Two-Dimensional Nonequilibrium Noncohesive and Cohesive Sediment Transport Model

The purpose of this paper is to develop an unsteady 2D depth-averaged model for nonuniform sediment transport in alluvial channels. In this model, the orthogonal curvilinear coordinate system is adopted; the transport mechanisms of cohesive and noncohesive sediment are both embedded; the suspended load and bed load are treated separately. In addition, the processes of hydraulic sorting, armoring, and bed consolidation are also included in the model. The implicit two-step split-operator approach is used to solve the flow governing equations and the coupling approach with iterative method are used to solve the mass-conservation equation of suspended sediment, mass-conservation equation of active-layer sediment, and global mass-conservation equation for bed sediment simultaneously. Three sets of data, including suspension transport, degradation and aggradation cases for noncohesive sediment, and aggradation, degradation, and consolidation cases for cohesive sediment, have been demonstrated to show the rationality and accuracy of the model. Finally, the model is applied to evaluate the desilting efficiency for Ah Gong Diann Reservoir located in Taiwan to show its applicability.     

Aspect Ratio to Maximize Sediment Transport in Rigid Bank Channels

The continuity equation, Manning’s equation, Einstein’s wall correction procedure and sediment transport equations are combined to indicate channel aspect ratios which maximize sediment transport for a given water discharge in rigid-bank trapezoidal and rectangular channels with fixed slope. Higher aspect ratios are required to maximize sediment transport for channels conveying bed load than for those with a dominant suspended load. A total load equation predicts optimum aspect ratios lying in between those for bed load and suspended load channels. The equations imply that the optimum aspect ratio increases markedly as the channel bank to channel bed roughness ratio increases. The resulting optimum ratios are smaller than the aspect ratios of many natural rivers.     

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.     

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.     

Unified View of Sediment Transport by Currents and Waves. III: Graded Beds

The problem of suspended load and bed load transport in river and coastal flows over graded beds is addressed. Two effects are important: the degree of exposure of the sediment particles of unequal size within a mixture (hiding of smaller particles resting or moving between the larger particles) and the nonlinear dependence of transport on particle diameter. The former effect can be modeled by modifying the critical bed-shear stress through a correction factor and by modifying the effective grain roughness through another correction factor. The modeling of the effective bed-shear stress parameter is studied by using various alternative methods. Based on comparison with suspended load and bed load transport data for graded beds in steady and oscillatory flow, the most promising method is selected. The proposed prediction method is found to work well for the fine sand bed range as well as the coarse sand-gravel bed range.     

Multiple Time Scales of Fluvial Processes with Bed Load Sediment and Implications for Mathematical Modeling

Fluvial bed load transport is often considered to assume a capacity regime exclusively determined by local flow conditions, but its applicability in naturally occurring unsteady flows remains to be theoretically justified. In addition, mathematical river models are often decoupled, being based on simplified conservation equations and ignoring the feedback impacts of bed deformation to a certain extent. So far whether the decoupling could have considerable impacts on the fluvial processes with bed load transport remains poorly understood. This paper presents a theoretical investigation of both issues. The multiple time scales of fluvial processes with bed load sediment are evaluated to examine the applicability of bed load transport capacity and decoupled models. Numerical case studies involving active bed load transport by highly unsteady flows complement the analysis of the time scales. It is found that bed load transport can sufficiently rapidly adapt to capacity in line with local flow because sediment exchange with the bed overwhelms the advection of bed load sediment by the mean flow. The present work provides theoretical justification of the concept of bed load transport capacity in most circumstances, which is underpinned by existing observations of bed load transport by flash floods. For fluvial processes with bed load transport, the feedback impacts of bed deformation are limited; therefore, decoupled modeling is, in this sense, appropriate.     

Modeling Nonuniform Suspended Sediment Transport in Alluvial Rivers

Problems and difficulties in modeling sediment transport in alluvial rivers arise when one uses the theory of equilibrium transport of uniform sediment to simulate riverbed variation. A two-dimensional mathematical model for nonuniform suspended sediment transport is presented to simulate riverbed deformation. Through dividing sediment mixture into several size groups in which the sediment particles are thought to be uniform, the nonuniformity and the exchange between suspended sediment and bed material are considered. The change of concentration along the flow direction, size redistribution, and cross-sectional bed variation can then be described reasonably well by the model. In simulating the flow field with big dry-wet flats, moving boundary problems are solved very well by introducing a so-called finite-slot technique. Verification with laboratory data shows that the model has a good ability to simulate channel bed variations. Last, the model was applied to a real alluvial river system. Variables such as water level, sediment concentration, suspended sediment size distribution, and riverbed variation were obtained with encouraging results.     

Equilibrium Near-Bed Concentration of Suspended Sediment

A new approach is presented for calculating the equilibrium near-bed concentration of suspended sediment in an alluvial channel flow. It is formulated from the balance between bed sediment entrainment and suspended sediment deposition across the near-bed boundary. The entrainment flux is determined making use of a turbulent bursting outer-scale-based function and the flux of deposition by the product of near-bed concentration and hindered settling velocity of sediment. A number of flume data records in the literature are analyzed to calibrate and verify the present approach. The observed near-bed concentrations for the data records are obtained by first isolating the suspended load transport rate from the observed total load transport rate using Engelund and Fredsoe's bed-load formula and then equating the suspended load transport rate to the shape integration of Dyer and Soulsby. The present approach is shown to perform satisfactorily compared to the results of data analysis. It is found that the near-bed concentration is evidently dependent on sediment particle size in addition to the Shields parameter due to skin friction. This finding seems to challenge previous relationships that simply represent the near-bed concentration as empirical functions of the purely skin-friction-related Shields parameter.     

Method for Estimating Sediment Transport in Ice-Covered Channels

A method is proposed for estimating rates of sediment transport in ice-covered alluvial channels. The method extends existing, open-water procedures for estimating rates of sediment transport to conditions of ice-covered flow. A key aspect of the method is the assessment of flow resistance attributable to bed-surface drag. That assessment is used to estimate rates of bed load and suspended load, and thereby total bed-sediment transport rate. Estimation of ice-covered suspended load additionally entails an approximation whereby open-water suspended load is scaled in proportion to the ratio of a reference sediment concentration for ice-covered flow relative to that for open-water flow. The reference concentration is calculated in terms of bed-load rate and shear velocity attributed to bed-surface drag. Flume data are used to develop the method and tentatively verify it. Field verification of the method presently is hampered by the absence of field data on bed sediment transport in ice-covered channels.     

Unified View of Sediment Transport by Currents and Waves. II: Suspended Transport

The problem of suspended sediment transport in river and coastal flows is addressed. High-quality field data of river and coastal flows have been selected and clustered into four particle size classes (60–100, 100–200, 200–400, and 400–600?μm). The suspended sand transport is found to be strongly dependent on particle size and on current velocity. The suspended sand transport in the coastal zone is found to be strongly dependent on the relative wave height (Hs/h), particularly for current velocities in the range 0.2–0.5?m/s. The time-averaged (over the wave period) advection–diffusion equation is applied to compute the time-averaged sand concentration profile for combined current and wave conditions. Flocculation, hindered settling, and stratification effects are included by fairly simple expressions. The bed-shear stress is based on a new bed roughness predictor. The reference concentration function has been recalibrated using laboratory and field data for combined steady and oscillatory flow. The computed transport rates show reasonably good agreement (within a factor of 2) with measured values for velocities in the range of 0.6–1.8?m/s and sediments in the range of 60–600?μm. The proposed method underpredicts in the low-velocity range (<0.6?m/s). A new simplified transport formula is presented, which can be used to obtain a quick estimate of suspended transport. The modeling of wash load transport in river flow based on the energy concept of Bagnold shows that an extremely large amount of very fine sediment (clay and very fine silt) can be transported by the flow.     

Numerical Modeling of Bed Deformation in Laboratory Channels

A depth-average model using a finite-volume method with boundary-fitted grids has been developed to calculate bed deformation in alluvial channels. The model system consists of an unsteady hydrodynamic module, a sediment transport module and a bed-deformation module. The hydrodynamic module is based on the two-dimensional shallow water equations. The sediment transport module is comprised of semiempirical models of suspended load and nonequilibrium bedload. The bed-deformation module is based on the mass balance for sediment. The secondary flow transport effects are taken into account by adjusting the dimensionless diffusivity coefficient in the depth-average version of the k–ε turbulence model. A quasi-three-dimensional flow approach is used to simulate the effect of secondary flows due to channel curvature on bed-load transport. The effects of bed slope on the rate and direction of bed-load transport are also taken into account. The developed model has been validated by computing the scour hole and the deposition dune produced by a jet discharged into a shallow pool with movable bed. Two further applications of the model are presented in which the bed deformation is calculated in curved alluvial channels under steady- and unsteady-flow conditions. The predictions are compared with data from laboratory measurements. Generally good agreement is obtained.     

Experimental Study of Bed Load Transport through Emergent Vegetation

Vegetation is an important agent in fluvial geomorphology and sedimentary processes, through its influence on the local hydraulics that determine sediment transport. Within stands of emergent vegetation, bed shear is substantially reduced through the absorption of momentum by drag on the stems. This stimulates deposition of sediment and reduces capacity for bed load transport. The effect of emergent vegetation on hydraulic parameters (including equilibrium bed gradient, flow depth, and velocity) and on bed load transport rate has been investigated experimentally for one sediment size, stem diameter, and stem spacing. Bed load transport rate was found to be closely related to bed-shear stress, which must be estimated by partitioning total flow resistance between stem drag and bed shear.     

Accuracy of Cross-Channel Sampled Sediment Transport in Large Sand-Gravel-Bed Rivers

The accuracy of cross-channel integrated sediment transport of bed material is determined with an elaborate set of field measurements in the Waal River, The Netherlands. The measurements were done during a discharge wave in the upstream part of the river, which has a bimodal sand-gravel bed. The sampling strategy should take both spatial and temporal aspects into account to obtain maximum accuracy. Presence of moving bedforms, differences in bed-sediment grain size in the cross section, and presence of preferential transport lanes dictate that at least five subsections for sampling in the cross section are necessary. The accuracy of cross-channel integrated bedload transport depends mainly on the measurement strategy. An uncertainty of <20% (bedload) and 7% (suspended load) of cross-channel integrated sediment transport is shown to be feasible if 30 samples of bedload and two vertical profiles of suspended bed-material load are taken in one subsection, provided that the cross section of the river is divided into at least five subsections. The samples in one subsection should be distributed over the length of the bed form. Changes of discharge during the measurements cause systematic differences between the subsections. To minimize this uncertainty a compromise between the spatial and temporal accuracy is necessary. Therefore, when only one vessel with instruments is available for doing the measurements, the number of sampling positions and subsections must be reduced if the rate of change of discharge is large. Based on the results a prediction method is given to estimate the feasible accuracy in the planning phase of future campaigns, and the necessary time and financial investment for that accuracy.     

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.     

3D Numerical Simulation for Water Flows and Sediment Deposition in Dam Areas of the Three Gorges Project

This paper presents a three-dimensional (3D) mathematical model for suspended load transport in turbulent flows. Based on the stochastic theory of turbulent flow proposed by Dou, numerical schemes of Reynolds stresses for anisotropic turbulent flows are obtained. Instead of a logarithmic law, a specific wall function is used to describe the velocity profile close to wall boundaries. The equations for two-dimensional suspended load motion and sorting of bed material have been improved for a 3D case. Numerical results are in good agreement with the measured data of the Gezhouba Project. The present method has been employed to simulate sediment erosion and deposition in the vicinity of the Three Gorges Dam. The size distribution of the deposits and bed material, and flow and sediment concentration at different times and elevations, are predicted. The results agree well with the observations in physical experiments. Thus, a new method is established for 3D simulation of sediment motion in the vicinity of dams.     

Suspended Wash Load Transport of Nonuniform Sediments

The results of an experimental study on transport of suspended wash load through a coarse-bed stream are presented. The experiments were conducted under different concentrations of fine suspended sediment (wash load of uniform size, 0.064 mm diameter) and with three different coarse-bed sediments: two having uniform sizes and one with nonuniform size distribution. For any equilibrium concentration of wash load in suspension, a definite proportion of the wash material was observed to be present within the bed material. No difference is found in this regard between wash load and suspended load transport. Therefore, the relationship, as stated by Samaga et al., for the parameter representing sheltering—exposure and interference effects in the suspended load transport of nonuniform sediments was applied in a modified form by using the present data and the data collected from the literature.     

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.     

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.