Journal of Hydraulic Engineering

Inundation models based on the shallow water equations (SWE) have been shown to perform well for a wide variety of situations even at the limit of their theoretical applicability and, arguably, somewhat beyond. One of these situations is the catastrophic event of floods induced by dyke breach and consequent dyke erosion. The dyke collapse is often not sudden—as assumed by many flood simulations in which the dyke boundary is treated as a “dam-break.” The dyke erosion is a gradual and complex process that delays the onset of the flood, affecting the hydrograph of the flow. To simulate correct temporal passage of a flood, it is important to understand the rate at which these dykes collapse. In this paper, an overtopping flood event combined with dyke erosion is simulated. The model is built upon the two-dimensional (2D) shallow water equations together with sediment-flow interactions and incorporates a sediment transport equation. The model is solved using a second-order Godunov-type finite volume method that is accurate and robust. For breach formation, the lateral erosion collapse due to slope instabilities has a significant impact and must be considered, in this paper a simple mathematical approach in two dimensions is proposed to evaluate the stability of lateral bed slope. Several experimental tests are used for validating the morphodynamic model. It is verified that the simulated results agree well with measured data, and that the model predicts such flow phenomena effectively. The validated model is applied to predict a flood event caused by dyke breach with an initial trapezoidal shape due to flow overtopping. The predicted results for the flood event indicate that the 2D process-based morphodynamic model is capable of simulating the spatial and temporal changes of the flood event, including predicting the outflow hydrograph with good agreement, as well as the erosion of the dyke and subsequent deposition process.

The standard experimental methods used for sampling suspended loads in large rivers are usually time consuming, unsafe, rather expensive, and have a limited spatial resolution. Acoustic Doppler current profilers (ADCPs), usually applied to measure the flow discharge, may also be used to assess the suspended sediment concentration by analyzing the backscattering acoustic strength. Though important efforts have been dedicated to test this method, results are not as reliable as engineering practices require, especially in large fluvial systems. In this paper, the correlation between the corrected backscatter from a 1,200 kHz ADCP and the suspended concentration from a depth-integrated sampler is presented and discussed. Despite the assumptions required to utilize this method (i.e., monosized grain and homogeneous vertical concentration), the results showed acceptable differences when they were compared with traditional methods. An evaluation of the backscatter and attenuation of sound produced by fine and coarse material is presented. Finally, the total suspended load of bed sediment is assessed using moving-boat ADCP measurements and compared with results from the corresponding standard method. Differences are at most 46%.

Sediment trapping behavior of slit-check dams and related design criteria are usually evaluated assuming the hypothesis of steady-state hydraulic conditions associated with the peak of the design flood. A novel approach based on the use of a 1D unsteady flow numerical model to simulate in detail transport processes upstream from slit-check dams during flood events is presented in this paper. The adopted model is validated by comparison with results of laboratory experiments from the literature showing the ability to reproduce accurately the temporal evolution of the sediment deposit behind the dam. The presented model-based approach enabled a realistic evaluation of the sediment trapping efficiency of the dam during the flood, i.e., the percent trapped portion of sediment volume transported by the flood, for different sizes of the dam slit. Especially for narrow slits, simulations revealed lower trapping efficiencies of slit-check dams at the flow peak condition compared to an approach from literature based on the steady-state flow assumption. Also, simulations allowed for the evaluation of the behavior of the dam at the end of the flood event, revealing the potential of the model-based approach to analyze the morphological evolution of the river downstream of the dam.

Cases of damages experienced in stilling basins and on the toe of chute spillways are recognized to be due to global instantaneous uplift force resulting from imbalance between the instantaneous pressure distribution both above and below slabs. The latter is due to pressure fluctuation propagation forced though unsealed slab joints. In the past, several theoretical approaches were developed to estimate the uplift contribution due to pressure transmission underneath the slabs. In the paper, a model is presented, based on unsteady flow analysis of seepage through porous media, that shows that the propagation models proposed in literature are particular cases of this more comprehensive formulation. In addition, the use of the unsteady seepage model makes it possible to account for finite thickness foundation layers, typical in the cases of earth dams, rock-fill dams, and in other dam types, whenever the slabs are posed on alluvial substrates. Experimental results obtained in laboratory facilities, as reported in literature, might underestimate the stable slab thickness due to limits in accurately reproducing the foundation layer.

The consequences of rapid and extreme flooding events, such as tsunamis, riverine flooding, and dam breaks show the necessity of developing efficient and accurate tools for studying these flow fields and devising appropriate mitigation plans for threatened sites. Two-dimensional simulations of these flows can provide information about the temporal evolution of water depth and velocities, but the accurate prediction of the arrival time of floods and the extent of inundated areas still poses a significant challenge for numerical models of rapid flows over rough and variable topographies. Careful numerical treatments are required to reproduce the sudden changes in velocities and water depths, evolving under strong nonlinear conditions that often lead to breaking waves or bores. In addition, new controlled experiments of flood propagation in complex geometries are also needed to provide data for testing the models and evaluating their performance in more realistic conditions. This work implements a robust, well-balanced numerical model to solve the nonlinear shallow water equations (NSWEs) in a nonorthogonal boundary fitted curvilinear coordinate system. It is shown that the model is capable of computing flows over highly variable topographies, preserving the positivity of the water depth, and providing accurate predictions for the wetting and drying processes. The model is validated against benchmark cases that consider the use of boundary fitted discretizations of the computational domain. In addition, a laboratory experiment is performed of a rapid flood over a complex topography, measuring the propagation of a dam break wave on a scaled physical model, registering time series of water depth in 19 cross sections along the flow direction. The data from this experiment are used to test the numerical model, and compare the performance of the current model with the numerical results of two other recognized NSWE models, showing that the current model is a reliable tool for efficiently and accurately predicting extreme inundation events and long-wave propagation over complex topographies.

The motion of graded gravels under steady and spatially uniform turbulent flow is investigated in laboratory conditions using particle tracking velocimetry (PTV). The gravel bed is subjected to flows approaching critical armor velocity, and water worked until static armor is reached. A digital particle tracking (DPT) algorithm, based on image subtraction between subsequent frames, is developed and applied on the particle scale as the graded gravel bed is water-worked. The dynamic evolution of graded gravels is quantified continuously for up to 8 h. Characteristics of particle motion are identified, and movement patterns under complex flow conditions are analyzed. Particle tracking is applied to low-frequency (0.67-fps) and high-frequency (30-fps) data. This study provides a new perspective on gravel particle transport distances, trajectory sinuosity, sediment transport rate, fractional sediment transport rates, particle movement patterns, and instantaneous particle velocities.

In the last two decades, energy dissipation in unsteady-state pressurized pipe flow has been examined by various authors, where the instantaneous wall shear stress is split into a quasi-steady and an unsteady shear stress component. The focus of most past studies is on formulating expressions for the unsteady wall shear stress, but there has been less work on the key parameters governing the dominance of unsteady friction in transient flows. This paper derives an expression for the head envelope damping for turbulent flows in smooth and rough pipes and provides new and carefully measured field data for the initial (i.e., pretransient) Reynolds number, ${\mathsf{R}}_{\mathbf{0}}$, that ranges from 97,000 to 380,000. The analytical solutions is derived on the basis of one-dimensional (1D) water hammer equations in which the unsteady component is represented by existing convolutional unsteady friction formulas for both smooth and rough turbulent subregimes. The analytical solution is used to formulate general, encompassing and theoretically-based dimensionless parameters to assess the importance of unsteady friction in comparison to the quasi-steady component. In addition, the analytical solution furnishes the similitude relations that allowed the damping behavior from existing laboratory tests, the field tests conducted as part of this research, and the weighting function-based (WFB) models to be investigated and compared in a coherent manner in a single graph. The analysis confirms that the magnitude of ${\mathsf{R}}_{\mathbf{0}}$ has a significant impact on the damping for transients generated by flow stoppage. In addition, the results show that convolutional unsteady friction model that uses the frozen eddy viscosity hypothesis and ${\mathsf{R}}_{\mathbf{0}}$ has accuracy that decreases with time. An improvement for this shortcoming is proposed and verified and involves the use of the instantaneous Reynolds number in lieu of the pretransient Reynolds number in the evaluation of the WFB models. The result is a modified unsteady friction model that provides improved matches for both laboratory and field data compared with the original model.

An analytical solution of a model of contaminant transport in the advective zone of rivers is presented and evaluated. An existing model that accounts for transport in the advective zone by dividing the channel into flowing and stagnant zones is solved with Laplace transforms for the case of a Gaussian pulse injected into the center of the channel. The effects of the two main parameters of the model, the fraction of the channel occupied by the stagnant zone and a transfer coefficient, are consistent with expectations from the theory of shear dispersion. Another parameter, which is related to the streamwise width of the initial pulse, determines whether a separate pulse appears in the tracer-response curves. A procedure for determining the parameters from temporal moments of measured concentration curves is described and applied to measurements in the advective zone of a mountain stream. Predictions from the model of Reichert and Wanner fit the measurements—especially the peak concentration—better than predictions from the one-dimensional model.

A mathematical model describing the transient hydraulic head distribution induced by constant-head pumping/injection at a partially penetrating well in a radial two-zone confined aquifer is a mixed-type boundary value problem. The analytical solution of the model is in terms of an improper integral with an integrand having a singularity at the origin. The solution should rely on numerical methods to evaluate the integral and handle the problems of convergence and singularity. This study aims at developing a new approximate solution describing the transient hydraulic head distribution for a constant-head test (CHT) at a partially penetrating well in the aquifer. This approximate solution is acquired based on a time-dependent diffusion layer approximation proposed in the field of electrochemistry. The diffusion layer can be analogous to the radius of influence in the area of well hydraulics. The approximate solution is in terms of modified Bessel functions for aquifers with a partially penetrating well and can reduce to a simpler form in terms of a natural logarithmic function for the case of well full penetration. The predicted hydraulic heads from the present approximate solution are compared with those estimated by the Laplace-domain solution of the model. The result shows that the predicted spatial head distributions are accurate in the formation zone and fairly good in the skin zone. In addition, the present solution gives an accurate temporal head distribution at a specific location when the radius of influence is far away from the observation wells. This newly developed approximate solution has advantages of easy computing and good accuracy from practical viewpoint, and thus is a handy tool to evaluate temporal and spatial hydraulic head distributions for the CHT.

Results of eddy-resolving numerical simulations are used to investigate flow and turbulence structure around an isolated abutment with sloped sidewalls at conditions corresponding to the start (flatbed) and the end (equilibrium bathymetry) of the scour process. Besides cases where the abutment is not protected against scour using riprap, the paper considers cases where a riprap apron of constant width is present around the base of the abutment at the start of the scour process. The paper also discusses the effect of large-scale turbulence (e.g., horseshoe vortex system, eddies shed in the separated shear layer, vortices forming in the recirculation regions) on sediment entrainment and transport. Using information about the position and coherence of the large-scale turbulent structures present in the vicinity of the bed surface, the paper discusses some of the reasons for the very different bed scour patterns observed at equilibrium scour conditions for cases without and with a riprap apron. The effect of the degree of bluntness of the upstream side of the abutment on flow and turbulence structure is discussed based on comparison of results obtained for abutments with sloped sidewalls with those obtained for a vertical-wall abutment of similar length. The later type of abutment is characterized by a stronger downflow, the formation of a more coherent horseshoe vortex system, and the formation of a deeper scour hole.

Trajectories of bubbly jets in crossflows by injecting air-water mixtures vertically through a circular nozzle were experimentally studied. Bubbles separated from the water jets in strong crossflow, similarly to that of multiphase plumes in crossflow reported in the literature. Based on dimensional analysis, a semiempirical relation was developed to predict the separation height for bubbly jets with strong initial momentum. Centerline trajectories of both the water and air phases of bubbly jets were examined. After the separation, the air-phase centerlines can be treated as straight lines. The spreading rates of half-thickness and half-width of the air phase were studied along the air-phase centerline. They decreased substantially after the bubble separation from the water jets and their terminal values appeared to increase with mean bubble diameter.