Numerical Modeling of Breach Erosion of River Embankments

The process of breach erosion of river embankments depends on the interaction among flow, sediment transport, and the corresponding morphological changes. Levees often consist of noncohesive material with a wide range of grain sizes. The dam material is mainly eroded due to the transport capacity of the overtopping water. Both bed load and suspended load are of importance. For breach formation, the lateral erosion due to slope instabilities has a significant impact. A depth averaged, two-dimensional numerical model was developed to account for these processes. The sensitivity of the discharge through the breach related to different processes and material parameters was investigated and compared to experimental and field data. The results show that the most sensitive parameter of an erosion-based dike-breach simulation is the breach side-slope angle which determines the lateral erosion. The application of the described Model 2dMb to different embankment failures at the Elbe River illustrates its capability in simulating overtopping breaching.     

Diffusive Modeling of Aggradation and Degradation in Artificial Channels

The unsteady flow and solid transport simulation problem in artificial channels is solved using a three-equation model, coupled with a local erosion law. The three equations are the water mass and momentum balance equations, as well as the total solid load balance equation. It is shown that even during severe hydrological events inertial terms can be neglected in the momentum equation without any substantial change in the solution sought. Empirical equilibrium formulas were used to estimate the solid load as a function of the flow variables. Local erosion, due to the scour generated at the jump between two channels connected at different bottom elevations, was estimated adapting a literature formulation. The double order approximation time and space marching scheme, previously proposed for the solution of the unsteady flow problem in the fixed-bed case, is applied to the solution of the new system. The model was validated with both literature and new laboratory experimental data. No parameter calibration was used to fit the computed results to the experimental ones.     

Sensitivity Analysis of Nonequilibrium Adaptation Parameters for Modeling Mining-Pit Migration

The nonequilibrium adaptation parameters of a depth-averaged two-dimensional hydrodynamic and sediment transport model were examined in the study. Calculated results were compared to data measured in two sets of published laboratory experiments that investigated mining-pit migration under well-controlled boundary conditions including steady flow and uniform rectangular cross sections along the flume except in the vicinity of the experimental mining area. The two sets of experiments were chosen as representatives of bed-load-dominated and suspended-load-dominated cases, respectively. A sensitivity analysis was conducted to estimate the influence of the nonequilibrium adaptation parameters on mining-pit migration simulation. Calculated results indicate that appropriate selection of the adaptation parameters is critical in order to close the nonequilibrium sediment transport formulas when modeling mining-pit migration.     

Simulating Bed-Load Transport in a Complex Gravel-Bed River

An existing two-dimensional mobile-bed hydrodynamic model has been modified to simulate bed-load transport in a complex gravel-bed river. We investigated the sensitivity of predicted bed load to control parameters, and compared model predictions of flow depth, shear stress, and gravel transport with field measurements made from the river. The predictions are based on concurrent field data of flow discharge, water level, and sediment for model input. The model takes into account multiple-fraction transport rates, and continuously updates the river bed and surface grain-size distribution. The model predictions are in reasonable agreement with field measurements.     

Sediment Transport in River Models with Overbank Flows

Some laboratory sediment-transport experiments are described in which a compound channel with a mobile-bed composed of uniform sand with a d50 of 0.88?mm was subjected to overbank flows. The main river channel was monitored to determine the effect of floodplain roughness on conveyance capacity, bed-form geometry, resistance, bed-load transport, and dune migration rate. The floodplain roughness was varied to simulate a wide range of conditions, commensurate with conditions that can occur in a natural river. For a given discharge, the main river channel bed was found to adjust itself to a quasi-equilibrium condition governed by the lateral momentum transfer between the floodplain and main channel flows and the local alluvial resistance relationship appropriate for the proportion of total flow in the main river channel. The sediment transport rate was found to reflect all these influences. The data are summarized in equation form for comparison with other experimental studies and for checking numerical river simulation models.     

Modeling Noncohesive Suspended Sediment Transport in Stream Channels Using an Ensemble-Averaged Conservation Equation

The governing conservation equation for the transport of noncohesive suspended sediment in erodible channels is recognized as a stochastic partial differential equation due to the uncertainties in the parameters, and a deterministic ensemble-averaged equation is developed. Variables in this one-dimensional equation are represented as averaged quantities, and their covariances are also taken into account. Lateral inflows and deposition and entrainment of sediment are incorporated in the formulation. A hypothetical test problem is constructed to examine the model behavior. Manning’s coefficient, bed slope and bottom width are taken as the primary random parameters. Results from the solution of the ensemble-averaged equation are compared to results from Monte Carlo simulations. For comparison purposes, predicted values are also obtained by solving the deterministic transport equation without the covariance terms. It is found that predictions obtained from this latter approach deviate significantly from Monte Carlo simulation results. On the other hand, the ensemble-averaged predictions compare favorably to the Monte Carlo simulation results indicating that this promising technique needs further exploration.     

Three-Dimensional Modeling of Nonuniform Sediment Transport in an S-Shaped Channel

A three-dimensional numerical model was applied to compute uniform and nonuniform sediment transport and bed deformation in an S-shaped laboratory channel located at the University of Innsbruck, where detailed measurements of the velocity field and bed elevation changes were made. The channel had two bends, a trapezoidal cross section, and a slope of S = 0.005. Gravel with a mean diameter of 4.2?mm was used as movable bed material and for sediment feeding. Wu’s formula for multiple grain sizes was compared with van Rijn’s formula using one grain size. Fairly good agreement was found between the computed and measured bed elevations for both approaches, whereas Wu’s formula could further improve the numerical results. Looking at the physics of the erosion pattern, the computed scour areas were located slightly more downstream than what was observed in the physical model. The current study also includes several parameter tests: grid distribution in vertical, lateral, and longitudinal direction; time step; number of inner iterations/time step; active sediment layer thickness; and the Shields coefficient. The variation of those parameters gave some differences in the results, but the overall pattern of bed elevation changes remained the same.     

Depth-Averaged Two-Dimensional Numerical Modeling of Unsteady Flow and Nonuniform Sediment Transport in Open Channels

A depth-averaged two-dimensional (2D) numerical model for unsteady flow and nonuniform sediment transport in open channels is established using the finite volume method on a nonstaggered, curvilinear grid. The 2D shallow water equations are solved by the SIMPLE(C) algorithms with the Rhie and Chow’s momentum interpolation technique. The proposed sediment transport model adopts a nonequilibrium approach for nonuniform total-load sediment transport. The bed load and suspended load are calculated separately or jointly according to sediment transport mode. The sediment transport capacity is determined by four formulas which are capable of accounting for the hiding and exposure effects among different size classes. An empirical formula is proposed to consider the effects of the gravity on the sediment transport capacity and the bed-load movement direction in channels with steep slopes. Flow and sediment transport are simulated in a decoupled manner, but the sediment module adopts a coupling procedure for the computations of sediment transport, bed change, and bed material sorting. The model has been tested against several experimental and field cases, showing good agreement between the simulated results and measured data.     

Flood Inundation Modeling with an Adaptive Quadtree Grid Shallow Water Equation Solver

Flood risk studies require hydraulic modeling in order to estimate flow depths and other hydraulic variables in the floodplain for a wide range of input conditions. Currently there is a need to improve the computational efficiency of fully two-dimensional numerical models for large-scale flood simulation. This paper describes an adaptive quadtree grid-based shallow water equation solver and demonstrates its capability for flood inundation modeling. Due to the grid dynamically adapting to dominant flow features such as steep water surface gradients and wet-dry fronts, the approach is both efficient and accurate. The quadtree model is applied to a realistic scenario of flood inundation over an urban area of 36?km2, resulting from the flood defenses breaching at Thamesmead on the River Thames, United Kingdom. The results of the simulation are in close agreement with alternative predictions obtained using the commercially available software TUFLOW.     

HSPF Simulation of Runoff and Sediment Loads in the Upper Changjiang River Basin, China

To evaluate the performance of a computer model simulating runoff and sediment load in the upper region of the Changjiang (Yangtze River) basin over a relatively short time interval, including examining the applicability of the input precipitation data generated from global circulation models and satellite data, we used a spatially distributed model, HSPF with the International Satellite Land Surface Climatology Project (ISLSCP) precipitation data for 1987 and 1988 as input data. The Nash–Sutcliffe coefficient (R2) for 5-day average streamflow was 0.94 in the calibration period and 0.95 in the verification period for the whole upper region. Moreover, the model simulated the 5-day average streamflow well in each main tributary, as shown by R2 values of 0.46–0.96, except that it underestimated the peak flow rates during the flood season over 2 years by up to 71% in Tuojiang and 61% in Jialingjiang. The model simulated the 5-day concentrations of suspended solids (SS) fairly well in the headwaters and upper regions of the Jinshajiang, Yalongjiang, and Minjiang watersheds, as shown by R2 values of 0.31–0.65. In the other regions, however, the model underestimated the SS load by up to 72%, and rarely simulated the fluctuation of SS concentration in each river channel during the flood season. These errors led to the underestimation of sediment runoff volume from the whole upper region during the flood season, as shown by the ratio of the simulated sediment load to the observed data at Yichang: 0.69 in the calibration period and 0.68 in the verification period. The ISLSCP precipitation tended to be more frequent and less intense than the measured precipitation. This was probably the main reason why the HSPF did not perform well in all regions at all times.     

Near-Field Mixing Downstream of a Multiport Diffuser in a Shallow River

Near-field mixing downstream of a multiport diffuser in a wide shallow river was studied with a field dye test. Dye concentrations at different depths and lateral locations were measured. The near-field mixing was analyzed in four zones: the free jet zone, the jet surface-impingement zone, the merging zone, and the vertical mixing zone. Analytical models were proposed to derive the three-dimensional concentration field after the jets impinged the water surface. After the impingement, the dye concentration can be predicted well by treating the multiple jets as a simple mathematical summation of individual jets. The vertical mixing zone was dominated by the riverbed friction-induced turbulence, with little effect from the effluent momentum and buoyancy. The results of the field data were also used to validate the applicability of some existing models for multiport diffusers.     

Head Reconstruction Method to Balance Flux and Source Terms in Shallow Water Equations

This paper presents the head reconstruction method (HRM), a new technique that can be used within the finite volume framework to make shallow water models well balanced, i.e., to correct the imbalance that exists between flux and source terms in the equation discretization in the case of irregular bathymetry thus providing unphysical solutions. This technique, based on considering, within each computational cell, the total head of the flow (i.e., the sum of the elevation, pressure and kinetic energies per unit weight of the fluid) as an equilibrium variable, enables the preservation of dynamic equilibria under subcritical, transcritical, and supercritical flow conditions. The new technique is applied to the one-dimensional total variation diminishing (TVD) MUSCL-Hancock scheme and the conservation property is then proven mathematically for this scheme under static equilibrium conditions. Furthermore, the effectiveness of the HRM is tested and compared with two other well balancing techniques based on considering the water elevation as an equilibrium variable in various steady flow case studies. In the end the robustness of the HRM is tested in the simulation of dam-break flow over irregular bathymetry.     

Numerical Simulation of Relatively Wide, Shallow Channels with Erodible Banks

A two-dimensional numerical model was developed to simulate relatively wide, shallow rivers with an erodible bed and banks composed of well-sorted, sandy materials. A moving boundary-fitted coordinate system was used to calculate water flow, bed change, and bank erosion. The cubic interpolated pseudoparticle method was used to calculate flow, which introduced little numerical diffusion. The sediment-transport equation for the streamline and transverse transport was used to estimate bed and bank evolution over time, while considering the secondary flow. Bank erosion was simulated when the gradient in the cross-sectional direction of the banks was steeper than the submerged angle of repose because of bed erosion near the banks. The numerical model reproduced the features of central bars well, such as bar growth, channel widening due to divergence of the flow around the bars, scour holes at the lee of the bars, and the increase of bar size with time. These features were in accordance with the observations for laboratory experiments. It also reproduced the features of braided rivers, such as the generation of new channels and abandonment of old channels, the bifurcation and confluence of channels, and the lateral migration of the channels. The model showed that the sediment discharge rate fluctuated with time, one of the dynamic features observed in braided channels.     

Prediction of Sediment Load Concentration in Rivers using Artificial Neural Network Model

An artificial neural model is used to estimate the natural sediment discharge in rivers in terms of sediment concentration. This is achieved by training the network to extrapolate several natural streams data collected from reliable sources. The selection of water and sediment variables used in the model is based on the prior knowledge of the conventional analyses, based on the dynamic laws of flow and sediment. Choosing an appropriate neural network structure and providing field data to that network for training purpose are addressed by using a constructive back-propagation algorithm. The model parameters, as well as fluvial variables, are extensively investigated in order to get the most accurate results. In verification, the estimated sediment concentration values agree well with the measured ones. The model is evaluated by applying it to other groups of data from different rivers. In general, the new approach gives better results compared to several commonly used formulas of sediment discharge.     

Three-Dimensional Modeling of Sediment Transport in a Narrow 90° Channel Bend

A three-dimensional numerical model was used for calculating the velocity and bed level changes over time in a 90° bended channel. The numerical model solved the Reynolds-averaged Navier-Stokes equations in three dimensions to compute the water flow and used the finite-volume method as the discretization scheme. The k-ε model predicted the turbulence, and the SIMPLE method computed the pressure. The suspended sediment transport was calculated by solving the convection diffusion equation and the bed load transport quantity was determined with an empirical formula. The model was enhanced with relations for the movement of sediment particles on steep side slopes in river bends. Located on a transversally sloping bed, a sediment particle has a lower critical shear stress than on a flat bed. Also, the direction of its movement deviates from the direction of the shear stress near the bed. These phenomenona are considered to play an important role in the morphodynamic process in sharp channel bends. The calculated velocities as well as the bed changes over time were compared with data from a physical model study and good agreement was found.     

Limitations of Depth-Averaged Modeling for Shallow Wakes

Large-scale horizontal vortical structures are generic features of shallow flows which are often modeled using the two-dimensional (2D) depth-averaged equations. Such modeling is investigated for the well-defined case of shallow wakes of a conical island of small side slope for which a three-dimensional (3D) boundary-layer (3DBL) model has previously been validated through comparison with experiment. The 3DBL model used a 3D, two-mixing-length, eddy-viscosity turbulence model with a vertical mixing length of classical Prandtl form and a horizontal mixing length some multiple of this. A multiple of six gave good predictions. This mixing length approach is reduced to depth-averaged form, giving a horizontal mixing length of about half the water depth. The shallow wakes may be vortex shedding or steady/stable and are conventionally defined by a stability parameter. The critical value above which a stable wake is formed is considerably overestimated by the depth-averaged model (for a range of mixing lengths) and the length of stable wake bubble is considerably underestimated. It seems likely that this is because the amplification of friction coefficient due to horizontal strain rates is not represented. However, when vortex shedding is prominent the 2D and 3DBL wake structures are quite similar. These results show, for example, the limitations of depth-averaged models for the prediction of solute dispersion.     

Numerical Model of Sediment Pulses and Sediment-Supply Disturbances in Mountain Rivers

Sediment pulses in rivers can result from many mechanisms including landslides entering from side slopes and debris flows entering from tributaries. Artificial sediment pulses can be caused by the removal of a dam. This paper presents a numerical model for the simulation of gravel bedload transport and sediment pulse evolution in mountain rivers. A combination of the backwater and quasi-normal flow formulations is used to calculate flow parameters. Gravel bedload transport is calculated with the surface-based bedload equation of Parker in 1990. The Exner equation of sediment continuity is used to express the mass balance at different grain size groups and lithologies, as well as the abrasion of gravel. The river is assumed to have no geological controls such as bedrock outcrops and immobile boulder pavements. The results of nine numerical experiments designed to study various key parameters relevant to the evolution of sediment pulses are reported here. Results of the numerical runs indicate that the evolution of sediment pulses in mountain rivers is dominated by dispersion rather than translation. Here dispersion is an expression for the observation that a sediment pulse aggrades both upstream and downstream of its apex whereas its amplitude decreases in time. The results also indicate that grain abrasion is an important and yet often neglected mechanism in removing the excess sediment associated with pulse inputs from some mountain rivers.     

Comparison of Two Techniques to Measure Sediment Erodibility in the Fox River, Wisconsin

This paper compares the results of two sediment erodibility test methods that have been applied on surficial sediments at a number of locations on the Fox River in Wisconsin. The methods include a straight flume that is deployed in situ (the FLUME) and a straight laboratory flume (the SEDFLUME). The sediment erosion rates measured near the surface (in the top four centimeters) as a function of bottom stress were compared. On average, the erodibility measured by the SEDFLUME was about 5.5 times greater than that measured by the FLUME. A possible reason for the difference is the relatively short test section of the SEDFLUME.     

Compatibility of Reservoir Sediment Flushing and River Protection

In this paper, we propose a system of numerical models for the compatibility assessment of reservoir sediment flushing and protection of downstream river environments. The model system is made up of two simulation models. The first model simulates soil erosion in watershed slopes and sediment transport in the tributary of the reservoir by means of a weighted essentially nonoscillatory (WENO) method, which is conservative and fourth-order accurate in space and time. The second model simulates velocity and suspended solid concentration fields in the reservoirs. This model is based on the three-dimensional (3D) numerical integration of motion and concentration equations, expressed in contravariant form on a generalized boundary-conforming curvilinear coordinate system by using a conservative and higher-order accurate numerical scheme. The proposed system of models is applied to the Pieve di Cadore (Veneto, Italy) reservoir and to its catchment area. By comparing suspended solid concentrations that are discharged through the bottom outlets during flushing operations with suspended solid concentrations in the main river during natural flooding, we perform an assessment of the compatibility between sediment flushing and the protection of the river ecosystem downstream.