Well-balanced numerical modelling of non-uniform sediment transport in alluvial rivers

The last two decades have witnessed the development and application of well-balanced numerical models for shallow flows in natural rivers.However,until now there have been no such models for flows with non-uniform sediment transport.This paper presents a 1D well-balanced model to simulate flows and non-capacity transport of non-uniform sediment in alluvial rivers.The active layer formulation is adopted to resolve the change of bed sediment composition.In the framework of the finite volume Slope Llmiter Centred(SLIC) scheme,a surface gradient method is incorporated to attain well-balanced solutions to the governing equations.The proposed model is tested against typical cases with irregular topography,including the refilling of dredged trenches,aggradation due to sediment overloading and flood flow due to landslide dam failure.The agreement between the computed results and measured data is encouraging.Compared to a non-well-balanced model,the well-balanced model features improved performance in reproducing stage,velocity and bed deformation.It should find general applications for non-uniform sediment transport modelling in alluvial rivers,especially in mountain areas where the bed topography is mostly irregular.     

Reactive transport in stratified flow fields with idealized heterogeneity

A two-dimensional equation governing the steady state spatial concentration distribution of a reactive constituent within a heterogeneous advective–dispersive flow field is solved analytically. The solution which is developed for the case of a single point source can be generalized to represent analogous situations with any number of separate point sources. A limiting case of special interest has a line source of constant concentration spanning the domain’s upstream boundary. The work has relevance for improving understanding of reactive transport within various kinds of advection-dominated natural or engineered environments including rivers and streams, and bioreactors such as treatment wetlands. Simulations are used to examine quantitatively the impact that transverse dispersion (deviations from purely stochastic-convective flow) can have on mean concentration decline in the direction of flow. Results support the contention that transverse mixing serves to enhance the overall rate of reaction in such systems.     

Analytical solutions for transport of decaying solutes in rivers with transient storage

Analytical solutions are presented for solute transport in rivers including the effects of transient storage and first order decay. The solute transport model considers an advection–dispersion equation for transport in the main channel linked to a first order mass exchange between the main channel and the transient storage zones. In case of a conservative tracer, it is shown that different analytical solutions presented in the literature are mathematically identical. For non-conservative solutes, first order decay reactions are considered with different reaction rate coefficients in the main river channel and in the dead zones. New analytical solutions are presented for different boundary conditions, i.e. instantaneous injection in an infinite river reach, and variable concentration time series input in a semi-infinite river reach. The correctness and accuracy of the analytical solutions is verified by comparison with the OTIS numerical model. The results of analytical and numerical approaches compare favourably and small differences can be attributed to the influence of boundary conditions. It is concluded that the presented analytical solutions for solute transport in rivers with transient storage and solute decay are accurate and correct, and can be usefully applied for analyses of tracer experiments and transport characteristics in rivers with mass exchange in dead zones.     

A parallel mesh-free contaminant transport model based on the Analytic Element and Streamline Methods

This paper introduces a new method for simulating large-scale subsurface contaminant transport that combines an Analytic Element Method (AEM) groundwater flow solution with a split-operator Streamline Method for modeling reactive transport. The key feature of the method is the manner in which the vertically integrated AEM flow solution is used to construct three-dimensional particle tracks that define the geometry of the Streamline Method. The inherently parallel nature of the algorithm supports the development of reactive transport models for spatial domains much larger than current grid-based methods. The applicability of the new approach is verified for cases with negligible transverse dispersion through comparisons to analytic solutions and existing numerical solutions, and parallel performance is demonstrated through a realistic test problem based on the regional-scale transport of agricultural contaminants from spatially distributed sources.     

Probabilistic sensitivity and modeling of two-dimensional transport in porous media

A reliability approach is used to develop a probabilistic model of two-dimensional non-reactive and reactive contaminant transport in porous media. The reliability approach provides two important quantitative results: an estimate of the probability that contaminant concentration is exceeded at some location and time, and measures of the sensitivity of the probabilistic outcome to likely changes in the uncertain variables. The method requires that each uncertain variable be assigned at least a mean and variance; in this work we also incorporate and investigate the influence of marginal probability distributions. Uncertain variables includex andy components of average groundwater flow velocity,x andy components of dispersivity, diffusion coefficient, distribution coefficient, porosity and bulk density. The objective is to examine the relative importance of each uncertain variable, the marginal distribution assigned to each variable, and possible correlation between the variables. Results utilizing a two-dimensional analytical solution indicate that the probabilistic outcome is generally very sensitive to likely changes in the uncertain flow velocity. Uncertainty associated with dispersivity and diffusion coefficient is often not a significant issue with respect to the probabilistic analysis; therefore, dispersivity and diffusion coefficient can often be treated for practical analysis as deterministic constants. The probabilistic outcome is sensitive to the uncertainty of the reaction terms for early times in the flow event. At later times, when source contaminants are released at constant rate throughout the study period, the probabilistic outcome may not be sensitive to changes in the reaction terms. These results, although limited at present by assumptions and conceptual restrictions inherent to the closed-form analytical solution, provide insight into the critical issues to consider in a probabilistic analysis of contaminant transport. Such information concerning the most important uncertain parameters can be used to guide field and laboratory investigations.     

One-dimensional numerical simulation of non-uniform sediment transport under unsteady flows

One-dimensional numerical models are popularly used in sediment transport research because they can be easily programmed and cost less time compared with two- and three-dimensional numerical models. In particular, they possess greater capacity to be applied in large river basins with many tributaries. This paper presents a one-dimensional numerical model capable of calculating total-load sediment transport. The cross-section-averaged sediment transport capacity and recovery coefficient are addressed in the suspended load model. This one-dimensional model, therefore, can be applied to fine suspended loads and to hyperconcentrated flows in the Yellow River. Moreover, a new discretization scheme for the equation of unsteady non-uniform suspended sediment transport is proposed. The model is calibrated using data measured from the Yantan Reservoir on the Hongshui River and the Sanmenxia Reservoir on the Yellow River. A comparison of the calculated water level and river bed deformation with field measurements Shows that the improved numerical model is capable of predicting flow, sediment transport, bed changes, and bed-material sorting in various situations, with reasonable accuracy and reliability.     

Variable-density groundwater flow and solute transport in porous media containing nonuniform discrete fractures

Variations in fluid density can greatly affect fluid flow and solute transport in the subsurface. Heterogeneities such as fractures play a major role for the migration of variable-density fluids. Earlier modeling studies of density effects in fractured media were restricted to orthogonal fracture networks, consisting of only vertical and horizontal fractures. The present study addresses the phenomenon of 3D variable-density flow and transport in fractured porous media, where fractures of an arbitrary incline can occur. A general formulation of the body force vector is derived, which accounts for variable-density flow and transport in fractures of any orientation. Simulation results are presented that show the verification of the new model formulation, for the porous matrix and for inclined fractures. Simulations of variable-density flow and solute transport are then conducted for a single fracture, embedded in a porous matrix. The simulations show that density-driven flow in the fracture causes convective flow within the porous matrix and that the high-permeability fracture acts as a barrier for convection. Other simulations were run to investigate the influence of fracture incline on plume migration. Finally, tabular data of the tracer breakthrough curve in the inclined fracture is given to facilitate the verification of other codes.     

Evidence of distinct contaminant transport patterns in rivers using tracer tests and a multiple domain retention model

Solute transport in rivers is controlled by surface hydrodynamics and by mass exchanges with distinct retention zones. Surface and hyporheic retention processes can be accounted for separately in solute transport models with multiple storage compartments. In the simplest two component model, short term storage can be associated to in-channel transient retention, e.g. produced by riparian vegetation or surface dead zones, and the long-term storage can be associated to hyporheic exchange. The STIR (Solute Transport In Rivers) multiple domain transport model is applied here to tracer test data from three very different Mediterranean streams with distinctive characteristics in terms of flow discharge, vegetation and substrate material. The model is used with an exponential residence time distribution (RTD) to represent surface storage processes and two distinct modeling closures are tested to simulate hyporheic retention: a second exponential RTD and a power-law distribution approximating a known solution for bedform-induced hyporheic exchange. Each stream shows distinct retention patterns characterized by different timescales of the storage time distribution. Both modeling closures lead to very good approximations of the observed breakthrough curves in the two rivers with permeable bed exposed to the flow, where hyporheic flows are expected to occur. In the one case where the occurrence of hyporheic flows is inhibited by bottom vegetation, only the two exponential RTD model is acceptable and the time scales of the two components are of the same magnitude. The significant finding of this work is the recognition of a strong signature of the river properties on tracer data and the evidence of the ability of multiple-component models to describe individual stream responses. This evidence may open a new perspective in river contamination studies, where rivers could possibly be classified based on their ability to trap and release pollutants.     

Analytical solutions for 2D topography-driven flow in stratified and syncline aquifers

Two analytical solution methods are presented for regional steady-state groundwater flow in a two-dimensional stratified aquifer cross section where the water table is approximated by the topographic surface. For the first solution, the surficial aquifer is represented as a set of dipping parallel layers with different, but piecewise constant, anisotropic hydraulic conductivities, where the anisotropy is aligned with the dip of the layered formation. The model may be viewed as a generalization of the solutions developed by [Tóth JA. A theoretical analysis of groundwater flows in small drainage basins. J Geophys Res 1963;68(16):4795–812; Freeze R, Witherspoon P. Theoretical analysis of regional groundwater flow 1) analytical and numerical solution to the mathematical model, water resources research. Water Resour Res 1966;2(4):641–56; Selim HM. Water flow through multilayered stratified hillside. Water Resour Res 1975;11:949–57] to an multi-layer aquifer with general anisotropy, layer orientation, and a topographic surface that may intersect multiple layers. The second solution presumes curved (syncline) layer stratification with layer-dependent anisotropy aligned with the polar coordinate system. Both solutions are exact everywhere in the domain except at the topographic surface, where a Dirichlet condition is met in a least-squared sense at a set of control points; the governing equation and no-flow/continuity conditions are met exactly. The solutions are derived and demonstrated on multiple test cases. The error incurred at the location where the layer boundaries intersect the surface is assessed.     

Theoretical/numerical model for the transport of non-uniform suspended sediment in open channels

In this paper, we address the transport of multi-disperse suspended sediment mixtures in open channels, via the use of the two-fluid model. To that end, we extend previously developed frameworks for the dilute and non-dilute transport of suspended sediment. Within the scope of the Reynolds-averaged Navier-Stokes (RANS) equations, these modeling frameworks comprise mass and momentum equations for both phases (water and sediment). Here, we calculate the distribution of total volumetric concentration of sediment using two approaches: (1) by considering the mixture as represented by a single size; we call this approach Partial two-fluid model for uniform sediments (PTFMU); and (2) by combining the volumetric concentration of the sediment corresponding to several particle size classes; we call this approach Partial two-fluid model for non-uniform sediments (PTFMNU). In the second approach, we propose a methodology for the computation of the overall velocity of the disperse phase as a function of the velocities of each size class. k-ε type closures to account for the turbulence in the carrier phase (water) are applied. We also consider the coupling between the two phases through the drag force. Velocities of the carrier and disperse phases, and concentrations for each sediment class size are numerically solved by integrating the differential equations over control volumes. In order to validate our models, we compare numerical results to experimental data of Einstein and Chien [H.A. Einstein, N. Chien, Effects of heavy sediment concentration near the bed on velocity and sediment distribution, MRD sediment series report, University of California, Berkley, 1955] and Taggart et al. [W.C. Taggart, C.A. Yermoli, S. Montes, A. Ippen, Effects of sediment size and gradation on concentration profiles for turbulent flow, Massachusetts Institute of Technology, 1972]. Results of mean velocity of the carrier phase are in close agreement with the experimental data. For the prediction of sediment concentrations, we observe that there is a difference in the results using the two approaches mentioned above. We additionally obtain values of the Schmidt number needed to improve the agreement between predictions of the distribution of suspended sediment and the experimental data, and discuss the effect of sediment size and increasing sediment concentration on the values of the Schmidt number.     

Heavy metal content in relation to particle size and organic content of surficial sediments in Miami River and transport potential

Transport of contaminants in Miami River (Florida, USA) sediments with river currents is a concern due to their potential impact in areas that are away from the potential sources. Accumulation profiles of five metals (As, Cd, Hg, Zn, Pb) in the surficial sediments of the Miami River were evaluated in relation to grain size (from less than 0.075 mm to 6.3 mm) and organic content. Surficial sediment samples were collected along the river basin as well as in bay waters. Fine sediments ( o 0.106 mm) contained more than 10 times the levels of Cd and Hg and more than 6 times the levels of arsenic in comparison to the sediments that are larger than 0.850 mm. Zn and Pb levels were more than 10 times in the fine sediments ( o 0.106 mm) in comparison to those that were larger than 4.750 mm. Cd, Hg, and Zn levels had sig-nificant correlation with the total organic carbon content of the sediments. This indicates that Cd, Hg, and Zn in fine sediments have the potential to be metabolized in addition to potential to be mobilized with river currents. Analysis of the Gibbs settling velocities of particles showed that particles smaller than 0.5 mm can be transported with the river currents. The levels of heavy metal in fine sediments ( o 0.425 mm) along the river bed showed that fine particles had tendency to be mobilized and accu-mulate at locations where the rivers currents are low and carried out to the bay.     

Stochastic modelling of groundwater flow and solute transport in aquifers

This paper presents an introductory overview of recently developed stochastic theories for tackling spatial variability problems in predicting groundwater flow and solute transport. Advantages and limitations of the theories are discussed. Lastly, strategies based on the stochastic approaches to predict solute transport in aquifers are recommended.     

Mechanism of collision model for bedload transport

The current study introduces a new particle–particle collision model as well as a classical particle–wall collision model to simulate the process of bedload transport. Large eddy simulation and two-way coupling Lagrangian point–particle models also are applied. Flow conditions for all simulations are done based on previous experiments and four comparison cases are studied. The bedload function result obtained using this model agrees with the previous studies, which proves that the model is reasonable and effective in dealing with bedload transport in turbulent flow. Otherwise, failure to consider the particle–particle collision, Basset force, or Saffman lift force in the model lead to underestimating the bedload transport rate.     

Numerical simulation of dam-break flow and bed change considering the vegetation effects

Existing numerical investigations of dam-break flows rarely consider the effects of vegetation.This paper presents a depth-averaged two-dimensional model for dam-break flows over mobile and vegetated beds.In the model,both the consequences of reducing space for storing mass and momentum by the existence of vegetation and dragging the flow are considered:the former is considered by introducing a factor (1-c) to the flow depth,where c is the vegetation density;the later is considered by including an additional sink term in the momentum equations.The new governing equations are discretized by the finite volume method;and an existing second-order central-upwind scheme embedded with the hydrostatic reconstruction method for water depth,is used to estimate the fluxes;the source terms are estimated by either explicit or semi-explicit methods fulfilling the stability requirement.Laboratory experiments of dam-break flows or quasi-steady flows with/without vegetation effects/sediment transport are simulated.The good agreements between the measurements and the numerical simulations demonstrate a satisfactory performance of the model in reproducing the flow depth,velocity and bed deformation depth.Numerical case studies of six scenarios of dam-break flows over a mobile and vegetated bed are conducted.It is shown that when the area of the vegetation zone,the vegetation density,and the pattern of the vegetation distribution are varied,the resulted bed morphological change differs greatly,suggesting a great influence of vegetation on the dam-break flow evolution.Specifically,the vegetation may divert the direction of the main flow,hindering the flow and thus result in increased deposition upstream of the vegetation.     

The effect of non divergence-free velocity fields on field scale ground water solute transport

Solute plume subjected to field scale hydraulic conductivity heterogeneity shows a large dispersion/macrodispersion, which is the manifestation of existing fields scale heterogeneity on the solute plume. On the other hand, due to the scarcity of hydraulic conductivity measurements at field scale, hydraulic conductivity heterogeneity can only be defined statistically, which makes the hydraulic conductivity a random variable/function. Random hydraulic conductivity as a parameter in flow equation makes the pore flow velocity also random and the ground water solute transport equation is a stochastic differential equation now. In this study, the ensemble average of stochastic ground water solute transport equation is taken by the cumulant expansion method in order to upscale the laboratory scale transport equation to field scale by assuming pore flow velocity is a non stationary, non divergence-free and unsteady random function of space and time. Besides the stochastic explanation of macrodispersion and the velocity correction term obtained by Kavvas and Karakas (J Hydrol 179:321–351, 1996) before a new velocity correction term, which is a function of mean pore flow velocity divergence, is obtained in this study due to strict second order cumulant expansion (without omitting any term after the expansion) performed. The significance of the new velocity correction term is investigated on a one dimensional transport problem driven by a density dependent flow field.     

Tidal flow asymmetry in the diurnal regime: bed-load transport and morphologic changes around the Red River Delta

The relation between tidal flow asymmetry and net transport of sediment in the semidiurnal regime has been extensively described. This study reveals that in the diurnal regime, the direction of long-term net bed-load transport and resulting morphologic changes is partly determined by the phase-angle relationship of O₁, K₁, and M₂. Simple analytical formulations of time-averaged bed-load transport were derived which separate the relative contributions of tidal asymmetry from that of residual flow with tidal stirring. In this particular case, the Red River Delta in Vietnam, transports related to tidal asymmetry are larger than those induced by the monsoon currents, and are an order of magnitude larger than those associated with topographic residual flow around the delta. Tide-induced morphologic changes dominate at water depths between 10 and 25 m, of which the patterns of erosion and deposition overlap with observed bathymetric changes. Additional observed changes that occur in more shallow water cannot be explained by tidal asymmetry and are probably related to wave action and to deposition from the buoyant river plume.Responsible Editor: Jens Kappenberg     

Multi-functional heat pulse probe measurements of coupled vadose zone flow and transport

Simultaneous measurement of coupled water, heat, and solute transport in unsaturated porous media is made possible with the multi-functional heat pulse probe (MFHPP). The probe combines a heat pulse technique for estimating soil heat properties, water flux, and water content with a Wenner array measurement of bulk soil electrical conductivity (EC_bulk). To evaluate the MFHPP, we conducted controlled steady-state flow experiments in a sand column for a wide range of water saturations, flow velocities, and solute concentrations. Flow and transport processes were monitored continuously using the MFHPP. Experimental data were analyzed by inverse modeling of simultaneous water, heat, and solute transport using an adapted HYDRUS-2D model. Various optimization scenarios yielded simultaneous estimation of thermal, solute, and hydraulic parameters and variables, including thermal conductivity, volumetric water content, water flux, and thermal and solute dispersivities. We conclude that the MFHPP holds great promise as an excellent instrument for the continuous monitoring and characterization of the vadose zone.     

2DV modelling of sediment transport processes over full-scale ripples in regular asymmetric oscillatory flow

Wave-induced, steep vortex ripples are ubiquitous features in shallow coastal seas and it is therefore important to fully understand and model the sediment transport processes that occur over them. To this end, two two-dimensional vertical (2DV) models have been critically tested against detailed velocity and sediment concentration measurements above mobile ripples in regular asymmetric oscillatory flow. The two models are a k–ω turbulence-closure model and a discrete-vortex, particle-tracking (DVPT) model, while the data are obtained in the Aberdeen oscillatory flow tunnel (AOFT). The models and the data demonstrate that the time-dependent velocity and suspended sediment concentration above the ripple are dominated by the generation of lee-side vortices and their subsequent ejection at flow reversal. The DVPT model predicts the positions and strengths of the vortices reasonably well, but tends to overpredict the velocity close to the ripple surface. The k–ω model, on the other hand, underpredicts the height to which the vortices are lifted, but is better able to predict the velocity close to the bed. In terms of the cycle- and ripple-averaged horizontal velocity, both models are able to reproduce the observed offshore flow close to and below the ripple crest and the DVPT model is able to produce the onshore flow higher up. In the vicinity of the vortices, the DVPT model better represents the concentration (because of its better prediction of vorticity). The k–ω model, on the other hand, better represents the concentration close to the ripple surface and higher up in the flow (because of the better representation of the near-bed flow and background turbulence). The measured and predicted cycle- and ripple-averaged suspended sediment concentrations are in reasonable agreement and demonstrate the expected region of exponential decay. The models are able to reproduce the observed offshore cycle- and ripple-averaged suspended sediment flux from the ripple troughs upwards, and as a result, produce net offshore suspended sediment transport rates that are in reasonable agreement. The net measured offshore suspended transport rate, based on the integration of fluxes, was found to be consistent with the total net offshore transport measured in the tunnel as a whole once the onshore transport resulting from ripple migration was taken into account, as would be expected. This demonstrates the importance of models being able to predict ripple-migration rates. However, at present neither of the models is able to do so.     

The effect of bed mobility on resistance to overland flow

When sediment grains are transported as bed load in overland flow, there is a net transfer of momentum from the flow to the grains. When these grains collide with other grains, whether on the bed or in the flow, streamwise flow velocity decreases and resistance to flow increases. Resistance to flow generated in this manner is termed bed‐load transport resistance. Resistance to flow f over a plane bed may be partitioned into grain resistance f_g and bed‐load transport resistance f_bt. We use the symbols f_btf and f_btm to denote f_bt for flows over fixed beds and over mobile beds, respectively, and we compute the effect of bed mobility on flow resistance f_mob by subtracting f_btf from f_btm. The data for this study come from 54 flume experiments with fixed beds and 38 with mobile beds. On average f_mob is approximately equal to half of f_btm, which is about one‐quarter of f. Hence, f_mob is about one‐tenth of f. Predictive equations are developed for f_btf, f_btm and f_mob using dimensional analysis to identify the relevant independent variables and regression analysis to evaluate the coefficients associated with these variables. Values of f_mob are always positive which implies that mobile beds offer greater resistance to flow than do fixed beds. Evidently bed‐load grains colliding with mobile beds lose more momentum to the bed than do grains colliding with fixed beds. In other words, grain collisions with mobile beds are less elastic than those with fixed beds. Copyright © 2005 John Wiley & Sons, Ltd.     

LES-DEM simulations of sediment transport

In this work, a fully-coupled Computational Fluid Dynamics (CFD) model and Discrete Element Method (DEM) are used to simulate a unidirectional turbulent open-channel flow over the full range of sediment transport regimes. The fluid and particles are computed on separate grids using a dual-grid formulation to maintain consistency and avoid instability issues. The results of coupling the dispersed phase to a multiphase flow solver that uses volume-averaged Navier-Stokes equations are compared to those obtained from coupling through drag to a single flow solver. The current work also examines the applicability and limitations of lumping particles as a representative particle to reduce the cost of simulations. Insight to the impact of different turbulent events to the entrainment of particles is also given. The simulation results of sediment transport from both coupling techniques show good agreement with empirical formulas in the bedload regime, but under-predict sediment transport in the suspended load regime. In the suspended load regime, using partial coupling, the rate of sediment transport was found to be under-predicted as compared to full-coupling. The deviation in results in the suspended load regime was found to increase with increases in the applied shear stress. Both coupling methods revealed the same effect on the friction factor where friction increases in the bedload regime and decreases in the suspended load regime reaching a maximum at the transition between regimes. This result is contrary to past studies which have shown a discrete jump in the friction factor at the transition. Lumping particles as representative particles is shown to reduce the simulation cost by more than a factor of 5 when using a scaling factor of 2. By doing a quadrant analysis on information obtained from particle and flow field results, it was found that most of the particles are entrained by more frequent sweep events.