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.     

Calculation of Bed Changes in Mountain Streams

Simulation of flow and sediment transport in mountain streams is complicated by the presence of high gradients, abrupt changes in geometry, variations in regime of flow, and large roughness elements. Most of the numerical models to predict aggradation and degradation in alluvial channels have been developed for low-gradient rivers. This paper is devoted to the development of a numerical model to calculate bed elevation and grain size distribution changes in mountain streams where the maximum bed material size is in the range of boulders. An attempt is made to validate the model by using observed field data collected upstream from a small retention dam in a Venezuelan stream. After calibration of the sediment transport equation, reasonable agreement is obtained for the variations in the grain size distribution of the bed-surface material. An additional application is presented in the Cocorotico River, a small mountain stream located in the northwest region of Venezuela, which illustrates the adaptability of the model to handle a case of coarsest-bed-material removal from the active channel and to simulate the armoring process.     

Three-Dimensional CFD Modeling of Self-Forming Meandering Channel

A three-dimensional CFD model was used to compute the formation of the meandering pattern in an initially straight alluvial channel. The numerical model was based on the finite volume method using an unstructured grid with dominantly hexahedral cells. The k-ε model was used to predict turbulence and the SIMPLE method was used to compute the pressure. The sediment transport was computed as bed load in addition to solving the convection-diffusion equation for suspended sediment transport. The bed changes were calculated and the grid was altered during the computation as channel erosion and deposition caused wetting and drying. The model was tested by comparing with results from physical model studies carried out at Colorado State Univ., Fort Collins, Colo. The results showed successfully the replication of many of the meander characteristics, including secondary currents, cross-sectional profiles, meander planform, meander wavelength, downstream meander migration, and chute formation.     

Simulating Sediment Transport in a Flume with Forced Pool-Riffle Morphology: Examinations of Two One-Dimensional Numerical Models

One-dimensional numerical sediment transport models (DREAM-1 and DREAM-2) are used to simulate seven experimental runs designed to examine sediment pulse dynamics in a physical model of forced pool-riffle morphology. Comparisons with measured data indicate that DREAM-1 and -2 closely reproduce the sediment transport flux and channel bed adjustments following the introduction of fine and coarse sediment pulses, respectively. The cumulative sediment transport at the flume exit in a DREAM-1 simulation is within 10% of the measured values, and cumulative sediment transport at flume exit in a DREAM-2 simulation is within a factor of 2 of the measured values. Comparison of simulated and measured reach-averaged aggradation and degradation indicates that 84% of DREAM-1 simulation results have errors less than 3.3?mm, which is approximately 77% of the bed material geometric mean grain size or 3.7% of the average water depth. A similar reach-averaged comparison indicates that 84% of DREAM-2 simulation results have errors less than 7.0?mm, which is approximately 1.7 times the bed material geometric mean grain size or 11% of the average water depth. Simulations using measured thalweg profiles as the input for the initial model profile produced results with larger errors and unrealistic aggradation and degradation patterns, demonstrating that one-dimensional numerical sediment transport models need to be applied on a reach-averaged basis.     

3D Numerical Modeling of Flow and Sediment Transport in Laboratory Channel Bends

The development of a fully three-dimensional finite volume morphodynamic model, for simulating fluid and sediment transport in curved open channels with rigid walls, is described. For flow field simulation, the Reynolds-averaged Navier–Stokes equations are solved numerically, without reliance on the assumption of hydrostatic pressure distribution, in a curvilinear nonorthogonal coordinate system. Turbulence closure is provided by either a low-Reynolds number k?ω turbulence model or the standard k?ε turbulence model, both of which apply a Boussinesq eddy viscosity. The sediment concentration distribution is obtained using the convection-diffusion equation and the sediment continuity equation is applied to calculate channel bed evolution, based on consideration of both bed load and suspended sediment load. The governing equations are solved in a collocated grid system. Experimental data obtained from a laboratory study of flow in an S-shaped channel are utilized to check the accuracy of the model’s hydrodynamic computations. Also, data from a different laboratory study, of equilibrium bed morphology associated with flow through 90° and 135° channel bends, are used to validate the model’s simulated bed evolution. The numerically-modeled fluid and sediment transportation show generally good agreement with the measured data. The calculated results with both turbulence models show that the low-Reynolds k?ω model better predicts flow and sediment transport through channel bends than the standard k?ε model.     

Exact Discontinuous Solutions of Exner’s Bed Evolution Model: Simple Theory for Sediment Bores

Determining the evolution of the bed of a river or channel due to the transport of sediment was first examined in a theoretical context by Exner in 1925. In his work, Exner presents a simplified bed evolution model derived from the conservation of fluid mass and an “erosion” equation that is commonly referred to as the sediment continuity or Exner equation. Given that Exner’s model takes the form of a nonlinear hyperbolic equation, one expects, depending on the given initial condition of the bed, the formation of discontinuities in the solution in finite time. The analytical solution provided by Exner for his model is the so-called classical or genuine solution of the initial-value problem, which is valid while the solution is continuous. In this paper, using the general theory of nonlinear hyperbolic equations, we consider generalized solutions of Exner’s classic bed evolution model thereby developing a simple theory for the formation and propagation of discontinuities in the bed or so-called sediment bores.     

Applicability of Sediment Transport Capacity Formulas to Dam-Break Flows over Movable Beds

In this paper, we investigate the extent to which well-known sediment transport capacity formulas can be used in one-dimensional (1D) numerical modeling of dam-break waves over movable beds. The 1D model considered here is a one-layer model based on the shallow-water equations, a bed update (Exner) equation, a space-lag equation for the nonequilibrium sediment transport and an empirical formula calculating the sediment transport capacity of the flow. The model incorporates a variety of sediment transport capacity formulas proposed by Meyer-Peter and Müller, Bagnold, Engelund and Hansen, Ackers and White, Smart and Jaeggi, van Rijn, Rickenmann, Cheng, Abrahams and Camenen, and Larson. We examine the performance of each formula by simulating four idealized laboratory cases on dam-break waves over sandy beds. Comparisons between numerical results and measurements show that for each case better predictions are obtained using a particular formula, but overall, formulas proposed by Meyer-Peter and Müller (with the factor 8 being replaced by 12), Smart and J?ggi, Cheng, Abrahams and Camenen, and Larson rank as the best predictors for the entire range of conditions studied here. Moreover, results show that in the cases where a bed step exists, implementing a mass failure mechanism in the numerical modeling plays an important role in reproducing the bed and water profiles.     

Density Functions for Entrainment and Deposition Rates of Uniform Sediment

A model has been developed for the prediction of the density functions of bed-elevation and entrainment and deposition rates of sediment in sand bed streams within the lower regime flow condition. The model incorporates both statistical and deterministic parameters in its form. A total of 46 experimental runs have been carried out in a recirculating tilting flume under the equilibrium flow condition using three grain sizes of uniform gradation to validate the model and estimate its parameters. The model parameters are related to the hydraulic conditions of flow and fluid and sediment properties through dimensional and regression analyses. The study has shown that the density functions of bed elevation and entrainment and deposition rates can be approximated quite satisfactorily with the normal distribution curve. Transformation of the density functions into the standardized normal distribution curve provides a unique pattern for all the experimental runs regardless of the sediment grain size, flow condition, and shapes and dimensions of the bed forms. The developed density functions have been utilized to provide a closure for the probabilistic Exner equation for uniform sediment.     

Case Study: Equivalent Widths of the Middle Rio Grande, New Mexico

Successive reaches of the Rio Grande have maintained equivalent channel widths of 50 and 250?m, respectively, over long periods of time. It is hypothesized that alluvial channels adjust bed slope to match the long-term changes in channel width. Analytical relationships show that wider river reaches develop steeper slopes. A modeling approach using daily water and sediment discharges simulates the transient evolution of bed elevation changes. The analytical and numerical models are in very good agreement with the longitudinal profile measurements of the Bosque del Apache reach of the Rio Grande, NM, from 1992 to 1999. The slope of the 50?m wide reach was 50?cm/km and the slope of the 250?m wide reach of the same river increased to 80?cm/km. This unsteady daily transient model compares well with a steady transient solution at a constant discharge close to the mean annual flow. The transient slope adjustments can also be approximated with an exponential model. Accordingly, it takes about 20–25?years for the Rio Grande to achieve about 90% of its slope adjustment.     

Case Study: Delayed Sedimentation Response to Inflow and Operations at Sanmenxia Dam

This paper presents a study on the reservoir sedimentation processes in response to changes in incoming flow at the upstream and changes in the pool level at the downstream for Sanmenxia Reservoir, which is located on the middle reach of the Yellow River in China and has experienced serious sedimentation problems even since its impoundment in 1960. The hysteresis effect in reservoir sedimentation was used as the basis for analysis and its behavior was fully investigated throughout this study. The research found that the rise in the elevation of Tongguan, which is located in the backwater region at a distance of 113.5?km upstream of the Sanmenxia Dam, had a time delay of about 2?years compared with the sediment deposition in the reservoir area downstream of Tongguan. Moreover the accumulated sediment deposition in the reservoir area was closely related not only to the current year’s flow and dam operational conditions, but also to the preceding 3–4?years’ flow and dam operational conditions. Likewise the variation of Tongguan’s elevation was a function of 6?years’ linearly superimposed runoff, and the channel bed slope in the vicinity of Tongguan was determined by a moving average pool level over a 7?year period. The research results are of practical importance in particular for optimizing the operation of Sanmenxia Dam, and the finding of the hysteresis phenomenon in the sedimentation process of the reservoir is of merit to the advancement of sedimentation science.     

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.     

Numerical Modeling of Bed Evolution in Channel Bends

A two-dimensional numerical model is developed to predict the time variation of bed deformation in alluvial channel bends. In this model, the depth-averaged unsteady water flow equations along with the sediment continuity equation are solved by using the Beam and Warming alternating-direction implicit scheme. Unlike the present models based on Cartesian or cylindrical coordinate systems and steady flow equations, a body-fitted coordinate system and unsteady flow equations are used so that unsteady effects and natural channels may be modeled accurately. The effective stresses associated with the flow equations are modeled by using a constant eddy-viscosity approach. This study is restricted to beds of uniform particles, i.e., armoring and grain-sorting effects are neglected. To verify the model, the computed results are compared with the data measured in 140° and 180° curved laboratory flumes with straight reaches up- and downstream of the bend. The model predictions agree better with the measured data than those obtained by previous numerical models. The model is used to investigate the process of evolution and stability of bed deformation in circular bends.     

Dam-Break Wave-Front Celerity

This work is concerned with the role that friction and inertia effects can play on the magnitude of dam-break wave-front celerity. Classic analytical solutions are presented. A large collection of experimental data is used, covering a wide range of different initial conditions: fixed bed or mobile bed (five types of bed material), dry or wet bed downstream, and with or without bed step. To overcome the limitations of analytical solutions, a numerical model is used. The model is based on the shallow-water approach with contact-load dominated sediment transport, and it makes use of developments recently made in the study of sheet flows. The analytical and numerical results are compared with experimental data. It was found that the celerity is mainly dictated by the friction coefficient, by the sediment inertia, by the initial downstream water depth, and by the initial bed step height. For good data fitting, the friction coefficient must be influenced by the type of bed, fixed or mobile. In the latter, the coefficient must vary with the bed material characteristics. The dissimilarities between the experimental, analytical, and numerical results are interpreted.     

Influence of Vertical Resolution and Nonequilibrium Model on Three-Dimensional Calculations of Flow and Sediment Transport

This note, using a three-dimensional model of river flow and sediment transport, examines the effect of the vertical resolution and the choice a nonequilibrium adaptation length Ls in predicting flow and sediment transport around groins in China’s Yongding River. The results show that a fine vertical grid and nonequilibrium sediment transport model provide good predictions, especially on the river bed profile with an obvious main channel and flood plain.     

Effect of Bed Armoring on Bed Topography of Channel Bends

The two-dimensional numerical model previously developed by the writers for modeling the bed variations in a channel bend with uniform sediment is upgraded to incorporate the nonuniformity of sediment particles as well as bed armoring. In this model, the two-dimensional, depth-averaged, unsteady flow equations along with the bed-load mass conservation equation are solved in a body-fitted coordinate system by using the Beam and Warming alternating-direction implicit (ADI) scheme. A one-dimensional bed surface armoring approach is extended herein for application to a two-dimensional domain. The model is applied to a 180° bend with a constant radius under unsteady flow conditions. Numerical simulations are carried out to study the effect of bed armoring on the bed deformations in channel bends. Results show that bed armoring reduces scour in channel bends.     

Prediction of Concerted Sediment Flushing

A proprietary one-dimensional numerical model was developed for predicting the amounts of sediment flushed and deposited in the reservoirs in series, the bed evolutions, and variations of the suspended solids concentrations along a river during the concerted sediment flushing events. The model consists of a flow movement module and sediment transport module in which the bed material load is taken as sediment mixture. The nonuniform property of the bed material load is modeled by the introduction of a mixing layer, transition layer, and deposition strata. The model was calibrated on the basis of the field data at Dashidaira and Unazuki reservoirs on the Kurobe River in Japan. The calculated results are in good agreement with the measurements. For the reservoirs out of Japan, the Ashida and Michiue bed load formula used in the model should be verified or replaced by other formulas.     

Modeling Bed Changes in Meandering Rivers Using Triangular Finite Elements

A two-dimensional depth-averaged model was used for the simulation of scour and deposition in sand-bed meandering channels with fixed banks. The model employs unstructured meshes based on triangular elements and incorporates the effects of curvature-induced helical flow and transverse bed slope in the direction of bed-load sediment transport. The model was tested using experimental data from a well-known laboratory curved channel and a full scale meandering river. The numerical results agreed well with observed data, demonstrating that the model can reproduce the main features of bed profiles along meandering rivers, such as the formation of point bars and pools.     

Case Study of Fluvial Modeling of River Responses to Dam Removal

A plan was made to remove Matilija Dam on the Ventura River. With dam removal, the delta in the reservoir and the downstream channel were expected to undergo major changes in morphology. The FLUVIAL-12 model was employed to simulate reservoir and river channel responses after dam removal. As a first step, the model was calibrated using the Ventura River data to establish its validity. In calibration, the model was used to simulate the fluvial processes starting from the time of dam completion. The simulated sediment deposition above the Matilija Dam matches closely with the deposits measured by the U.S. Bureau of Reclamation. A large amount of sediment was stored in the reservoir; some of the stored sediment would be transported downstream after dam removal. An important consequence of dam removal is the major increase of sediment release to the river channel downstream. The sediment supply to the downstream reach is not only from the stored sediment in the reservoir but also from natural sediment inflow from the upstream watershed. Therefore, sediment supply to the downstream reach will exceed the natural sediment flow before the dam presence. This situation tends to overload the downstream reach with sediment, resulting in excessive deposition. The amount of sediment release from the area above the removed dam is closely related to the changes in reservoir morphology. It is necessary to model changes in the channel bed profile and channel width during erosion in order to determine the amount of sediment removal. The amount of sediment release may not be simulated using an erodible-bed model but it may be determined using an erodible boundary model.     

One-Dimensional Numerical Model for Nonuniform Sediment Transport under Unsteady Flows in Channel Networks

In this study, the proposed one-dimensional model simulates the nonequilibrium transport of nonuniform total load under unsteady flow conditions in dendritic channel networks with hydraulic structures. The equations of sediment transport, bed changes, and bed-material sorting are solved in a coupling procedure with a direct solution technique, while still decoupled from the flow model. This coupled model for sediment calculation is more stable and less likely to produce negative values for bed-material gradation than the traditional fully decoupled model. The sediment transport capacity is calculated by one of four formulas, which have taken into consideration the hiding and exposure mechanism of nonuniform sediment transport. The fluvial erosion at bank toes and the mass failure of banks are simulated to complement the modeling of bed morphological changes in channels. The tests in several cases show that the present model is capable of predicting sediment transport, bed changes, and bed-material sorting in various situations, with reasonable accuracy and reliability.     

Three-Dimensional Numerical Model for Flow and Bed Deformation around River Hydraulic Structures

This paper describes a numerical model developed to simulate flow and bed deformation around river hydraulic structures. The model solved the fully three-dimensional, Reynolds-averaged Navier–Stokes equation expressed in a moving boundary-fitted coordinate system to calculate the flow field with water and bed surfaces varying in time. A nonlinear k-ε turbulence model was employed in order to predict flow near the structure where three-dimensional flow is dominant. The temporal change in bed topography was calculated by coupling a stochastic model for sediment pickup and deposition using a momentum equation of sediment particles in order to account for the effect of nonequilibrium sediment transport. In validating the numerical model, a spur dike and a bridge pier, which are considered to be typical river-engineering structures, were selected. By comparing the numerical results with observed laboratory experimental data, the model was found to reproduce flow and scour geometry around these structures with sufficient accuracy.