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.     

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.     

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.     

Scale Independent Linear Behavior of Alluvial Channel Flow

For flow in a rigid open channel with no bed sediment, the achievement of the special state of stationary equilibrium yields a linear characteristic. To examine the existence of a linear characteristic in alluvial channel flow, this study presents a direct formulation of the special equilibrium state following a variational approach. It finds that a linear relationship between shear stress and width/depth ratio of alluvial channels emerges under the commonly identified flow resistance and sediment transport conditions. Most importantly, this linear relationship yields not only the theoretical equilibrium channel geometry that is very close to a widely identified empirical counterpart but also a nondimensional number H, defined as the ratio of the relative increment of shear stress to the increment of width/depth ratio. This study suggests that H needs to be adopted as a criterion of hydraulic similitude for modeling sediment (bed-load) transport in alluvial channels.     

Frequency Modeling of Open-Channel Flow

A good model is necessary to design automatic controllers for water distribution in an open-channel system. The frequency response of a canal governed by the Saint-Venant equations can be easily obtained in the uniform case. However, in realistic situations, open-channel systems are usually far from the uniform regime. This paper provides a new computational method to obtain a frequency domain model of the Saint-Venant equations linearized around any stationary regime (including backwater curves). The method computes the frequency response of the Saint-Venant transfer matrix, which can be used to design controllers with classical automatic control techniques. The precision and numerical efficiency of the proposed method compare favorably with classical numerical schemes (e.g., Runge–Kutta). The model is compared in nonuniform situations to the one given by a finite difference scheme applied to Saint-Venant equations (Preissmann scheme), first in the frequency domain, then in the time domain. The proposed scheme can be used, e.g., to validate finite difference schemes in the frequency domain.     

Influence of Coherent Flow Structures on the Dynamics of Suspended Sediment Transport in Open-Channel Flow

The influence of suspended sediments on coherent flow structures has been studied by simultaneously measuring the longitudinal and vertical components of the instantaneous velocity vector and the instantaneous suspended particle concentration with an acoustic particle flux profiler. The measurements were carried out in clear water and in particle-laden open-channel flows. In both cases, they clearly show the predominance of ejection and sweep phases that are part of a burst cycle. The analysis further demonstrates the importance of the ejection and sweep phases in sediment resuspension and transport. Ejections pick up the sediment at the bed and carry it up through the water column close to the surface. It is shown that ejections and sweeps are in near equality in the near-bottom layer, whereas ejections clearly dominate in the remaining water column. The implications of these results for sediment transport dynamics are discussed.     

Numerical Model of Sediment Pulses and Sediment-Supply Disturbances in Mountain Rivers

Sediment pulses in rivers can result from many mechanisms including landslides entering from side slopes and debris flows entering from tributaries. Artificial sediment pulses can be caused by the removal of a dam. This paper presents a numerical model for the simulation of gravel bedload transport and sediment pulse evolution in mountain rivers. A combination of the backwater and quasi-normal flow formulations is used to calculate flow parameters. Gravel bedload transport is calculated with the surface-based bedload equation of Parker in 1990. The Exner equation of sediment continuity is used to express the mass balance at different grain size groups and lithologies, as well as the abrasion of gravel. The river is assumed to have no geological controls such as bedrock outcrops and immobile boulder pavements. The results of nine numerical experiments designed to study various key parameters relevant to the evolution of sediment pulses are reported here. Results of the numerical runs indicate that the evolution of sediment pulses in mountain rivers is dominated by dispersion rather than translation. Here dispersion is an expression for the observation that a sediment pulse aggrades both upstream and downstream of its apex whereas its amplitude decreases in time. The results also indicate that grain abrasion is an important and yet often neglected mechanism in removing the excess sediment associated with pulse inputs from some mountain rivers.     

Conservative Scheme for Numerical Modeling of Flow in Natural Geometry

A numerical model is proposed to compute one-dimensional open channel flows in natural streams involving steep, nonrectangular, and nonprismatic channels and including subcritical, supercritical, and transcritical flows. The Saint-Venant equations, written in a conservative form, are solved by employing a predictor-corrector finite volume method. A recently proposed reformulation of the source terms related to the channel topography allows the mass and momentum fluxes to be precisely balanced. Conceptually and algorithmically simple, the present model requires neither the solution of the Riemann problem at each cell interface nor any special additional correction to capture discontinuities in the solution such as artificial viscosity or shock-capturing techniques. The resulting scheme has been extensively tested under steady and unsteady flow conditions by reproducing various open channel geometries, both ideal and real, with nonuniform grids and without any interpolation of topographic survey data. The proposed model provides a versatile, stable, and robust tool for simulating transcritical sections and conserving mass.     

Fluctuations of Suspended Sediment Concentration and Turbulent Sediment Fluxes in an Open-Channel Flow

A complex problem of turbulent-sediment interactions in an open-channel flow is approached experimentally, using specially designed field experiments in an irrigation canal. The experimental design included synchronous measurements of instantaneous three-dimensional (3D) velocities and suspended sediment concentration using acoustic Doppler velocimeters (ADV) and a water sampling system. Various statistical measures of sediment concentration fluctuations, turbulent sediment fluxes, and diffusion coefficients for fluid momentum and sediment are considered. Statistics, fractal behavior, and contributions of bursting events to vertical fluxes of fluid momentum and sediment are evaluated using quadrant analysis. It has been found that both turbulence and sediment events are organized in fractal clusters which introduce additional characteristic time and spatial scales into the problem and should be further explored. It is also shown that Barenblatt’s theory of sediment-laden flows appears to be a good approximation of experimental data.     

3D Unsteady RANS Modeling of Complex Hydraulic Engineering Flows. II: Model Validation and Flow Physics

A chimera overset grid flow solver is developed for solving the unsteady Reynolds-averaged Navier-Stokes (RANS) equations in arbitrarily complex, multiconnected domains. The details of the numerical method were presented in Part I of this paper. In this work, the method is validated and applied to investigate the physics of flow past a real-life bridge foundation mounted on a fixed flat bed. It is shown that the numerical model can reproduce large-scale unsteady vortices that contain a significant portion of the total turbulence kinetic energy. These coherent motions cannot be captured in previous steady three-dimensional (3D) models. To validate the importance of the unsteady motions, experiments are conducted in the Georgia Institute of Technology scour flume facility. The measured mean velocity and turbulence kinetic energy profiles are compared with the numerical simulation results and are shown to be in good agreement with the numerical simulations. A series of numerical tests is carried out to examine the sensitivity of the solutions to grid refinement and investigate the effect of inflow and far-field boundary conditions. As further validation of the numerical results, the sensitivity of the turbulence kinetic energy profiles on either side of the complex pier bent to a slight asymmetry of the approach flow observed in the experiments is reproduced by the numerical model. In addition, the computed flat-bed flow characteristics are analyzed in comparison with the scour patterns observed in the laboratory to identify key flow features responsible for the initiation of scour. Regions of maximum shear velocity are shown to correspond to maximum scour depths in the shear zone to either side of the upstream pier, but numerical values of vertical velocity are found to be very important in explaining scour and deposition patterns immediately upstream and downstream of the pier bent.     

Bed-Load Effects on Hydrodynamics of Rough-Bed Open-Channel Flows

The extent to which turbulent structure is affected by bed-load transport is investigated experimentally using a nonporous fixed planar bed comprising mixed-sized granular sediment with a d50 of 1.95?mm. Three different sizes of sediment (d50 = 0.77, 1.99, and 3.96?mm) were fed into the flow at two different rates (0.003 and 0.006?kg/m/s), and subsequently transported as bed load. Particle image velocimetry (PIV) was used to determine the turbulence characteristics over the fixed bed during clear water and sediment feed cases. Mean longitudinal flow velocities at any given depth were lower than their clear water counterparts for all but one of the mobile sediment cases. The exception was with the transport of fine grains at the higher feed rate. In this case, longitudinal mean flow velocities increased compared to the clear water condition. The coarse grains tended to augment bed roughness, but fine grains saturated the troughs and interstices in the bed topography, effectively causing the influence of bed irregularities to be smoothed. The PIV technique permitted examination of both temporal and spatial fluctuations in flow variables: therefore many results are presented in terms of double-averaged quantities (in temporal and spatial domains). In particular, the form-induced stress, which arises from spatially averaging the Reynolds averaged Navier–Stokes equations and is analogous to the Reynolds turbulent stress, contributed between 15 and 35% of the total measured shear stress in the roughness layer. Flow around protrusive roughness elements produced a significant proportion of the turbulent kinetic energy shear production, suggesting that this process is highly intermittent near rough beds.     

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

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

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

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

Evaluation of the Micromodel: An Extremely Small-Scale Movable Bed Model

The micromodel is an extremely small physical river model having a movable bed, varying discharge, and numerous innovations to achieve quick answers to river engineering problems. In addition to its size being as small as 4?cm in channel width, the vertical scale distortion up to 20, Froude number exaggeration up to 3.7, and no correspondence of stage in model and prototype, place the micromodel in a category by itself. The writer was assigned to evaluate the micromodel’s capabilities and limitations to ensure proper application. A portion of this evaluation documents the deviation of the micromodel from similarity considerations used in previous movable bed models. The primary basis for this evaluation is the comparison of the micromodel to the prototype. The writer looked for comparisons that had (1) a reasonable calibration of the micromodel and (2) about the same river engineering structures constructed in the prototype that were tested in the micromodel and (3) a prediction by the micromodel of the approximate trends in the prototype. Evaluation of these comparisons shows a lack of predictive capability by the micromodel. Differences in micromodel and prototype likely result from uncertainty in prototype data and the large relaxations in similitude. Based on the lack of predictive evidence, the micromodel should be limited to demonstration, education, and communication for which it has been useful and should be of value to the profession.     

Analysis of Suspended Sediment Transport in Open-Channel Flows: Kinetic-Model-Based Simulation

This paper presents a comprehensive analysis of suspended sediment transport in open channels under various flow conditions through a kinetic-model-based simulation. The kinetic model, accounting for both sediment-turbulence and sediment-sediment interactions, successfully represents experimentally observed diffusion and transport characteristics of suspended sediments with different densities and sizes. Without tuning any model coefficients, the nonmonotonic concentration distribution and the noticeable lag velocity with a negative value close to the wall are reasonably reproduced. Examination of flow conditions typical of suspension dominated rivers shows that the conventional method may overestimate or underestimate unit suspended-sediment discharge, depending on the Rouse number, sediment size, as well as shear velocity. The error may be less than 20% for dp<0.5?mm and might exceed 60% for dp>1.0?mm under typical flow conditions where shear velocity ranges from 1.0?to?12.5?cm/s and flow depth ranges from 1.0?to?5.0?m.     

Bed-Load Sediment Transport on Large Slopes: Model Formulation and Implementation within a RANS Solver

Standard bed-load sediment-transport formulas are extended using basic mechanical principles to include gravitational influence on large slopes of arbitrary orientation. The resulting sediment fluxes are then incorporated into a morphodynamics model in a general-purpose, three-dimensional, finite-volume, Reynolds-averaged Navier–Stokes (RANS) code. Major features are: (1) the downslope component of weight is combined with the fluid stress to form an effective bed stress (similar to the work of Wu in 2004); (2) the critical effective stress is reduced in proportion to the component of gravity normal to the slope; (3) a simple flux-based model for avalanching is implemented as a numerical means of preventing the local slope from exceeding the angle of repose; (4) an entirely vectorial formulation of bed-load transport is developed to account for arbitrary surface orientation; and (5) methods for reducing numerical instability in the morphodynamics equation are described. Sample computations are shown for scour and accretion in a channel bend and for the movement of sand mounds on erodible and nonerodible bases.     

Analysis of Dynamic Wave Model for Unsteady Flow in an Open Channel

The models for flood propagation in an open channel are governed by Saint-Venant’s equations or by their simplified forms. Assuming the full form of hyperbolic type nonlinear expressions, the complete or dynamic wave model is obtained. Hence, after first-order linearization procedure, the dispersion relation is obtained by using the classical Fourier analysis. From this expression, the phase and group speed and the variations of the amplitude of the waves are defined and investigated. Adopting Manning’s resistance formula, the effects of the variations of the Froude number, Courant number, and friction parameter are examined in the wave number domain for progressive and regressive waves. For small and high wave numbers, the simplified kinematic and gravity wave models are recovered, respectively. Moreover, the analysis confirms, according to the Vedernikov criterion, the Froude number value corresponding to the stability condition to contrast the development of roll waves. In addition, for stable flow on the group speed versus wave number curves, the results show critical points, maximum and minimum for progressive and regressive waves, respectively.     

Modeling Unsteady Flow Characteristics of Hydropeaking Operations and Their Implications on Fish Habitat

Reservoir releases associated with energy production and flood mitigation need to be reconciled with efforts to maintain healthy ecosystems in regulated rivers. Unsteady flow phenomena caused by hydropeaking operations typically affect riverbed erosion and fish displacement. A three-dimensional hydrodynamic model is used to simulate the flow characteristics during the passage of the rising limb of an observed hydropeaking event in a gravel-bed reach of Smith River, Virginia. The calculated time-dependent water surface elevations, velocities, and shear stresses are compared with field measurements. Further, comparison based on numerical simulations of this historical and a hypothetical “staggering” hydropeaking event reveals that the latter has the capability of reducing the area subject to erosion and prolonging refugia availability for juvenile brown trout. Issues related to the adoption of either a truly dynamic modeling approach or a quasi-steady methodology for simulating unsteady flows are examined through a proposed unsteadiness flow parameter. The insights obtained from this study can assist in properly accounting for the impact of hydropeaking operations on fish habitat and instream flow management.     

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.