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.     

Stochastic Prediction of Sediment Transport in Sand-Gravel Bed Rivers

Classical deterministic bedload transport predictors are applied to sand-gravel bed rivers. The turbulent bed shear stress is modeled according to a probability distribution to obtain realistic bedload transport rates at incipient motion. In extending the predictors to stochastic predictors for nonuniform sediment, many parameters that represent near-bed turbulence and the particle size distribution must be chosen. The parameters that give realistic results are chosen by analyzing the results of a new experimental flume dataset with relatively large water depths. Choosing other combinations of parameters may give equal total bedload transport rates, but at the cost of large errors in fractional transport rates. Attention is given to the hiding-exposure phenomenon and a hindrance effect related to nonuniform sediment. Validation based on two independent field datasets shows that successful predictions of particle sizes near the threshold for motion are feasible using the stochastic approach, while the deterministic approach gives successful predictions well above incipient motion.     

Formula for Sediment Transport in Rivers, Estuaries, and Coastal Waters

The aim of the present study is to develop a formula for the relationship between flow strength and sediment discharge. The appropriate definition of energy dissipation rate E in the theorem of Bagnold in 1966 is discussed and it is found that the sediment transport rate gt in unidirectional flows can be well predicted when E is defined as the product of bed shear stress τ0 and near bed velocity u*′. Then the linear relationship between u*′E and the sediment transport rate is examined using measured data. The good agreement between measured and predicted values indicates that the phenomena of sediment transport can be reasonably described by the near bed flow characteristics. As the hydrodynamic modelers are able to calculate the bed shear stress and near bed velocity in various cases now, thus the new relationship may provide numerical modelers a tool to calculate the sediment transport in rivers, estuaries and coastal waters. To prove this, the simplified analytical expressions of E and u*′ in wave-current flows and coastal waters are derived, the results are checked with the available data over a wide range of flow conditions; and good agreements are achieved, indicating that the presumption is valid in the cases investigated.     

Hans Albert Einstein: Innovation and Compromise in Formulating Sediment Transport by Rivers

This paper is written to mark the hundredth anniversary of the birth of Hans Albert Einstein (1904–1973). It casts his career as that of the archetypal researcher protagonist determined to master intellectually the way water flows and conveys alluvial sediment in rivers. In that effort, Einstein personified the mix of success and frustration experienced by many researchers who have attempted to formulate the complicated behavior of alluvial rivers in terms of mechanically based equations. His formulation of the relationship between rates of bed-sediment transport (especially bedload transport) and water flow comprised an innovative departure from the largely empirical approach that prevailed at the time. He introduced into that relationship the emerging fluid-mechanic concepts of turbulence and boundary layers, and concepts of probability theory. Inevitably the numerous complexities attending sediment transport mire formulation and prompt his use of several approximating compromises in order to make estimating bed-sediment transport practicable. His formulation nonetheless is a milestone in river engineering.     

Critical Shear Stress of Bimodal Sediment in Sand-Gravel Rivers

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

Criteria for the Formation of Sediment Plugs in Alluvial Rivers

A sediment plug is defined as aggradation in a river that completely blocks the main channel. Information from documented cases of sediment plug development in alluvial rivers was used to develop criteria for plug formation and to identify the setup conditions for sites that are prone to plug formation. Site characteristics, processes, and associated parameters were evaluated based on a comprehensive literature review and evaluation of data. A plug formation theory was developed and tested using a unique sediment transport/movable bed numerical model that simulates the key processes considered to affect plug formation. The theory and model were calibrated and validated against field data, and then used to develop simplified criteria that can be used to predict plug formation. Findings from this study can be used to identify sites that may be prone to plug formation, and the criteria can be used to evaluate the potential for plug formation based upon field site conditions when data are not available to complete a more detailed study.     

Conservative Semi-Lagrangian Algorithm for Pollutant Transport in Rivers

A conservative semi-Lagrangian numerical method for solute transport in steady nonuniform flows is presented. The method is an extension of earlier work on the authors' DISCUS method. Numerical results are compared against an exact solution for solute transport in a nonuniform flow with a linearly varying velocity coefficient and a quadratically varying dispersion coefficient. The method is stable and fully conservative at large Courant and grid Péclet numbers. Accuracy is also good and appears to be primarily related to spatial resolution and grid Péclet number. The method is significantly more computationally efficient than Eulerian numerical methods.     

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.     

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.     

Surface-based Transport Model for Mixed-Size Sediment

We present a transport model for mixed sand/gravel sediments. Fractional transport rates are referenced to the size distribution of the bed surface, rather than subsurface, making the model completely explicit and capable of predicting transient conditions. The model is developed using a new data set of 48 coupled observations of flow, transport, and bed surface grain size using five different sediments. The model incorporates a hiding function that resolves discrepancies observed among earlier hiding functions. The model uses the full size distribution of the bed surface, including sand, and incorporates a nonlinear effect of sand content on gravel transport rate not included in previous models. The model shares some common elements with two previous surface-based transport models, but differs in using the full surface size distribution and in that it is directly developed from a relatively comprehensive data set with unambiguous measurement of surface grain size over a range of flow, transport rate, and sediments.     

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.     

Simple Model for Downstream Variation of Median Sediment Size in Chilean Rivers

A simple theory is developed to account for the observed downstream variation of the median sediment size in Chilean rivers based on a reach-wise equilibrium sediment transport concept. The theory makes use of a bedload transport equation linked with a resistance equation to estimate the median sediment diameter as a function of channel slope, with the flow Reynolds number and bedload concentration as parameters. Both, Meyer-Peter and Müller’s and Ackers and White’s formulas are used alternatively as bedload equations. A Manning–Strickler type of formulation is used as a resistance relationship. The resulting model is validated against field data corresponding to 150 rivers in Central Chile, covering slopes in the range of 0.04–8.61%, with median sediment size in the range of 0.3–250 mm. Despite the simplicity of the present theory and the somewhat bold assumptions made in its derivation, the estimated variation of the median sediment size with channel slope follows the same trend as the field data. Most of the scatter of these data falls within the theoretical limits given by the estimated range of values of the parameters of the model.     

Prediction of Sediment Load Concentration in Rivers using Artificial Neural Network Model

An artificial neural model is used to estimate the natural sediment discharge in rivers in terms of sediment concentration. This is achieved by training the network to extrapolate several natural streams data collected from reliable sources. The selection of water and sediment variables used in the model is based on the prior knowledge of the conventional analyses, based on the dynamic laws of flow and sediment. Choosing an appropriate neural network structure and providing field data to that network for training purpose are addressed by using a constructive back-propagation algorithm. The model parameters, as well as fluvial variables, are extensively investigated in order to get the most accurate results. In verification, the estimated sediment concentration values agree well with the measured ones. The model is evaluated by applying it to other groups of data from different rivers. In general, the new approach gives better results compared to several commonly used formulas of sediment discharge.     

Bedload Transport in Gravel-Bed Streams with Unimodal Sediment

Bedload transport in many gravel-bed streams becomes highly complicated because of the nonuniformity of the grain size and the vertical stratification of channel bed material. A new relation for computing bedload transport rates in gravel-bed streams is proposed here. In an effort to account for the variation of the makeup of the surface material within a wide range of Shields stresses, the relation employs a two-parameter approach, one related to the material in the pavement and the other to that in the subpavement layers. The mode is used to represent the grain sizes of each layer. Available bedload transport data from gravel-bed streams with unimodal sediment are used to test the accuracy of the relation. A comparison with other bedload transport relations is also considered.