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.     

Experimental Observations of Flow and Bed Processes in Large-Amplitude Meandering Flume

Meanders of large amplitude often exhibit asymmetric planform shape or subsidiary bends. The present work is aimed at improving on understanding of the morphodynamic phenomena affecting the bed evolution of large amplitude meandering channels. Attention is focused on the development of the steady point bar-pool configuration and of the superimposed large-scale migrating bed forms; of particular interest is the role of the changing channel curvature and bed topography variation on flow pattern. A series of experiments was carried out in a sine-generated large-amplitude meandering flume, for two values of width-to-depth ratio. Maps documenting the bed topography and the flow pattern along the meandering bends are reported. Two point bars per bend were observed and seem to be part of a series of damped oscillations developing in response to the changing channel curvature. In response to the bed deformation, the maximum flow velocity moves at the outer bank at the entrance of the bend.     

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.     

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.     

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.     

Effects of Lifting Force on Bed Topography and Bed-Surface Sediment Size in Channel Bend

In bed-load sediment transport, the lifting force plays an important role in reducing the friction between sediment particles and the bed surface, and it makes particle transportation by the shear force easier. Because the lifting force is related to vorticity, a three-dimensional (3D) numerical model incorporating large eddy simulations was applied to simulate the vorticity field in a channel bend. The results show that the distribution of vorticity is highly nonuniform, and it can lead to significant variations in lifting force and bed-load sediment transport per unit width in a channel bend. Relevant theories are modified on the basis of physical reasoning and then incorporated into numerical models to investigate the lifting-force effects on the bed topography and bed-surface sediment size gradation in a channel bend. With the lifting-force effects considered, it is shown that the errors in simulated bed topography can be reduced by approximately 40% and in bed-surface sediment size by 50%.     

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.     

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.     

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.     

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.     

3D Numerical Modeling of Flow and Sediment Transport in Open Channels

A 3D numerical model for calculating flow and sediment transport in open channels is presented. The flow is calculated by solving the full Reynolds-averaged Navier-Stokes equations with the k ? ε turbulence model. Special free-surface and roughness treatments are introduced for open-channel flow; in particular the water level is determined from a 2D Poisson equation derived from 2D depth-averaged momentum equations. Suspended-load transport is simulated through the general convection-diffusion equation with an empirical settling-velocity term. This equation and the flow equations are solved numerically with a finite-volume method on an adaptive, nonstaggered grid. Bed-load transport is simulated with a nonequilibrium method and the bed deformation is obtained from an overall mass-balance equation. The suspended-load model is tested for channel flow situations with net entrainment from a loose bed and with net deposition, and the full 3D total-load model is validated by calculating the flow and sediment transport in a 180° channel bend with movable bed. In all cases, the agreement with measurements is generally good.     

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.     

Characteristics of Flow around Open Channel 90° Bends with Vanes

Sharp open-channel bends are commonly encountered in hydraulic engineering design. Disturbances such as secondary flows and flow separation caused by the bend may persist for considerable distances in the downstream channel. A simple way of reducing these disturbances is through the insertion of vertical vanes in the bend section. A laser Doppler anemometry (LDA) unit was used to measure the three-dimensional mean and turbulent velocity components of flow in an experimental rectangular open-channel bend. Flow characteristics of the bend with no vanes are compared with those of bends having one or three vertical vanes. The size of the flow separation zone at the inner wall of the bend was determined from dye visualization data and confirmed with mean streamwise velocity data. Results show that the vertical vanes are effective in considerably reducing flow separation, intensity of secondary flows, and turbulence energy in the downstream channel. Furthermore, energy loss for bends with vanes is slightly less than for the no-vane case.     

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.     

Case Study: River Training and Its Effects on Fluvial Processes in the Lower Yellow River, China

More than 50?years’ river training practices in the Lower Yellow River provide valuable experience in river management for flood control in rivers having rapid flow changes, silting beds, and active channel migrations and are of importance in understanding the fluvial processes in regulated rivers with high sediment loads. Planned channel alignments for river training in the Lower Yellow River usually consist of a series of consecutive moderate bends representing the natural tendency of flows. Flow guide works, namely spur dikes, were constructed on the concave banks of the planned bends to protect the channel against scouring and migration by deflecting the current away from bends and further guiding the main flow from one bend to the next one. As a result, well-planned flow guide works can play a crucial role in limiting channel shifting and migration and in establishing a relatively stable channel. Enough flow guide works, on both sides together reaching about 80% of the channel length, may change the transitional and braided channel patterns to a confined meandering pattern.     

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.     

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.     

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.     

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.