2D Modeling of Heterogeneous Dispersion in Meandering Channels

Two types of dispersion coefficient tensor for meandering channels were examined. The first type was estimated using measured vertical velocity profile in an S-curved channel, and the second type was based on the depth-averaged velocity field. A Petrov-Galerkin type finite element scheme was used in the numerical modeling, and the simulation results were compared with the experimental results from tracer tests in an S-curved channel. Comparison of the results show that the dispersion coefficient tensor obtained directly from velocity profiles provided a more realistic solution that can describe the abrupt expansion of tracer clouds in the transverse direction. Heterogeneous longitudinal and transverse dispersion coefficients were inversely estimated from the calculated dispersion coefficient tensor based on the velocity profiles. Extremely large transverse dispersion coefficients were formed at the apex of the channel bend, where there was a well-developed secondary current. The dimensionless transverse dispersion coefficient (DT/hu*) in the apex of the bend ranges from 0.495 to 2.60, which is about four times larger than that of the straight region.     

Behavior of Meandering Overbank Channels with Graded Sand Beds

Measurements of velocity distributions, depth variation, and sediment transport have been made under bankfull and overbank flow conditions in meandering channels with a graded sand bed, using the large-scale U.K. Flood Channel Facility. The overbank conditions depend upon the relative strength of opposing secondary circulation cells generated by shear at the channel crossover and centrifugal forces around the meander bend. Generally the shear-generated secondary flow either reversed or weakened the centrifugal circulation around the next downstream bend. This led to considerable modification of the main channel bed morphology, which, in turn, altered flow distributions. Measurements of the lateral distribution of bed load were made using a ?-scale Helley–Smith sampler. This demonstrated that the bed load was generally concentrated within a limited width of the channel and tended to take the shortest route through the meanders. Comparisons of observed and calculated bed material load gives an indication of how secondary circulation around meanders, under both bankfull and overbank conditions, affects the predictive performance of formulas derived for predominantly one-dimensional flow.     

Validation of a Three-Dimensional Numerical Code in the Simulation of Pseudo-Natural Meandering Flows

Validation of a three-dimensional finite volume code solving the Navier–Stokes equations with the standard k-ε turbulence model is conducted using a high quality and high spatial resolution data set. The data set was collected from a large-scale meandering channel with a self-formed fixed bed, and comprises detailed bed profiling and laser Doppler anemometer velocity measurements. Comparisons of the computed primary and secondary velocities are made with those observed and it is found that the lateral momentum transfer is generally under predicted. At the apices this results in the predicted position of the primary velocity maximum having a bias towards the channel center, compared to the position where it has been measured. Using a simplified two zone roughness distribution whereby a separate roughness height was prescribed for the channel center and channel sides relative to a single distributed roughness height, generally led to a slightly improved longitudinal velocity distribution; the higher velocities were located nearer to the outside of the bend. Improving both the free surface calculation and scheme for discretization of the convection terms led to no appreciable difference in the computed velocity distributions. A more detailed study involving turbulence measurements and bed form height distribution should discriminate whether using distributed roughness height is a precursor to using an anisotropic turbulence representation for the accurate prediction of three-dimensional river flows.     

Variation of Flow Pattern with Sinuosity in Sine-Generated Meandering Streams

The effect of channel sinuosity on flow pattern in meandering streams is investigated. The centerlines of the idealized meandering streams under consideration follow sine-generated curves, and the banks are rigid; the flow is turbulent and subcritical. This study focuses on the vertically averaged flow over a flat (horizontal at any cross section) bed formed by a granular material. The “flat bed” is viewed as the initial surface of a moveable bed at the beginning of an experiment (at time t = 0). A series of laboratory flow measurements involving the systematic variation of the deflection angle θ0 from 30 to 110°, is used. It is found that every different sinuosity (every different θ0) has its own convective flow pattern, i.e., its own distribution in plan of (the L/2 long) convergence–divergence zones of flow. As θ0 increases, a gradual change in flow pattern is observed. Two expressions defining the observed θ0 variation of the convective flow pattern are introduced. It is shown, with the aid of the sediment transport continuity equation, that the geometry of the developed bed at the end of an experiment is strongly related to the convective behavior of the vertically averaged (initial) flow over the flat bed at t = 0. In particular, information on the θ0 variation of the convective pattern of the initial flow can be used to estimate the location of erosion–deposition zones and the location(s) of the most intense erosion–deposition corresponding to any θ0.     

Evaluation of Dispersion Coefficients in Meandering Channels from Transient Tracer Tests

Mixing characteristics of conservative pollutants were examined two-dimensionally in a laboratory meandering channel, and a method to compute the dispersion coefficients was developed based on the measured concentration data. To investigate how the hydrodynamics influences pollutant mixing in meandering channels, both flow and tracer experiments were conducted in an S-curved laboratory channel. A two-dimensional routing procedure was presented to evaluate the longitudinal dispersion coefficient as well as the transverse dispersion coefficient under the unsteady concentration condition. The results of the tracer experiments showed that the tracer cloud behaved quite differently depending on whether or not the tracer cloud was transported following the filament of maximum velocity. Also, separation and reemerging of the tracer cloud were promoted by secondary currents. The observed transverse dispersion coefficients obtained by the routing procedure were close to those obtained by existing moment methods. The transverse dispersion coefficient tended to increase with an increasing aspect ratio, whereas it is not sensitive to the injection location. However, the longitudinal dispersion coefficient was sensitive to the injection location as well as the aspect ratio.     

Effects of Velocity Gradients and Secondary Flow on the Dispersion of Solutes in a Meandering Channel

Two contrasting mechanisms, created by channel curvature which strongly affect longitudinal dispersion of solutes in rivers are examined. In natural channels the large cross-sectional variability of the primary velocity component tends to increase longitudinal dispersion by providing a large difference between adjacent fast and slow moving zones of fluid. By contrast secondary circulation tends to decrease longitudinal dispersion by enhancing transverse mixing. A series of tests have been carried out in a very large flume containing a meandering water-formed sand bed channel to measure the longitudinal dispersion coefficient at various locations around a meander. These experimental observations are compared with experimental data obtained from meandering channels with smooth, fixed sides and regular cross-sectional shapes. All the data has been compared against predictions from two current modeling approaches. Finally, the significance of the two competing mechanisms in curved channels is discussed with regard to their relative influence on longitudinal mixing.     

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.     

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.     

Mathematical Modeling of Meandering Channels with a Generalized Depth Averaged Model

A two-dimensional depth averaged model is developed in a nonorthogonal curvilinear coordinate system. The ability of the model in handling complex mesh arrangements with high aspect ratios and skewness is investigated. It is shown that model formulation makes it able to handle large skewness in the grid lines. It is also shown that in predicting the water surface profile with a very distorted mesh, most of the errors arise from the large aspect ratio rather than the skewness of the grid lines. The model is then applied to three meandering channels (two simple and one compound), with specifications similar to those found in nature and the results are compared with experimental data. The comparison shows that the model predicted the water surface profile and velocity distribution well in simple channels. Predictions of the model in the main channel of the compound meandering channel were also in general agreement with the experimental results.     

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.     

Coupled and Decoupled Numerical Modeling of Flow and Morphological Evolution in Alluvial Rivers

Existing numerical river models are mostly built upon asynchronous solution of simplified governing equations. The strong coupling between water flow, sediment transport, and morphological evolution is thus ignored to a certain extent. An earlier study led to the development of a fully coupled model and identified the impacts of simplifications in the water-sediment mixture and global bed material continuity equations as well as of the asynchronous solution procedure for aggradation processes. This paper presents the results of an extended study along this line, highlighting the impacts on both aggradation and degradation processes. Simplifications in the continuity equations for the water-sediment mixture and bed material are found to have negligible effects on degradation. This is, however, in contrast to aggradation processes, in which the errors purely due to simplified continuity equations can be significant transiently. The asynchronous solution procedure is found to entail appreciable inaccuracy for both aggradation and degradation processes. Further, the asynchronous solution procedure can render the physical problem mathematically ill posed by invoking an extra upstream boundary condition in the supercritical flow regime. Finally, the impacts of simplified continuity equations and an asynchronous solution procedure are shown to be comparable with those of largely tuned friction factors, indicating their significance in calibrating numerical river models. It is concluded that the coupled system of complete governing equations needs to be synchronously solved for refined modeling of alluvial rivers.     

Flow and Velocity Distribution in Meandering Compound Channels

An investigation of flow and velocity distribution in meandering compound channels with over bank flow is described. Equations concerning the three-dimensional variation of longitudinal, transverse, and vertical velocity in the main channel and floodplain of compound section in terms of channel parameters are presented. The flow and velocity distributions in meandering compound channels are strongly governed by interaction between flow in the main channel and that in the floodplain. The proposed equations take adequate care of the interaction affect. Results from the formulations, simulating the three-dimensional velocity field in the main channel and in the floodplain of meandering compound channels are compared with their respective experimental channel data obtained from a series of symmetrical and unsymmetrical test channels with smooth and rough sections. The aspect ratio of the test channels varies from two to five. The equations are found to be in good agreement with the experimental data. The formulations are verified against the natural river and other meandering compound channel data. The power laws used for simulating the three-dimensional velocity structure are found to be quite adequate.     

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.     

Mass Conservative Transport Scheme for the Application of the ELCIRC Model to Water Quality Computation

An attempt was made to couple the water quality model of Danshuei River to the three-dimensional unstructured-grid hydrodynamic model [Eulerian–Lagrangian circulation model (ELCIRC)]. The Eulerian–Lagrangian scheme for the solution of the transport equations of salt in ELCIRC was demonstrated to be not mass conservative. The scheme was replaced with a finite-volume/finite-difference upwind scheme to ensure mass conservation both locally and globally. The same scheme was also used for the scalar transport equation in the water quality model. The representation of mass flux in the scalar transport equation is carefully formulated to be consistent with that of volume flux used in the continuity equations of ELCIRC. It was demonstrated that the newly revised scheme (1) conserved mass locally and globally; (2) conserved mass for both conservative and nonconservative substances subjected to biogeochemical transformation; and (3) preserved the integrity of the wetting-and-drying scheme. Further, the baroclinic simulation using the newly revised scheme showed a better result in terms of salt intrusion and salinity distribution in the Danshuei River estuary.     

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 Computational Fluid Dynamics-Based Models of Ultraviolet Disinfection Channels

Various numerical modeling approaches, all based on computational fluid dynamics (CFD) solutions for the flow field, are studied for an ultraviolet disinfection system in which the lamps are oriented perpendicular to the flow direction. A two-dimensional model assumption is made in all simulations, for which turbulent flow solutions were obtained with commercial CFD software (FIDAP). Two modeling approaches were studied. A continuum Eulerian approach was taken in formulating an appropriate advection–diffusion equation which is solved for the viable micro-organism concentration. Alternatively, a Lagrangian approach, in which particles are numerically introduced into the flow and their trajectories through a spatially varying field of ultraviolet intensities were computed, was also investigated. The effect of modeling unsteady-flow features associated with vortex shedding and motion on the extent of disinfection was examined by comparing time-averaged results based on an unsteady-flow continuum model with the results from an analogous simulation assuming a steady flow. Under the steady-flow assumption, differences between predictions of the Eulerian continuum approach and the Lagrangian particle-trajectory approach were also considered. Both modeling approaches yielded similar predictions over a range of loadings, and tended to underestimate the extent of disinfection when compared to measurements at the pilot scale.