Sediment Continuity Equation Research Articles

Effects of the Gully Land Consolidation Project on soil erosion and sediment yield on the Loess Plateau, China

AbstractLand consolidation can increase the area of arable land and improve the ecology and environment and is widely used worldwide. The Gully Land Consolidation (GLC), as a special type of land consolidation, significantly impacts soil erosion. The purpose of this study was to investigate the effect of the GLC on soil erosion and sediment yield under different rainfall events and hydrological years in the Xingshuyaozi watershed on the Chinese Loess Plateau, where the GLC area accounted for 10.36% of the watershed. A computer model integrated with the Chinese soil loss equation (CSLE) and the continuity equation of sediment was used. Sediment connectivity before and after the GLC was compared to illustrate the effect of the GLC on sediment yield. The results showed that the reduction in soil loss increased with increasing rainfall amount, and the reduction rate of soil erosion was over 50%. The GLC had the greatest effect on soil erosion in wet years. The GLC effectively decreased sediment at the outlet of the watershed, with over 99% of the sediment being trapped. The reduction efficiency of soil erosion and sediment yield decreased in order of wet year, normal year and dry year. The decreased soil erosion and sediment yield resulted from the significantly lowered slope gradients and sediment connectivity after the GLC. These results indicate that the GLC is an effective soil and water conservation measure. These results can provide technical support for the application of the GLC and policymaking.

Effect of sediment transport, flow depth and infiltration on soil moisture profiles in irrigation furrows

A numerical model was used to analyze the effect of sediment transport and flow depth on soil moisture profiles from a simulation of the hypothetical irrigation furrows. The Saint Venant and sediment continuity equations were solved by using MacCormack scheme based on finite difference method to analyze the overland flow and sediment transport, and Richards equation was used to analyze the subsurface flow, which was solved by using a mass conservative fully implicit finite difference method. Flow depth significantly affected the moisture profiles in irrigation channels while the effect of sediment-laden water on the moisture profiles was observed insignificant. The model was used to study the effect of infiltration on moisture profiles and soil water retention curve (SWRCs) in irrigation furrows. It was observed that infiltration significantly affected and altered the moisture profiles and soil water retention curve (SWRC). Among the different soil parameters (av and nv ) and saturated hydraulic conductivity () significantly affected the moisture profiles, while and influenced the soil water retention curve (SWRC) as compared to other retention parameters.

Transportational Cyclic Steps Created by Submarine Long-Runout Turbidity Currents

In recent years, it has become a common understanding among researchers that one of the significant agents for forming a variety of submarine geomorphologies is turbidity currents that travel long distances, so-called long-runout turbidity currents. In this study, we present a mathematical model of the formation of cyclic steps due to long-runout turbidity currents based on the assumption that the highly concentrated layer near the bottom of the turbidity currents achieves an equilibrium state. The model uses the four governing equations: the momentum equation, the continuity equation, the diffusion/dispersion equation of suspended sediment, and the continuity equation of sediment on the bed (the Exner equation). We simplify the governing equations by ignoring the entrainment from ambient water since there is a distinct density interface above the highly concentrated lower layer of long-runout turbidity currents. We determine the dimensions of cyclic steps based on the solution. Agreement between the predictions and field observations turns out to be reasonable.

ANALISIS ABRASI DAN AKRESI PERAIRAN PANTAI BARUS TAPANULI TENGAH DENGAN MODEL CEDAS 2.0

Barus is an area where most of the people are fishermen, this is because Barus is an area located on the coast. The existing condition shows the shoreline on the east side of the seawall building, the condition of the shoreline is experiencing abrasion resulting in the retreat of the coastline and almost reaches the fisherman's flat building area, this is due to the port building in the form of a massive trester jutting into the sea resulting in sediment supply to the retained flat towers and the coastline has declined.To maintain the stability of the coastline, it is necessary to make an effort to control the damage to water in this area. The shoreline model is a numerical forecast model based on the sediment continuity equation and the sediment transport rate equation along the coast. Sediment transport rates along the coast are a function of the variation in height and direction of waves along the coast formed by the effects of refraction and diffraction.
 The results of the shoreline change model with the protection of the fisherman's flat area from waves by building sea walls is the east side of the fisherman's towers abrasion ± 7 m and sedimentation ± 5 m, the front area of the fisherman's towers does not occur sedimentation or abrasion, the western side of the fisherman's towers does not sedimentation and abrasion occurred, the east side of Barus Jetty did not occur abrasion or sedimentation, the area of Barus Jetty occurred ± 20 m sedimentation, and the west side of Barus Jetty occurred sedimentation ± 9 m. These results indicate that for handling conditions by making a seawall in front of the flat area shows that the location is safe from scouring of waves

Hydrodynamics and sediment transport under a dam-break-driven swash: An experimental study

An experimental study is presented consisting of swash zone hydrodynamics, sediment transport flux estimates, and bed changes under a single dam-break-driven swash event over a steep (1:7), movable sand bed. The study provides resolved measurements of instantaneous water depths, cross-shore flow velocities, sheet flow and suspended sediment concentrations, and morphological response. An ensemble-averaging over 24 repetitions of the swash event allows convergence in the time-averaged measured swash quantities. The sand bed profile was re-constructed after each run with a re-smoothing procedure that allowed for minimum variations that are within the profiler system accuracy (<0.006 m). High-resolution measurements are employed to reconstruct the spatial-temporal evolution of the flow velocity field. Temporal extrapolation and spatial logarithmic/exponential fits are employed to fill velocity gaps in the measured data for the estimation of instantaneous and depth-integrated sediment flux. The spatial gradients of instantaneous sediment flux indicate that the sheet flow sediment dominates over the suspended load during the most relevant phases for sediment transport. Upon bore arrival and initial uprush, the relative contribution of the sheet flow load is larger than during the backwash phase and is decreasingly dominant onshore. Depth-integrated instantaneous sediment flux and total sediment transport estimates, based on two different approaches, are compared with equivalent total sediment transport estimates obtained from the observed morphological changes and the sediment continuity equation. The close agreement between the various approaches indicates that existing models and empirical estimates for the sheet load concentration profile can be used as first order estimates for sediment transport in the swash zone.

Numerical and experimental investigations on aggradation and degradation in irrigation canals accounting for infiltration*

AbstractA numerical model was used in the present study to predict aggradation, degradation, and subsurface moisture content in irrigation canals. The numerical model solved Saint‐Venant and sediment continuity equations to analyse overland flow and sediment transport, whereas Richard's equation was used to analyse subsurface movement of water. Saint‐Venant and sediment continuity equations were solved by using the MacCormack scheme based on the finite difference method, and the Richard's equation was solved by using a mass‐conservative fully implicit finite difference method. Extensive irrigation canal experiments involving measurement of aggradation, degradation, and subsurface moisture content were conducted to assess the performance of the numerical model. The predicted aggradation and degradation represented a good agreement with data recorded in laboratory. Soil moisture profiles were estimated for sediment‐laden water and clear water conditions in irrigation canals. But the effect of sediment‐laden water on the moisture profiles was observed as insignificant. The observed and the model‐predicted soil moisture varied marginally as the observed moisture was attributed to errors during the collection of soil samples from the experimental field.

A Numerical Model for 1D Bed Morphology Calculations

The present work proposes a new morphodynamic model for flow simulation in open channels. The governing one dimensional (1D) shallow water equations along with the Exner sediment continuity equation are solved here using coupled approach. A TVD based MacCormack predictor corrector method is used here for solution of the coupled governing equations. The developed numerical model is used to replicate several test cases of known experimental and approximate solutions. These cases include bed aggradation due to sediment overloading, bed degradation due to sediment shut-off, dam break flow over erodible bed and movable bump due to subcritical and transcritical flows. The results obtained are found to be excellent and free from oscillations near sharp gradient. The numerical model is also found to be capable of capturing the wave-fronts of both water surface and bed sediment. Quantitative analysis of the results in terms of two statistical parameters establishes the potential of the present model in more complicated practical problems.

Best groyne series as countermeasure against river bend scour

A new approach for finding a cost-effective combination of groynes in a channel bend for the prevention of bend scour is presented. A linked simulation–optimisation model is proposed for this purpose. The morphological flow simulation model was developed by solving the shallow-water equations and the Exner sediment continuity equation in a boundary-fitted coordinate system. The optimisation model was developed utilising a binary-coded genetic algorithm. The proposed model can automatically provide a cost-effective groyne series in terms of their number, length and position in any vulnerable channel bend. A constraint in terms of bend scour is also incorporated in the optimisation model, which allows the optimisation model to obtain the best groyne combination for no bend scour. To appraise the performance of the model, it was applied to a hypothetical vulnerable channel bend. The model produced the minimised cost of installation of the groyne system at that location, at the same time as making the location free from bend scour.

The use of a morphological acceleration factor in the simulation of large-scale fluvial morphodynamics

Numerical simulation of fluvial morphodynamic processes can identify important dynamics at time and space scales difficult to observe in the field. However, simulations involving large spatial scales and/or the long timescales characteristic of morphodynamic processes are often untenable because of long computation times. The morphological acceleration factor (morfac) applies a scalar multiplier to the sediment continuity equation, and is often applied in morphodynamic simulations to reduce computational time. Although the use of morfac in coastal simulations is relatively common, its applicability in field-scale fluvial models is generally confined to steady-flow simulations over reach-scale spatial domains. Here we explore the viability of using morfac to simulate large-scale, long-term morphodynamics in a gravel-bed river. We use Delft3D to simulate a 60-d period with a significant discharge event in the Nooksack River, Washington. We systematically adjust morfac values (ranging from 5 to 50) to compare with a baseline condition of no acceleration. Model results suggest that morfac-based modification of the inflow hydrograph time-series reduces peak flow magnitudes and flood wave celerities. Higher morfac values result in greater flood-wave attenuation and lower celerity, reducing the simulated morphological impact at locations farther downstream. In general, relative error compared to the model baseline increases farther downstream because of the altered flood-wave propagation. However, error analysis also shows a positive relationship with channel slope and a negative relationship with channel width; hence, errors increase in the steeper, confined reaches of the upper part of the domain. Even for the lowest morfac values absolute cumulative volume change errors are on the order of 10%, indicating that the use of morfac in fluvial simulations is best restricted to short-term and/or smaller-scale modeling efforts. Wider channel sections with lower gradients are shown to produce lower morfac-related errors. Therefore, morphological acceleration as examined here is potentially more appropriate for limited reaches rather than large-scale domains.

Three-dimensional simulation of horseshoe vortex and local scour around a vertical cylinder using an unstructured finite-volume technique

A Large Eddy Simulation model is developed to simulate the hydrodynamics and scour process around a circular cylinder. The Navier-Stokes solver is based on the projection method and a second-order unstructured finite-volume method. A sigma-coordinate system is used to obtain an accurate representation of the evolution of the sediment-water interface. Bed erosion is simulated by solving the sediment continuity equation using a mass-conservating sand-slide algorithm and a bedload transport rate, which is based on a description of physical processes (Engelund & Fredsøe, 1976). Simulations of flow around a vertical cylinder for free-slip bed, rigid bed, and live-bed cases are done. The mean velocity profile and shear stress validate the accuracy of this model. Horseshoe vortex and lee-wake vortex shedding structure are simulated, and the results are thoroughly discussed in depth. The formation and the temporal development of the scour hole and other topographic bed features are successfully reproduced. The current paper reports the first known investigation of both scour evolution and coherent structure using large-eddy simulation.

A novel well-balanced scheme for spatial and temporal bed evolution in rapidly varying flow

This paper presents a novel method of preserving well-balanced conditions for dam-break flows on irregular beds. The research on preservation of well-balanced conditions commonly deals only with spatial variation of beds. It is challenging to design a well-balanced scheme that can model both spatial and temporal variation of beds particularly on domains discretized with unstructured meshes. This challenge arises due to the non-trivial nature of the governing equations modeling hydro-morpho dynamics. This study proposes a new and simple well-balanced method applicable for both spatial and temporal bed variations without requiring additional treatment and complicated discretization of slope source terms. The work relies on a cell-centered Godunov-type finite volume method for solving coupled Saint Venant and sediment continuity equations. The two most important issues, i.e., the ‘lake at rest condition’ and ‘water depth positivity’ of shallow-water flows over irregular beds, are tested and verified in the proposed numerical scheme. The authors employed Riemann solvers to compute fluxes through the control volume surfaces. The proposed scheme is evaluated for various benchmark cases of dam-break flows on rigid and erodible beds. Comparisons between the results of the proposed numerical scheme, analytical solution, experimental data, and previous numerical observations show significant improvement for some cases and a good agreement in the rest.

A model for simulation of debris flow sedimentation in slit detention-dam reservoirs

Debris flow is a natural phenomenon that requires appropriate structural measures such as detention dams to reduce hazards resulting from it. The objective of this paper is to present a two-dimensional numerical model to investigate debris flow deposition in the reservoir of the detention slit dams. The governing equations include shallow water equations considering the bed level variation, sediment continuity, and debris-flow transport equations. Shallow water equations were discretized using the MacCormack scheme and then Banihabib Scheme was applied for solving sediment continuity equation. The governing equations were solved in an iterative procedure and as a result, flow properties and bed level variations were obtained in silt dam reservoir. The model performance was evaluated against experimental and numerical models in two aspects including the outflow hydrograph and reservoir bed level variations or trapping efficiency. The model performed quite well in outflow hydrograph simulation, and the comparison of the bed level variations or trapping efficiency illustrated that the simulated values were acceptable. A sensitivity analysis of the parameters was carried out to analyze the influence of parameters variation on outflow and sedimentation volume. The results of this sensitivity analysis revealed sedimentation is more sensitive to the parameter variation than outflow hydrograph. Generally, the proposed numerical method can provide insights on the debris flow deposition in slit dam reservoir, which could be useful for slit dam design.

Experimental Investigation and Numerical Simulation of Morphological Changes in Natural Channel Bend

Sediment transport is an important process in maintaining balance of the form of river. The transport of bed load particles affects the processes of aggradation and degradation of the riverbed significantly. To predict the evolution process of the river morphology, the numerical model is considered as a useful tool. This study developed a two-dimensional (2D) depth-averaged model for the morphological change in the river bend. The flow module is represented by the shallow water equations, and the river morphological changes are represented by the sediment continuity equation. The sediment transport module treats bed load as mixtures of multiple grain-size sediments. A finite difference method was applied to solving the governing equations. The developed model was applied to predict bed-load transport rate on one set of the laboratory experiment. A field study was further applied to demonstrate the capability of the developed model in predicting morphological change in the curved river section in South Korea. The simulation results of the developed model were in good agreement with field data both laboratory experiment and natural channel bend.

Prediction of bed level variations in nonuniform sediment bed channel

In the present study, a numerical model, based on one-dimensional de Saint-Venant equations along with sediment continuity equation, is developed for prediction of bed levels in non-cohesive sediments in aggrading alluvial channels. One-dimensional, unsteady flow equations and sediment continuity equations are solved using ‘shock-capturing’, second order accurate, explicit MacCormack finite difference scheme while considering upstream and downstream boundary conditions in the channel. Series of experimental investigations have been undertaken for measurements of bed and water levels in an aggrading channel due to overloading of nonuniform sediments, extracted from the bed of Tapi River at Surat City, in a flume installed in Advanced Hydraulics Laboratory of SVNIT, Surat, India. A satisfactory coupling between the water flow and sediment flow has been achieved. The sediment continuity equation is used for the each size class to compute the volume of each size class after each time step at any computational node in the computational grid. The fractional bed and suspended load transport capacities for different size fractions have been computed using fractional transport laws for nonuniform sediments. The active bed layer concept has been implemented in finite difference scheme to consider the interaction and exchange of sediment and water flow near the mixing layer. The performance of developed numerical model has been satisfactorily verified with independent experimental data of nonuniform sediment bed. Also, consideration of sediment nonuniformity in computation of bed level variation has been demonstrated by comparing the results based on sediment transport functions of uniform and nonuniform sediments.

Regional-scale probabilistic shoreline evolution modelling for flood-risk assessment

Rapid deterministic modelling of shoreline evolution at regional and coastal-scheme scale enables Monte-Carlo simulations by which long-term shoreline statistics can be estimated. This paper describes UnaLinea, a fast, accurate finite difference solver of the one-line sediment continuity equation. The model is verified for the evolution of an initially straight shoreline of a plane beach subject to regular breaking waves at constant angle of incidence in the presence of either a groyne or a continuous single-point feed of sediment. Grid convergence and stability tests are used to obtain accurate, stable results, with satisfactory computational efficiency. Influences of wave input filtering and event-based sediment loading are considered. The rapid deterministic model is applied to Monte-Carlo simulations of the evolution of the west coast of Calabria, Italy for different scenarios including increased sediment load from a river and selected beach nourishment. The potential role of probabilistic shoreline evolution in regional coastal flood-risk assessment is explored through application to an idealised stretch of the Holderness coastline, U.K., where flood depths and expected damage are estimated for a 1000 year return period event.

A Surface Model for Aeolian Dune Topography

A surface model for aeolian bedform topography is adapted from a surface model of subaqueous bedform topography. The aeolian bedform surface model is developed using a uniform grid with a cell-centered finite volume approximation of the sediment continuity equation. The resulting modeling framework approximates the dynamic motions of aeolian bedform topography driven by bedform field boundary conditions. The numerical model is applied to simulate bedforms growing from unimodal and bimodal transport regimes from both a fixed elevation (sediment source area) and within a domain with fully periodic boundary conditions. The rates at which modeled aeolian bedforms grow and morphologically mature are sensitive to the chosen boundary conditions. Video files of model simulations and source code for the presented aeolian bedform surface modeling framework are available in supplemental materials. The aeolian bedform surface model code is malleable and readily modified for exploratory study of dynamic bedform topography that inherits morphological traits from aeolian bedform field boundary conditions.

Local Scour Upstream of a Slit Weir: Ordinary Differential Equation–Based Model under Steady and Unsteady Flow Conditions

AbstractTime-varying scouring upstream of a sediment release gate during a flood needs to be accurately predicted for reducing sedimentation around a water intake. This paper presents an ordinary differential equation–based model for computing time variation of scoured volume and maximum scour depth upstream of a slit weir for steady and unsteady flow. The model is based on the sediment continuity equation and sediment entrainment volume from a scour hole. There are some hypotheses in the model, and these hypotheses were examined by carrying out (1) 45 runs of scour inception tests, (2) 36 runs of numerical tests using computational fluid dynamics, and (3) 33 runs of physical scour tests measuring time variation of scoured topography. The model was validated with the scour tests for steady and unsteady flow conducted in the present study in addition to those reported in different research. The model was found to agree well with the data of time variation of the scoured volume and maximum scour depth, allo...

A numerical scheme for coastal morphodynamic modelling on unstructured grids

Over the last decade, modelling systems based on unstructured grids have been appearing increasingly attractive to investigate the dynamics of coastal zones. However, the resolution of the sediment continuity equation to simulate bed evolution is a complex problem which often leads to the development of numerical oscillations. To overcome this problem, addition of artificial diffusion or bathymetric filters are commonly employed methods, although these techniques can potentially over-smooth the bathymetry. This study aims to present a numerical scheme based on the Weighted Essentially Non-Oscillatory (WENO) formalism to solve the bed continuity equation on unstructured grids in a finite volume formulation. The new solution is compared against a classical method, which combines a basic node-centered finite volume method with artificial diffusion, for three idealized test cases. This comparison reveals that a higher accuracy is obtained with our new method while the addition of diffusion appears inappropriate mainly due to the arbitrary choice of the diffusion coefficient. Moreover, the increased computation time associated with the WENO-based method to solve the bed continuity equation is negligible when considering a fully-coupled simulation with tides and waves. Finally, the application of the new method to the pluri-monthly evolution of an idealized inlet subjected to tides and waves shows the development of realistic bed features (e.g. secondary flood channels, ebb-delta sandbars, or oblique sandbars at the adjacent beaches), that are smoothed or nonexistent when using additional diffusion.

Effect of Infiltration on Sediment Transport in Irrigated Channels

AbstractThis paper develops a numerical model for the analysis of sediment transport in irrigated channels. The overland flow equation considers infiltration into the subsurface. The model solves Saint Venant and sediment continuity equations to analyze overland flow and sediment transport, while Richard’s equation is used to analyze subsurface flow. Saint Venant and sediment continuity equations are solved using MacCormack-scheme-based finite-difference method and Richard’s equation is solved using a mass conservative fully implicit finite-difference method. The model is validated by comparing model-predicted aggradation with experimental observations. The model is used to study the effect of infiltration on aggradation of a channel bed during sediment-laden flows. It was observed that infiltration significantly affects and alters the aggradation phenomenon and aggradation considering infiltration is found to be higher than that without considering infiltration. Among the different unsaturated soil param...

Numerical Simulation of Bed Level Variation in Open Channels Under Steady Flow Conditions

Bed load transport is an important process in maintaining balance and stabilising channel geometry for restoring the form and function of river ecosystems. The amount and spatial distribution of bed load sediment particles contribute significantly to riverbed level changes. The prediction of bed load sediment transport evolution is an important aspect of catchment planning. This work can be effectively supported through numerical simulation by detailed analyses of flow components and sediment transport inside watersheds. The purpose of this research is to develop a twodimensional depth-averaged numerical model for flow and sediment transport using eight bed load transport equations to predict the time variation of bed deformation in steep slope, torrents and mountain river areas. The two-dimensional depth-averaged shallow water equations, along with the sediment continuity equation, are solved by using the Marker and Cell explicit scheme. Applying the eight bed load transport formulas to both ADM and MLSHM experimental flumes. After we will choice to the most appropriate formula to simulate the bed load transport rate and bed elevation change in the Yang yang mountains river in South Korea. The differences found between the measured experimental data and the numerical simulation for both flow and the time variations of bed deformation showed that the numerical model used in this research is useful for the analysis and prediction of riverbed level variations.