Sediment Transport Equations Research Articles

Scaling and Self-Similarity of One-Dimensional Unsteady Suspended Sediment Transport with Emphasis on Unscaled Sediment Material Properties

AbstractCurrent methods utilized in scaling sediment transport in unsteady open-channel flow result in a number of model and scale effects, decreasing the accuracy and applicability of scale models. Identifying the conditions under which the governing equations of sediment transport are self-similar, and require no sediment diameter or density scaling, can reduce scale effects and increase model applicability. Conditions for self-similarity of one-dimensional unsteady suspended sediment transport are identified by applying the one-parameter Lie group of point scaling transformations, both for the general case and with unscaled sediment diameters. Under the scaling ratio relations found when holding sediment diameter to be unscaled, sediment diameter, density, critical and total shear, porosity, kinematic viscosity, and particle Reynolds number are all unscaled. It is shown that under Lie group scaling, the unsteady one-dimensional suspended sediment transport process as an initial-boundary value problem i...

Evaluation of Parameter and Model Uncertainty in Simple Applications of a 1D Sediment Transport Model

AbstractThis paper separately evaluates two methods from Bayesian Statistics to estimate parameter and model uncertainty in simulations from a one-dimensional (1D) sediment transport model. The first method, multivariate shuffled complex evolution metropolis-uncertainty analysis (MSU), is an algorithm that identifies the most likely parameter values and estimates parameter uncertainty for models with multiple outputs. The second method, Bayesian model averaging (BMA), determines a combined prediction based on three sediment transport equations that are calibrated with MSU and evaluates the uncertainty associated with the selection of the transport equation. These tools are applied to simulations of three flume experiments. For these cases, MSU does not converge substantially faster than a previously used and simpler parameter uncertainty method, but its ability to consider correlation between parameters improves its estimate of the uncertainty. Also, the BMA results suggest that a combination of transport...

Numerical modeling of oscillatory turbulent boundary layer flows and sediment suspension

In this study, an integrated numerical model is developed and applied to simulate oscillatory boundary layer flows and the corresponding sediment suspension. The model solves the Reynolds-averaged Navier–Stokes (RANS) equations for flows and the transient transport equation for sediment. The turbulence closure is accomplished by the baseline (BSL) $$k$$ – $$\omega $$ two-equation model. The model is capable of simulating oscillatory boundary flows at different Reynolds number regimes, namely, laminar, transitional and turbulent. The model can provide detailed mean (ensemble average) flow velocity, turbulence characteristics and sediment suspension within the boundary layer. The numerical results of mean flow velocity and turbulence kinetic energy are in agreement with the available experimental data and analytical solutions. In addition, the calculated results of period-averaged sediment concentration are also validated against the measurement data, yet the instantaneous results exhibit small phase differences. The proposed model improves the predictive capability for sediment suspension within boundary layers, which is helpful in defining a suitable model for relevant practical applications in coastal engineering.

Semi-two dimensional numerical prediction of non-equilibrium sediment transport in reservoir using stream tubes and theory of minimum stream power

This paper presents numerical modeling methods to predict long term reservoir sedimentation. The Generalized Stream Tube computer models for Alluvial River Simulation version 3.0 (GSTARS3) model which has capability of semi-two dimensional hydraulic computation and sediment routing by using stream tube concept combined with the theory of minimum stream power was implemented. In GSTARS3, non-equilibrium sediment transport equation is incorporated in accounting for the reservoir sedimentation processes. Capability of numerical simulation with and without applying stream tube concept, theory of minimum stream power, and non-equilibrium sediment transport equation was evaluated with nine years of sedimentation in the Kardeh Reservoir, Iran, and the best combinations of theories were investigated in this study. Simulated thalweg profile and channel geometry were compared to the measured results. From the comparisons, non-equilibrium sediment transport equation is preferably recommended method to predict reservoir sedimentation. The application of theory of minimum stream power improved the performance of model predictions significantly. In addition, simulations with three stream tubes were slightly better than the one with five stream tubes. Numerical simulations indicated that a semi-two dimensional modeling with non-equilibrium sediment transport equation, three stream tubes, and theory of minimum stream power is applicable to a long term prediction of reservoir sedimentation.

Dynamical modelling of river deltas on Titan and Earth

The surface of Titan hosts a unique Earth-like environment with lakes and rivers, and active ‘hydrologic’ cycle of methane. We investigate sediment transport in Titanian rivers and deposition in Titanian lakes with particular attention to formation of river deltas. The obtained results are compared with analogous terrestrial processes. The numerical model based on Navier–Stokes equations for depth-integrated two dimensional turbulent flow and additional equations for bed-load and suspended-load sediment transport was used in our research. It is found that transport of icy grains in Titanian rivers is more effective than silicate grains of the same size in terrestrial rivers for the same assumed total discharge. This effect is explained theoretically using dimensionless form of equations or comparing forces acting on the grains. Our calculations confirm previous results (Burr et al., 2006. Icarus. 181, 235–242). We calculate also models with organic sediments of different densities, namely 1500 and 800kgm−3. We found substantial differences between materials of varying densities on Titan, but they are less pronounced than differences between Titan and Earth.

Some Exact Solutions for Sediment Transport Equations

This paper presents some exact solutions for the nonlinear hyperbolic partial differential equations (PDEs), governing sediment transport in channels and rivers. The infinitesimal transformations for the governing system of PDEs are derived by using Lie group analysis. These are used to reduce the number of independent variables and consequently reduces the original system of PDEs into system of ordinary differential equations (ODEs). Moreover, the reduced system of ODEs are solved and new classes of exact group invariant solutions for the governing PDEs are constructed.

Testing the Effects of Detachment Limits and Transport Capacity Formulation on Sediment Runoff Predictions Using the U.S. Army Corps of Engineers GSSHA Model

The physics-based Gridded Surface Subsurface Hydrologic Analysis (GSSHA) model was developed by the U.S. Army Corps of Engineers for hydrologic, sediment transport, and water quality analyses. GSSHA simulates erosion and transport of sediments on the overland flow plain based on rainfall intensity and overland flow depth and velocity. The original sediment transport capabilities in GSSHA were taken from the GSSHA predecessor, CASC2D-SED. Independent testing of the sediment transport methods in CASC2D-SED by researchers identified several deficiencies in the formulation that caused significant overestimation of sediment yield during hydrologic events that were much larger than a calibration event. Sediment detachment limits and a variety of overland sediment transport equations were incorporated into the GSSHA model to address these deficiencies. This paper presents an evaluation of these modifications in terms of GSSHA sediment yield predictions of both single-event and summer growing season sediment yields. Simulation results are compared with research-quality sediment discharge data set from the USDA Goodwin Creek Experimental Watershed (GCEW). Results show that the reformulated GSSHA sediment transport model predicts event-total sediment discharge volume within (±) 50% over hydrologic events that vary by three orders of magnitude. The transport capacity method selected for use in the simulation had a large effect on the model results.

H2D morphodynamic model considering wave, current and sediment interaction

A morphodynamic model for weakly dispersive wave and shallow flows in horizontal two-dimensional (H2D) space is proposed. The horizontal density variation and the bottom evolution are incorporated into a fully nonlinear Boussinesq equation including vorticity effects. By coupling the flow equation with the depth-integrated sediment transport equation, morphodynamic simulation is made possible. A fourth-order finite volume method with an approximate Riemann solver is used to solve the governing equations. For the hydrodynamic test under strong wave–current interaction environment, the accuracy of the computed velocity and water surface was verified. For the three typical morphological benchmark tests, such as tsunami, regular wave and dam break flow, good agreement was obtained when proper parameters were provided. Therefore, the proposed morphodynamic model can be a useful tool for a wide range of shallow and wavy flows under dispersive and nonhydrostatic environments associated with wave, current, and sediment interaction.

Three-Dimensional Numerical Modeling of Dam-Break Flows with Sediment Transport over Movable Beds

A three-dimensional (3D) numerical model has been developed to simulate dam-break flows with sediment transport over movable beds. The hydrodynamic model solves the 3D Reynolds-averaged Navier-Stokes equations using a finite-volume method on collocated hexahedral meshes. The volume-of-fluid (VOF) technique with the compressive interface capturing scheme for arbitrary meshes is used to track the water surface boundary. The sediment transport model solves the nonequilibrium transport equations of suspended load and bed load separately, and in turn calculates the resulting bed change. A moving mesh technique is adopted to track the time evolution of bed topography. The grid moving velocity and computational cell volume change due to the moving mesh are taken into consideration when the hydrodynamic and sediment transport equations are discretized. The developed model has been tested using several experimental dam-break flows over movable beds. The calculated temporal and spatial variations of water and bed surfaces are in generally good agreement with the measured data. The effects of 3D features of the flow on morphological changes are discussed by comparing the results of the present model with results calculated by one-dimensional (1D) and two-dimensional (2D) models documented in the literature. The comparisons reveal that the present 3D model improves the accuracy of calculated morphological changes at the initial stages of dam-break flow, near the wave front, and around in-stream structures.

Two dimensional river flow and sediment transport model

This work presents the development and calibration of a two dimensional river flow, sediment transport and bed evolution model that couples the active-layer and multiple size-class approach for sediment transport modeling with an enhanced advection algorithm. The governing equations are solved using the fractional step method. This resulted in three successive steps (advection, diffusion and continuity) for the flow equations, and two steps (advection and diffusion) for the sediment transport and bed evolution equations. The focus of the research is the improvement of the advection computation (both in water and sediment computation) by reducing the limitation it imposes on the time step. Overcoming this restriction is enabled by introducing modifications to the characteristic method. Implementing these adjustments allows the characteristic curve to extend throughout multiple computational cells. After evaluating the advection computation for both flow and sediment transport by comparison of the proposed algorithm with various classical methods, the developed model is assessed using field measurements conducted on the Danube River. Analysis of the measured and computed values confirmed the developed model’s reliability.

Simulating unsteady flow and sediment transport in vegetated channel network

This paper presents a one-dimensional model for simulating flood routing and sediment transport over mobile alluvium in a vegetated channel network. The modified St. Venant equations together with the governing equations for suspended sediment and bed load transport were solved simultaneously to obtain flow properties and sediment transport rate. The Godunov-type finite volume method is employed to discretize the governing equations. Then, the Exner equation was solved for bed elevation change. Since sediment transport is non-equilibrium when bed is degrading or aggrading, a recovery coefficient for suspended sediment and an adaptation length for bed load transport were used to quantify the differences between equilibrium and non-equilibrium sediment transport rate. The influence of vegetation on floodplain and main channel was accounted for by adjusting resistance terms in the momentum equations for flow field. A procedure to separate the grain resistance from the total resistance was proposed and implemented to calculate sediment transport rate. The model was tested by a flume experiment case and an unprecedented flood event occurred in the Santa Cruz River, Tucson, Arizona, in July 2006. Simulated results of flow discharge and bed elevation changes showed satisfactory agreements with the measurements. The impacts of vegetation density on sediment transport and significance of non-equilibrium sediment transport model were discussed.

Modelling gravel beach dynamics with XBeach

Numerical cross-shore profile evolution models have been good at predicting beach erosion during storm conditions, but have difficulty in predicting the accretion of the beach during calm periods. This paper describes the progress made in modifying and applying the public domain XBeach code to the prediction and explanation of the observed behaviour of coarse-grained beaches in the laboratory and the field under accretive conditions. The paper outlines in details the changes made to the original code (version 12), including the introduction of a new morphological module based upon Soulsby's sediment transport equation for waves and currents, and the incorporation of Packwood's infiltration approach in the unsaturated area of the swash region. The competence of this modified model during calm conditions for describing the steepening of the profile, and the growth of the beach berm is demonstrated. Preliminary results on the behaviour of the beach subject to both waves and tides are presented. Good agreement is found between the model simulations and large-scale laboratory measurements, as well as field observations from a composite beach in the UK. The reasons for the model's capabilities are discussed.

2D Process-Based Morphodynamic Model for Flooding by Noncohesive Dyke Breach

AbstractInundation models based on the shallow water equations (SWE) have been shown to perform well for a wide variety of situations even at the limit of their theoretical applicability and, arguably, somewhat beyond. One of these situations is the catastrophic event of floods induced by dyke breach and consequent dyke erosion. The dyke collapse is often not sudden—as assumed by many flood simulations in which the dyke boundary is treated as a “dam-break.” The dyke erosion is a gradual and complex process that delays the onset of the flood, affecting the hydrograph of the flow. To simulate correct temporal passage of a flood, it is important to understand the rate at which these dykes collapse. In this paper, an overtopping flood event combined with dyke erosion is simulated. The model is built upon the two-dimensional (2D) shallow water equations together with sediment-flow interactions and incorporates a sediment transport equation. The model is solved using a second-order Godunov-type finite volume me...

3D Modeling of sediment movement by ships-generated wakes in confined shipping channel

Ship-generated waves and return currents are capable of re-suspending significant quantities of bottom and bank sediments. However, most of the previous studies done on the subject do not show how and where sediment is re-suspended by the wakes and the directions of net transport. In this paper, a 3D numerical model based on hydro-sedimentary coupling is presented to search the relationship between the sediment movement, and the pattern of ship-generated waves around and far away from the vessel and the return currents around the ships. The hydrodynamic model is based on 3D Navier-Stokes equations including the standard k-ε model for turbulence processes, and the sediment transport model is based on a 3D equation for the re-suspended sediment transport. The computation results show that the areas of sediment concentration and transport (whether by resuspension or by the bedload) depend mainly on the position, the speed of the ship in the waterways, the kinematics of ship-generated waves and on the return flows. Thus, a map of sediment distribution and the modes of sediment transport generated by the passage of the ship are presented.

Integrating 1D and 2D hydrodynamic, sediment transport model for dam-break flow using finite volume method

The purpose of this study is to set up a dynamically linked 1D and 2D hydrodynamic and sediment transport models for dam break flow. The 1D-2D coupling model solves the generalized shallow water equations, the non-equilibrium sediment transport and bed change equations in a coupled fashion using an explicit finite volume method. It considers interactions among transient flow, strong sediment transport and rapid bed change by including bed change and variable flow density in the flow continuity and momentum equations. An unstructured Quadtree rectangular grid with local refinement is used in the 2D model. The intercell flux is computed by the HLL approximate Riemann solver with shock captured capability for computing the dry-to-wet interface for all models. The effects of pressure and gravity are included in source term in this coupling model which can simplify the computation and eliminate numerical imbalance between source and flux terms. The developed model has been tested against experimental and real-life case of dam-break flow over fix bed and movable bed. The results are compared with analytical solution and measured data with good agreement. The simulation results demonstrate that the coupling model is capable of calculating the flow, erosion and deposition for dam break flows in complicated natural domains.

Semianalytical Solutions for One-Dimensional Unsteady Nonequilibrium Suspended Sediment Transport in Channels with Arbitrary Eddy Viscosity Distributions and Realistic Boundary Conditions

AbstractThis paper presents a new semianalytical approach for the solution of suspended sediment transport in channels under uniform conditions using generalized integral transform technique (GITT). Comparing with previous analytical work, this new approach is not limited by the sediment diffusivity distribution and boundary conditions. Instead, it solves the suspended sediment transport equation with arbitrary distribution of eddy diffusivity. The solutions also consider realistic boundary conditions at the free surface and the bed. The new solutions converge fast and compare well with previous analytical solutions as well as numerical solutions from a high-resolution spectral code. With this new analytical approach, a library of solutions for suspended sediment concentration can be developed. It gives deeper insight into the physical process of the problem and provides benchmarks for the validation of numerical models.

A Hybrid Lattice Boltzmann Method–Finite Difference Method Model for Sediment Transport and Riverbed Deformation

AbstractIn this study, a two‐dimensional hybrid numerical model for sediment transport based on lattice Boltzmann method and finite difference method is presented. The governing equations for water flow and suspended sediment transport are the shallow water equations and the advection–diffusion equations, respectively. Sediment load is also involved, so that riverbed deformation is numerically simulated. The model is verified by testing transportation of bank‐slump sediment in a sharp bended channel with the comparison to the results of well‐accepted finite volume method, illustrating the effectiveness of the proposed hybrid model. Copyright © 2014 John Wiley & Sons, Ltd.

Assessment of the caesium-137 flux adsorbed to suspended sediment in a reservoir in the contaminated Fukushima region in Japan

We estimated the flux of caesium-137 adsorbed to suspended sediment in the Kusaki Dam reservoir in the Fukushima region of eastern Japan, which was contaminated by the Fukushima Nuclear Power Plant accident. The amount and rate of reservoir sedimentation and the caesium-137 concentration were validated based on the mixed-particle distribution and a sediment transport equation. The caesium-137 and sediment flux data suggested that wash load, suspended load sediment, and caesium-137 were deposited and the discharge and transport processes generated acute pollution, especially during extreme rainfall-runoff events. Additionally, we qualitatively assessed future changes in caesium-137 and sediment fluxes in the reservoir. The higher deposition and discharge at the start of the projection compared to the 2090s are most likely explained by the radioactive decay of caesium-137 and the effects of reservoir sedimentation. Predictions of the impacts of future climate on sediment and caesium-137 fluxes are crucial for environmental planning and management.

MODELLING OF SEDIMENTS CONCENTRATION DISTRIBUTION IN DREDGED CANALS OF THE NIGER DELTA ESTUARINE REGION, NIGERIA

Previous sediments concentration distribution models used in the study of sediment characteristics of the dredged canals in the Niger-Delta estuarine region, Nigeria; did not take into consideration the lateral inflow due to tidal effects, which affects tremendously, the sediment intake into the estuarine waters. In the current research, existing models are modified by incorporating the missing lateral inflow parameters, which are peculiar to the Niger Delta environment, to obtain more accurate model results. Details are given herein, of the development and application of a 3-dimensional numerical model (EKU 2.8 Models) to predict sediment concentration distribution (total suspended sediment & bed sediment loads) in the Niger Delta estuarine canals, with Ekulama well 19 access canal as a case study. The approach in this paper involved coupling a sediment transport equation (with the inclusion of lateral inflow parameters), with an estuarine hydro-dynamics equation to generate a generic 3-dimensional sediment concentration distribution model, using deterministic approach. Predicted results using this model compared favorably with measured field results. Average sediment concentration of 29mg/l was obtained compared with 31mg/l measured in the field for bed sediment loads. Finally, the predicted sediment concentration distribution (TSS), when compared with field results, gave average correlation coefficient of 0.9.; hence, the present model will assist in generating adequate information /data on sediment characteristics and transport mechanism, required for effective design of canals to reduce rate of siltation. The application of the above knowledge/parameters generated from this model to effectively design canals to reduce siltation will be treated in subsequent articles.

MODELLING OF SEDIMENTS CONCENTRATION DISTRIBUTION IN DREDGED CANALS OF THE NIGER DELTA ESTUARINE REGION, NIGERIA

Previous sediments concentration distribution models used in the study of sediment characteristics of the dredged canals in the Niger-Delta estuarine region, Nigeria; did not take into consideration the lateral inflow due to tidal effects, which affects tremendously, the sediment intake into the estuarine waters. In the current research, existing models are modified by incorporating the missing lateral inflow parameters, which are peculiar to the Niger Delta environment, to obtain more accurate model results. Details are given herein, of the development and application of a 3-dimensional numerical model (EKU 2.8 Models) to predict sediment concentration distribution (total suspended sediment & bed sediment loads) in the Niger Delta estuarine canals, with Ekulama well 19 access canal as a case study. The approach in this paper involved coupling a sediment transport equation (with the inclusion of lateral inflow parameters), with an estuarine hydro-dynamics equation to generate a generic 3-dimensional sediment concentration distribution model, using deterministic approach. Predicted results using this model compared favorably with measured field results. Average sediment concentration of 29mg/l was obtained compared with 31mg/l measured in the field for bed sediment loads. Finally, the predicted sediment concentration distribution (TSS), when compared with field results, gave average correlation coefficient of 0.9.; hence, the present model will assist in generating adequate information /data on sediment characteristics and transport mechanism, required for effective design of canals to reduce rate of siltation. The application of the above knowledge/parameters generated from this model to effectively design canals to reduce siltation will be treated in subsequent articles.