the foundations of structures. The reported preliminary laboratory study shows that a bubble screen can generate cross-stream circulation that redistributes velocities and hence, would modify the topography. In straight flow, the bubble-generated cross-stream circulation cell covers a spanwise extent of about four times the water depth and has maximum transverse velocities of about $0.2{\mathrm{ms}}^{-1}$ . In sharply curved flow, it is slightly weaker and narrower with a spanwise extent of about three times the flow depth. It shifts the counter-rotating curvature-induced cross-stream circulation cell in the inwards direction. Maximum bubble-generated cross-stream circulation velocities are of a similar order of magnitude to typical curvature-induced cross-stream circulation velocities in natural open-channel bends. The bubble screen technique is adjustable, reversible, and ecologically favorable. Detailed data on the 3D flow field in open-channel bends is provided, which can be useful for validation of numerical models.

Two types of dispersion coefficient tensor for meandering channels were examined. The first type was estimated using measured vertical velocity profile in an S-curved channel, and the second type was based on the depth-averaged velocity field. A Petrov-Galerkin type finite element scheme was used in the numerical modeling, and the simulation results were compared with the experimental results from tracer tests in an S-curved channel. Comparison of the results show that the dispersion coefficient tensor obtained directly from velocity profiles provided a more realistic solution that can describe the abrupt expansion of tracer clouds in the transverse direction. Heterogeneous longitudinal and transverse dispersion coefficients were inversely estimated from the calculated dispersion coefficient tensor based on the velocity profiles. Extremely large transverse dispersion coefficients were formed at the apex of the channel bend, where there was a well-developed secondary current. The dimensionless transverse dispersion coefficient $(D_T∕{\mathit{hu}}^{*})$ in the apex of the bend ranges from 0.495 to 2.60, which is about four times larger than that of the straight region.

Semianalytical equations were derived for distribution of shear stress in straight open channels with rectangular, trapezoidal, and compound cross sections. These equations are based on a simplified streamwise vorticity equation that includes secondary Reynolds stresses. Reynolds stresses were then modeled and their different terms were evaluated based on the work of previous researchers and experimental data. Substitution of these terms into the simplified vorticity equation yielded the relative shear stress distribution equation along the width of different channel cross sections. In compound channels the effect of additional secondary flows due to the shear layer between the main channel and the flood plain were also considered. Comparisons between predictions of the model and experimental data, predictions of other analytical or three dimensional numerical models with advanced turbulent closures, were made with good agreement.

Many sediment deposits contain not only a granular but also a mineral and/or organic cohesive fraction, which has the potential to change significantly the erosion response when compared to noncohesive sediment deposits. Sediment deposits containing a low proportion of cohesive sediment display a specific, transitional behavior between cohesive and noncohesive sediments. In the past, several studies have examined partly cohesive sediment, however, the quantification of its erosion behavior is still unsatisfactory. In an attempt to advance the understanding and qualitative description of erosion and transport of mixed sediments in pipes, a comprehensive experimental investigation on the erosion behavior was designed. Tests were conducted in a flume with semicircular cross section with a diameter of $0.39\mathrm{m}$ using fine sand with a $d_{50}=0.19\mathrm{mm}$ and partly cohesive sediment deposits being a mixture of sand and clay with proportion of 3–10% by weight of clay. Tests covered a range of flow conditions with Froude numbers up to 0.6. Data on bed form geometries, friction characteristics, and sediment transport rates were collected. In steady sediment transport conditions the eroded partly cohesive bed produces an active granular top layer over an intact substrate, the thickness of which is up to ten times smaller than in the case of a granular bed. The cohesion of the substrate reduces the height and length of bed forms, bed form friction, and sediment transport rates. A comparison of the mobility of noncohesive sediments in circular pipes obtained in other studies is presented to indicate the generality of these results.

An approach for calculating turbulent flows in a wave-current boundary layer over a slowly varying bed is presented. Waves are periodic in time with several harmonics. In this paper, we adopt a time invariant eddy viscosity model, in which the eddy viscosity is linearly proportional to the distance from the bed. The boundary-layer flow field is solved analytically in terms of Fourier components. The approach allows fast computations and can be easily included in a phase resolving wave propagation model. As a part of the results, bottom shear stress and the spatial variation of the boundary layer thickness are also obtained. Present results compare well with experimental data and can explain the asymmetries in the bottom shear stress under sawtooth shaped waves.

A simple yet precise relation between the flux gradient and the bed slope source term is presented, which produces a net force within the cell with an inclined water surface, but ensures still water condition when there is no flow across the boundaries. The proposed method consists of calculating the pressure term based on the water depths at the cell vertices, which may be computed by a higher order scheme and the bed slope source term by a centered discretization technique. The methodology is demonstrated with a Godunov-type upwind finite volume formulation. The inviscid fluxes are calculated using Roe’s approximate Riemann solver and a second-order spatial accuracy is obtained by implementing multidimensional gradient reconstruction and slope limiting techniques. The accuracy and applicability of the numerical model is verified with a couple of test problems and a real flow example of tidal water movement in a stretch of River Hooghly in India.

The spectrum of this survey turns on the evaluation of some eminent Riemann solvers (or the so-called solver), for the shallow water equations, when employed with high-order Runge–Kutta discontinuous Galerkin (RKDG) methods. Based on the assumption that: The higher is the accuracy order of a numerical method, the less crucial is the choice of Riemann solver; actual literature rather use the Lax-Friedrich solver as it is easy and less costly, whereas many others could be also applied such as the Godunov, Roe, Osher, HLL, HLLC, and HLLE. In practical applications, the flow can be dominated by geometry, and friction effects have to be taken into consideration. With the intention of obtaining a suitable choice of the Riemann solver function for high-order RKDG methods, a one-dimensional numerical investigation was performed. Three traditional hydraulic problems were computed by this collection of solvers cooperated with high-order RKDG methods. A comparison of the performance of the solvers was carried out discussing the issue of $L^1$ -errors magnitude, CPU time cost, discontinuity resolution and source term effects.

In recent years, design floods have increased beyond spillway capacity at numerous large dams. When additional spillway capacity is difficult or expensive to develop, designers may consider allowing the overtopping of a dam during extreme events. For concrete arch dams, this often raises issues of potential erosion and scour downstream from the dam, where the free jet initiating at the dam crest impacts the abutments and the downstream river channel. A recent review has shown that a commonly cited equation for predicting the trajectory of free jets is flawed, producing jet trajectories that are much too flat in this application. This could lead analysts to underestimate the amount of scour that could occur near a dam foundation, or conversely to overestimate the extent of scour protection required. This technical note presents the correct and incorrect jet trajectory equations, quantifies the errors associated with the flawed equation, and summarizes practical information needed to model the trajectory of free jets overtopping dam crests.

The mean settling velocities of suspended sediments in turbulence have been examined. The settling velocities in a flume are directly measured by using an acoustic Doppler velocimeter. The results indicate the same trend as previous work in homogeneous isotropic turbulence. In addition to the flume experiment, the numerical experiments were conducted in the velocity field of homogeneous isotropic turbulence simulated by Kraichnan’s technique. The experimental and numerical results show that at high turbulence intensity the relative settling velocity increases with the increasing relative turbulence intensity regardless of the Stokes number. At intermediate turbulence intensity, it seems that the settling data bifurcate, i.e., the particles at the large Stokes number tend to be slowed, whereas the settling velocity of particles is increased at the small Stokes number.

This study presents measured and computational results of a flow pattern at a junction with equal and opposing flows in the upstream channel that collide and turn $90°$ into the branch channel. The computational results are obtained using a two-dimensional, depth-averaged model with the $k\text{-}\epsilon$ turbulent closure scheme. The aim is to predict the recirculation zones that form as the flow turns into the branch channel. The simulated depth and velocity profiles in the upstream main and the downstream branch channels are found to compare well with the measurements made in the physical model for various inlet Froude numbers and width ratios of the main channel to the branch channel. The absolute relative error between the measured and computed contraction coefficient, a measure of the recirculation zone size, is less than 4.7%. The computational model is then used to develop curves for the contraction coefficient for various inlet Froude numbers and ratios of main channel width to the branch channel width for design purposes.

A numerical study to describe the transition regime between the skimming and wake interference flows due to the influence of an idealized bed roughness in a water flume was carried out here using the lattice model approach. The model reproduced the skimming, transition, and wake interference regimes for different aspect ratios that determine the bed roughness geometry. The simulated turbulent structures were visualized by drawing the trajectories of a large number of passive tracer particles released in the computational domain, and the results agreed with those reported by the research works. The dimensionless streamwise and vertical turbulent intensities were calculated at five test sections. The results obtained supported the visualized flow patterns permitting us to detect the presence of a shear layer developed at the top of the roughness element, whose strength varied according to the flow regime simulated.