Numerical Simulation of Longitudinal and Lateral Channel Deformations in the Braided Reach of the Lower Yellow River

Bank erosion frequently occurs in the Lower Yellow River (LYR), playing an important role in the evolution of this braided river. A two-dimensional (2D) composite model is developed herein that consists of a depth-averaged 2D flow and sediment transport submodel and a bank-erosion submodel. The model incorporates a new technique for updating bank geometry during either degradational or aggradational bed evolution, allowing the two submodels to be closely combined. Using the model, the fluvial processes in the braided reach of the LYR between Huayuankou and Laitongzhai are simulated, and the calculated results generally agree with the field measurements, including the water-surface elevation, variation of water-surface width, and variations of cross-sectional profiles. The calculated average water-surface elevation in the study reach was 0.09?m greater than the observed initial value, and the calculated mean bed elevation for six cross sections was 0.11?m lower than the observed value after 24 days. These errors are attributed to the large variability of flow and sediment transport processes. Sensitivity tests of three groups of parameters are conducted, and these groups of parameters are related to flow and sediment transport, bank erosion, and model application, respectively. Analysis results of parameter sensitivity tests indicate that bank erodibility coefficient and critical shear stress for bank material are sensitive to the simulated bank erosion process. The lateral erosion distance at Huayuankou will increase by 19% as the value of bank erodibility coefficient changes from 0.1 to 0.3, and it will decrease by 57% as the value of critical shear stress for bank increases from 0.6 to 1.2?N/m2. Limited changes of other parameters have relatively small effects on the simulated results for this reach, and the maximum change extent of calculated results is less than 5%. Because the process of sediment transport and bank erosion in the braided reach of the LYR is very complicated, further study is needed to verify the model.     

Case Study: Two-Dimensional Model Simulation of Channel Migration Processes in West Jordan River, Utah

The paper presents the application of a two-dimensional depth-averaged numerical model to simulate the lateral migration processes of a meandering reach in the West Jordan River in the state of Utah. A new bank erosion model was developed and then integrated with a depth-averaged two-dimensional hydrodynamic model. The rate of bank erosion is determined by bed degradation, lateral erosion, and bank failure. Because bank material in the West Jordan River is stratified with layers of cohesive and noncohesive materials, a specific bank erosion model was developed to consider stratified layers in the bank surface. This bank erosion model distinguishes itself from other models by relating bank erosion rate with not only flow but also sediment transport near the bank. Additionally, bank height, slope, and thickness of two layers in the bank surface were considered when calculating the rate of bank erosion. The developed model was then applied to simulate the processes of meandering migration in the study reach from 1981 to 1992. Historical real-time hydrographic data, as well as field survey data of channel geometry and bed and bank materials, were used as the input data. Simulated cross-sectional geometries after this 12-year period agreed with field measurements, and the R2 value for predicting thalweg elevation and bank shift are 0.881 and 0.706, respectively.     

Coupling Bank Stability and Bed Deformation Models to Predict Equilibrium Bed Topography in River Bends

Attempts to include river bank erosion predictors within morphological models are becoming increasingly common, but uncertainty surrounds the procedures used to couple bed deformation and bank erosion submodels in a way that maintains the mass continuity of eroded bank sediment. Herein we present a coupling procedure that comprises two discrete elements. First, immediately following bank failure, the slumped debris comes to rest at the bank toe as a planar surface inclined at an “angle of repose.” Second, we use a fractional transport model to simulate the subsequent erosion and deposition of the failed bank material debris. The method is demonstrated with an example in which an equilibrium bed topography model is combined with a river bank erosion model to predict the morphological response of a river bend to a large flow event.     

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.     

Stream Bank Erosion: In Situ Flume Tests

A new technique for testing the erodibility of cohesive stream banks using an in situ flume is presented. The erosion rate is estimated from direct measurements of bed surface elevations by acoustic sensors. The sediment resuspension rate is obtained using data on sediment concentrations measured by optical backscatter sensors and from water samples. The bed-load contribution to the total erosion rate is evaluated from the conservation equation for sediments. Temporal patterns of erosion and resuspension rates are studied employing stepwise increments of bed-shear stress. The data show that bed load plays a significant role in cohesive bank erosion. The data analysis suggests that erosion and resuspension thresholds observed in experiments were very low or equal to zero. The data support the power type equation for the erosion and resuspension rates with bed-shear stress as the key factor. The data also highlights the potential importance of mud content and water content on erosion.     

Critical Shear Stress of Bimodal Sediment in Sand-Gravel Rivers

A new model for the critical shear stress and the transport of graded sediment is presented. The model is based on the size distribution of the bed surface and can be used to compute sediment transport rates in numerical simulations with an active layer model. This model makes a distinction between unimodal and bimodal sediments. It is assumed that all size fractions of unimodal sediments have the same critical shear stress while there is selective transport for the gravel fractions of bimodal sediments. A recently published laboratory transport data set is used to calibrate our model.     

Numerical Model for Sediment Transport and Bed Degradation in the Yangtze River Channel Downstream of Three Gorges Reservoir

This paper presents a two-dimensional morphological model for unsteady flow and both suspended-load and bed-load transport of multiple grain size to simulate transport of graded sediments downstream from the Three Gorges Reservoir. The model system includes a hydrodynamic module and a sediment module. The hydrodynamic module is based on the depth-averaged shallow water equations in orthogonal curvilinear coordinates. The sediment module describing nonuniform sediment transport is developed to include nonequilibrium transport processes, bed deformation, and bed material sorting. The model was calibrated using field observations through application to a 63-km-long alluvial river channel on the middle Yangtze River in China. A total of 16 size groups and a loose layer method of three sublayers were considered for the transport of the nonuniform bed materials in a long-term simulation. Predictions are compared with preliminary results of field observations and factors affecting the reliability of the simulated results are discussed. The results may be helpful to the development of more accurate simulation models in the future.     

Effects of Vanes and W-Weir on Sediment Transport in Meandering Channels

Sediment transport patterns in a meandering channel with instream restoration structures (vane and W-weir) have been studied. Laboratory experiments were conducted in a large-scale mobile-bed channel with graded materials under bank-full and overbank flow conditions. Bed-load samples were collected with a calibrated minisampler. Vanes, constructed against the outer bank in a meander bend, relocated the scour hole toward midchannel, thereby protecting the bank from erosion. The sediment sizes (d50,d90) in the bend became slightly more coarse and more uniform in the center of the channel. The W-weir installed immediately below a riffle section created two scour holes without affecting the upstream bed or the natural sediment transport of the channel. Predictions of bed-load transport by selected deterministic and stochastic methods showed large deviation from measurements using Helley–Smith sampler in sections downstream of the bend apex. In addition to creating local scour holes, the structures also relocated the locus of sediment transport at downstream sections. This issue should be considered when installing vanes and weirs in meandering rivers with significant bed-load transport.     

Modeling Sediment Transport Using Depth-Averaged and Moment Equations

A 1D mathematical model to calculate bed variations in alluvial channels is presented. The model is based on the depth-averaged and moment equations for unsteady flow and sediment transport in open channels. Particularly, the moment equation for suspended sediment transport is originally derived by the assumption of a simple vertical distribution for suspended sediment concentration. By introducing sediment-carrying capacity, suspended sediment concentration can be solved directly from sediment transport and its moment equations. Differential equations are then solved by using the control-volume formulation, which has been proven to have good convergence. Numerical experiments are performed to test the sensitivity of the calibrated coefficients α and k in the modeling of the bed deposition and erosion. Finally, the computed results are compared with available experimental data obtained in laboratory flumes. Comparisons of this model with HEC-6 and other numerical models are also presented. Good agreement is found in the comparisons.     

Modeling the Evolution of Incised Streams. III: Model Application

Incision and the ensuing widening of alluvial stream channels represent important forms of channel adjustment. Two accompanying papers have presented a robust computational model for simulating the long-term evolution of incised and restored or rehabilitated stream corridors. This work reports on applications of the model to two incised streams in northern Mississippi, James Creek, and the Yalobusha River, to assess: (1) its capability to simulate the temporal progression of incised streams through the different stages of channel evolution; and (2) model performance when available input data regarding channel geometry and physical properties of channel boundary materials are limited (in the case of James Creek). Model results show that temporal changes in channel geometry are satisfactorily simulated. The mean absolute deviation (MAD) between observed and simulated changes in thalweg elevations is 0.16?m for the Yalobusha River and 0.57?m for James Creek, which is approximately 8.1 and 23% of the average degradation of the respective streams. The MAD between observed and simulated changes in channel top width is 5.7% of the channel top width along the Yalobusha River and 31% of the channel top width along James Creek. The larger discrepancies for James Creek are mainly due to unknown initial channel geometry along its upper part. The model applications also emphasize the importance of accurate characterization of channel boundary materials and geometry.     

Development of Storm-Water Management Design Criteria to Maintain Geomorphic Stability in Kansas City Metropolitan Area Streams

Fifty-three years of historical precipitation data were applied to the U.S. Environmental Protection Agency Storm Water Management Model (SWMM) to conduct hydrologic and hydraulic simulations, generating continuous stream flow hydrographs in the receiving stream channels. On-site BMP and regional detention criteria were selected to allow postdevelopment replication of predevelopment peak flow frequency exceedance curves and the critical portions of shear stress duration curves. Instream continuous stage data generated by SWMM were used to examine erosion potential through the use of an erosion potential index. Coarse stream bed material were found to be less sensitive to changes in erosion potential due to urbanization, and extended detention ponds designed for flood control and water quality treatment were effective in reducing erosion potential. These controls were less effective in reducing erosion potential of fine loam bed material, indicating reductions of runoff volumes are required to minimize increases in channel erosion. Findings indicate that regional analysis based on local hydrologic and geomorphic characteristics are necessary to identify appropriate storm-water control requirements.     

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.     

Numerical Analysis of River Channel Processes with Bank Erosion

This paper presents a numerical analysis of river channel processes with bank erosion. The model can be used for investigating both bed-deformation and bankline shifting in 2D plan form. The basic equations are used in a moving boundary fitted-coordinate system, and a new formulation of nonequilibrium sediment transport is introduced to reproduce the channel processes. The model was applied to examine the morphological behavior of experimental channels. Temporal changes in the plan form in a meandering channel can be classified into two patterns: meander developing and meander straightening. Comparison of the observed and calculated results indicates that the model is applicable to both channel changes under various hydraulic conditions. On the basis of the numerical findings, the paper clarifies the influence of hydraulic variables on the location of bank erosion and bed scouring. The model also was used to investigate the effect of alternate bars on bank erosion and to investigate the development of channel meandering from an initially straight channel.     

Modeling the Evolution of Incised Streams. II: Streambank Erosion

Incision and ensuing widening of alluvial stream channels is widespread in the midsouth and midwestern United States and represents an important form of channel adjustment. Streambanks have been found to contribute as much as 80% of the total suspended load. The location, timing, and magnitude of streambank erosion are difficult to predict. Results from field studies to characterize the resistance of fine-grained materials to hydraulic and geotechnical erosion, the impact of pore-water pressures on failure dimensions and shearing resistance, and the role of riparian vegetation on matric suction, streambank permeability, and shearing resistance are used to enhance the channel evolution model CONCEPTS (conservational channel evolution and pollutant transport system). This paper discusses the conceptualization of the above-mentioned physical processes, and demonstrates the ability of the derived model to simulate streambank-failure processes. The model is tested against observed streambank erosion of a bendway on Goodwin Creek, Miss. between March 1996 and March 2001, where it accurately predicts the rate of retreat of the outside bank of the bendway. The observed change in average channel width within the central section of the bendway is 2.96?m over the simulation period, whereas a retreat of 3.18?m (7.4% larger) is simulated. The observed top-bank retreat within the central section of the bendway is 3.54?m over the simulation period, whereas a retreat of 3.01?m (15% smaller) is simulated.     

Reduction of Bend Scour by an Outer Bank Footing: Footing Design and Bed Topography

Protection of banks against erosion is an important but very expensive task in river management. The outer banks in river bends are most vulnerable to erosion and require an enhanced protection. This paper investigates, in an experimental flume, the efficiency of scour reduction and bank protection near the outer banks in open-channel bends by means of a horizontal foundation, called footing, protruding into the flow. First it is experimentally verified that bed mobility has a minor influence on the bed topography, which is mainly shaped by bend effects. Subsequently, the influence of the footing width and vertical elevation on the bed topography is investigated under clear water scour conditions. A maximum scour reduction of more than 40% was obtained with a footing placed at one-third of the maximum scour depth without bank protection and a footing width of about two-thirds of this maximum scour value. But a footing that is too narrow and/or not deep enough is vulnerable to underscour and subsequent bank failure. The experiments convincingly demonstrate the efficiency of this bank protection technique. The optimal footing parameters in the presented experiments should merely be seen as indicative, however, as they are expected to be case dependent.     

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.     

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.     

Simplified Model for Assessing Meander Bend Migration Rates

This paper describes a simple analytical model for assessing meander bend migration rates. The new model is innovative in that it can be applied directly using output data from one-dimensional hydraulic models. The method is designed as a first approximation that can be applied rapidly to large reaches of river systems, and should not be considered as a replacement for more detailed bank stability assessments. The model is based on a conversion factor for one-dimensional shear stress. Comparison of the conversion factor with existing data sets is presented. Converted shear stresses are translated to bank erosion volumes, which in turn are related to meander bend migration rates, using bank geometry and an appropriate sediment transport law. Results are presented for an evaluation of meander bend migration rates for a restoration feasibility study for a project on the Williamson River, Oregon.     

Numerical Model for Channel Flow and Morphological Change Studies

In this paper a depth-integrated 2D hydrodynamic and sediment transport model, CCHE2D, is presented. It can be used to study steady and unsteady free surface flow, sediment transport, and morphological processes in natural rivers. The efficient element method is applied to discretize the governing equations, and the time marching technique is used for temporal variations. The moving boundaries were treated by locating the wet and dry nodes automatically in the cases of simulating unsteady flows with changing free surface elevation in channels with irregular bed and bank topography. Two eddy viscosity models, a depth-averaged parabolic model and a depth-averaged mixing length model, are used as turbulent closures. Channel morphological changes are computed with considerations of the effects of bed slope and the secondary flow in curved channels. Physical model data have been used to verify this model with satisfactory results. The feasibility studies of simulating morphological formation in meandering channels and flows in natural streams with in-stream structures have been conducted to demonstrate its applicability to hydraulic engineering research∕design studies of stream stabilization and ecological quality among other problems.     

Integrated Two-Dimensional Surface and Three-Dimensional Subsurface Contaminant Transport Model Considering Soil Erosion and Sorption

To investigate the complex hydrological, morphodynamic, and environmental processes in watersheds, a physically-based integrated two-dimensional (2D) surface and three-dimensional (3D) subsurface model for flow, soil erosion and transport, and contaminant transport in the surface-subsurface system is presented in this paper. The model simulates the rainfall-induced surface flow by solving the depth-averaged 2D diffusion wave equation and the variably-saturated subsurface flow by solving the 3D mixed-form Richards equation. The surface and subsurface flow equations are coupled using the continuity conditions of pressure and exchange flux at the ground surface. The model uses the concept of nonequilibrium in the depth-averaged 2D simulation of nonuniform total-load sediment transport in upland fields, considering detachments by rainsplash and hydraulic erosion driven by surface flow. The integrated 2D surface and 3D subsurface contaminant transport model takes into account the contaminant changes due to sediment sorption and desorption, as well as exchanges between surface and subsurface domains due to infiltration, diffusion, and bed change. The model applies the same set of surface equations of flow, sediment, and contaminant transport for describing both upland areas and streams, so that no special treatments are required at their interface. The established model has been evaluated by comparisons with published experimental, numerical, and analytical data and then applied in an agricultural watershed. The model is suitable for wetland areas and agricultural watersheds in which streams are not very narrow and deep, and meanwhile a relatively fine mesh that can distinguish the streams is preferred.