Non-equilibrium Sediment Transport Research Articles

Morphodynamics of sine-generated meandering streams under variations of the width-to-depth ratio: A numerical investigation

Meandering is one of the most common planforms of rivers, however, the ecological and fluvial integrity of meandering rivers are under challenges, resulting from increased anthropogenic pressure and extreme climate events. The present study elucidates the morphodynamics of meandering streams under variations of width-to-depth ratio (B/h) by delving into the two dynamic processes underlying within the flow, i.e. cross-circulatory motion and convective redistribution of the longitudinal flow velocity. Series of numerical simulations are performed in 70° sine-generated meandering streams under increasing flow depth that necessitates a wide range of B/h, characterizing flume experiments to large scale natural rivers. The radial flow structures and the early bed deformation patterns are computed and elucidated. Among the classical cross-circulatory flow patterns, outer bank cell occurs for flows having B/h < 9. Next, the different bed deformation patterns reveal the shift of significance in the driving forces of the bed deformation regarding different B/h ratio. At B/h = 100, bed deformation is dominated by the convective redistribution of the downstream velocity that causes longitudinal adjacent erosion–deposition zones. This implies downstream migration tendency of meander loops. At B/h = 12, the intensified cross-circulatory flow deflects the sediment trajectory, causing extra laterally adjacent erosion–deposition zones that necessitate the lateral expansion tendency of the loop. Decrement of B/h ratio (from 100 on ward) critically enhances the non-equilibrium transport of sediment that can lead to active fluvial evolution of meandering rivers. Overall, the results can be used to improve river management and restoration.

Effect of equilibrium and non-equilibrium sediment transport flows on the shear velocity in an open channel.

Equilibrium and non-equilibrium sediment transport flow in natural rivers and artificial channels can result in degradation or aggradation of the river bed, which will affect many hydraulic parameters, one of which is shear velocity. This study evaluates the influence of sediment transport on shear velocity in open channels. In this study, laboratory experiments were carried out using a sediment-recirculating flume, and measurements of the velocity and Reynolds shear stress distributions were measured using a Sontek-acoustic Doppler velocimeter (ADV). This experimental study measured 120 velocity distributions, and Reynolds stress profiles, consisting of 12 different sets of measurements involving flow with sediment transport and movable sand bed. The results showed an average shear velocity, u*, difference between sediment feeding and without sediment feeding by 9.41%. For the integration constant Br value, the average difference between sediment feeding and without sediment feeding was 5.58%.

Evaluating Manning's Roughness Coefficient for Flows with Equilibrium and Non-equilibrium Sediment Transport

One of the challenges in using Manning’s equation lies in accurately determining Manning’s roughness coefficient, especially due to sediment transport. The condition of sediment transport within a specific section of a river can be in equilibrium, meaning that the amount of sediment entering and exiting the segment is balanced or it can be in non-equilibrium, where there is an imbalance between the sediment entering and leaving the segment. Experiments were carried out in the laboratory to simulate both transport conditions, one involving sediment feeding (equilibrium condition) and the other without sediment feeding (non-equilibrium condition). A total of 180 mean velocity profiles were measured using an acoustic doppler velocimeter (ADV) in fixed and movable bed flows. The present experiment was combined with theoretical approaches to evaluate Manning’s coefficient in open channels under sediment transport-flow conditions and reach conclusive results. The shape of the velocity profile, u/U, for flows over a movable bed with sediment feeding is “slender” compared to those without sediment feeding. The presence of sediment transport affects the shape of the velocity profile, especially in the inner region, influencing Manning's roughness coefficient. This coefficient can be determined from two-point velocity measurements at z/H = 0.1 and 0.2 for fixed and movable bed flows with and without sediment feeding, respectively. On average, sediment feeding increases the coefficient by 19% compared to the non-sediment feeding case. KEYWORDS: Manning’s roughness coefficient, Velocity profile, Equilibrium and non-equilibrium, Sediment transport, Open-channel flow

Non-equilibrium concentration profile formulas of suspended sediment and their preliminary applications

The vertical concentration profiles in non-equilibrium sediment transport processes generally deviate from the equilibrium concentration distribution of suspended sediment. The non-equilibrium concentration profile formulas currently available are those of Han and Brown, respectively. However, the complexity of these formulas limits their use in practical calculations. To improve the usefulness of these formulas, the unknown parameters in Han's formula are reduced from three to two, and the three different forms of Brown's formula are transformed into one. These formulas then are proved to be essentially the same to some extent, and only different in the expression form of the exponent. Han's formula then is improved, based on which the theoretical calculation methods and distribution characteristics of non-equilibrium profiles are presented. Han's and Brown's formulas are verified qualitatively and quantitatively. Finally, these formulas are applied in the investigation of the characteristics of certain physical quantities, such as the recovery factor of sediment concentration, near-bottom sediment flux, and the non-equilibrium Péclet number in the non-equilibrium sediment transport process. These results clearly reveal that the magnitude of these physical quantities decreases in the erosion process and increases in the deposition process. The results also show that the formulas are largely applicable for the non-equilibrium sediment transport conditions.

Numerical model of local scour considering the unsteady sediment inflow and sediment sorting: Application to scour upstream of slit weir

The current study proposes a novel framework for the numerical model for estimating the temporal scour considering unsteady sediment inflow and the sediment sorting process. The framework was applied to local scour upstream of a slit weir. The scour model is based on an ordinary nonlinear differential equation derived from sediment continuity and scour rate equations. A one-dimensional (1-D) Boussinesq-type model coupled with nonequilibrium sediment transport was incorporated in the scour model to consider unsteady sediment inflow. In addition, a mixing layer approach was incorporated to determine temporal variations in particle size in the scour hole. The proposed framework was validated using scour experiments conducted under conditions that include non-uniform sediment, live-bed scour, and unsteady flow rate. The simulation results showed satisfactory agreement with experimental results for the scour upstream of a slit weir. The proposed model appropriately explained the hysteresis process for flow unsteadiness, refilling process for live-bed scour, and armoring process for non-uniform sediments. In addition, the model framework proposed in the current study is applicable to local scour around other hydraulic structures (e.g., bridge piers) upon establishing the scour rate equation. Therefore, the current study provides a novel approach for modeling temporal scour that is required to consider unsteady sediment inflow and sediment sorting.

Equilibrium approach for modeling erosional failure of granular dams

Erosional failure of granular dams by an overtopping body of water is investigated using a depth-averaged morphodynamic model. The transport of sediment by the flow assumes the sediment flux to remain in equilibrium with the local bed shear stress. Accordingly, the shallow-water hydrodynamic equations are coupled with the Exner equation for mass conservation of the sediment. The system of equations is solved using a fully coupled well-balanced finite volume method, second-order accurate in time and space. The effect of the steep bed slope of a dam face is incorporated into both the hydrodynamics and sediment transport equations, leading to improved predictions. Comparison with results obtained from nonequilibrium sediment transport models indicates that such models perform poorly while predicting the bed evolution near the toe of an eroding dam. Observations from experimental studies demonstrate that the amount of sediment entrained by the flow is not significant, except during the initial moments of failure. This suggests that the vertical exchange of mass between the bed and the flow layer, as assumed by the nonequilibrium models, may not be completely valid during the failure. The equilibrium model results, reproducing the key flow features of the overtopping failure process, are validated by experimental measurements. The study provides fresh insights into the sediment transport processes associated with the erosion of a granular dam by overtopping, establishes the appropriateness of the equilibrium approach for its numerical modeling, and proposes a well-balanced second-order accurate solution technique for solving the resulting coupled equations of flow and sediment transport.

Effects of non-locality on unsteady nonequilibrium sediment transport in turbulent flows: A study using space fractional ADE with fractional divergence

This study aims to develop a mathematical model that can describe the vertical distribution of suspended sediment particles in an open channel turbulent flow under unsteady nonequilibrium condition with non-local mixing effect. A space non-local transport of sediment is considered that arises due to turbulent bursting where the hopping height of a particle is not limited to a small distance as described by classical theory of turbulence, rather it can jump upto any height. To take into account this fact unlike previous researchers who used Rouse equation, Hunt equation or traditional advection–diffusion equation as the governing equation, the present study uses fractional advection–diffusion equation (fADE) where space fractional derivative for the local diffusive flux has been used that counts the effect of non-locality. The fractional derivative is considered in Caputo sense and the order α of the fractional derivative corresponds to α-order Le´vy stable distribution with value 1<α≤2. The non-local effect has been considered in the boundary conditions as well as in the non-linear models of sediment diffusivity. Four types of sediment diffusivity are considered which are generalized non-linear models for broad applicability of the study. The fADE together with the boundary and initial conditions, is solved by Chebyshev collocation method and Euler backward method. This proposed method is unconditionally convergent and converges more rapidly than other previous methods used in similar studies. Effects of non-local mixing have been investigated for transient and bottom concentration distributions. Proposed models have been validated for sediment distribution under steady and unsteady condition with existing experimental data and satisfactory results are obtained for all choices of sediment diffusivity. The variation of transient and bottom concentration with non-local effects are physically justified. Validation results show that the model can be applied to describe vertical concentration distribution in unsteady and steady turbulent flows in practical situation.

Transport characteristics of non-uniform suspended sediment in the Jingjiang Reach after the Three Gorges Project operation

三峡工程运用后，坝下游荆江段来沙量大幅度减小，处于严重的不平衡输沙状态，次饱和水流冲刷河床使悬沙量沿程恢复.基于实测水沙资料，分析了三峡工程运用后荆江段非均匀悬沙恢复特点.提出了恢复效率的概念用以表征悬移质沿程恢复的程度，并根据实测水沙资料计算了荆江段1994-2017年非均匀悬沙的恢复效率.结果表明：三峡工程运用前，荆江段各粒径组悬沙恢复效率绝对值均接近0，故该时期内各粒径组泥沙冲淤幅度不大；三峡工程运用后，各粒径组悬沙恢复效率绝对值均明显增大，且粗沙（d>0.125 mm）恢复效率绝对值远大于细沙（d<0.125 mm），故粗沙恢复程度更高.这主要是由于荆江段床沙组成中粗沙部分含量大，而细沙含量小.最后建立了三峡水库蓄水后非均匀悬沙恢复效率与来水来沙条件（来沙系数）的关系，结果表明：各粒径组悬移质恢复效率均与来沙系数呈正相关关系，全沙、细沙和中沙的决定系数（R²）分别为0.89、0.67和0.69，相关性较高，故荆江段各粒径组悬移质泥沙恢复效率较大程度上受到来水来沙条件的影响.;The amount of suspended sediment entering the Jingjiang Reach of the middle Yangtze River has been greatly reduced owing to the operation of the Three Gorges Project (TGP), which caused the sediment transport of the reach at a severe non-equilibrium state, and the suspended sediment concentration recovered during the channel scour process. Therefore, the characteristics of non-equilibrium transport of non-uniform suspended sediment were analyzed based on the measured flow and sediment data. In addition, the recovery efficiency was proposed to represent the recovery speed for suspended sediment load, and the corresponding values were calculated annually from 1994 to 2017 based on the measured data of the Jingjiang Reach. Calculated results show that the suspended sediment recovery efficiency of all particle-size groups was very close to zero before the TGP operation, which means that the channel deformation was small during this period. However, the recovery efficiency of each particle-size group increased greatly after the operation of TGP, and the recovery efficiency of coarse sediment (d>0.125 mm) was much higher than that of fine sediment (d<0.125 mm). This is mainly because the content of coarse sediment in bed-material of Jingjiang Reach is large, while the content of fine sediment is relatively small. Finally, empirical relationship was developed between the recovery efficiency and incoming flow-sediment regime, which shows that the recovery efficiency of each group was negatively related to incoming sediment coefficient, with the correlation coefficient for the total, fine and coarse sediment being 0.89, 0.67 and 0.69, respectively. Therefore, it can be concluded that the recovery efficiency of suspended sediment was significantly affected by the incoming flow and sediment conditions.

A new one-dimensional numerical model for unsteady hydraulics of sediments in rivers

This paper presents the model UMHYSER-1D (Unsteady Model for the HYdraulics of SEdiments in Rivers 1-D), a one-dimensional hydromorphodynamic model capable of representing water surface profiles in a single river or a multiriver network, with different flow regimes considering cohesive or non-cohesive sediment transport. It has both steady and unsteady flow and sediment modules. For steady gradually varied flows, UMHYSER-1D uses the standard step method to solve the energy equation and the “NewC” scheme for the de St Venant equations. For sediment transport, UMHYSER-1D uses two methods: for long-term simulation, the unsteady terms of the sediment transport continuity equation are ignored, and a non-equilibrium sediment transport method is used. For short-term simulation, the convection–diffusion equation, with a source term arising from sediment erosion/deposition is solved using the fractional step method. The equation without the source term is solved with an implicit finite-volume method, then the equation with source term is solved. Internal boundary conditions, such as time-stage tables, rating curves, weirs, bridges, and gates are simulated. Incorporated is the active layer concept, which allows selective erosion, enabling the simulation of bed armoring. Non-cohesive sediment transport equations and cohesive sediment physical processes are applied to calculate the sediment deposition and erosion. Finally, UMHYSER-1D empirically accounts for bed geometry adjustments by using a relationship between erosion width and flow rate, an angle of repose condition for bank stability and three minimization theories. The presented validation and application cases show UMHYSER-1D’s capabilities and predicts its promising role in solving complex, real engineering cases.

Riverbed armoring and sediment exchange process in a sand–gravel bed reach after the Three Gorges Project operation

Upstream damming greatly altered the flow and sediment regime entering downstream reaches in the Middle Yangtze River, and the bed material in a sand–gravel bed reach coarsened continuously, which had a significant influence on the sediment transport and bed evolution. In order to study the riverbed armoring, the sediment exchange process (SEP) among bed material, bed load and suspended load in a sand–gravel bed river is firstly clarified, and then, the three-state transition probability model (Markov chain) is proposed in this study, with the hiding-exposure effect of non-uniform sediment being considered. Finally, the equilibrium equation of sediment quantity in an active layer is presented to calculate the grain size distribution of bed material. In this model, the influences of flow and sediment conditions, riverbed erosion and deposition on the SEP are discussed. The results show that the composition of surface bed material at the Zhicheng station became obviously coarse, and the median grain size (d50) of surface bed material increased from 0.230 to 0.424 mm in 2003–2017, with an upward increasing trend. The proposed probabilistic model was validated against field measurements of bed material, and calculated results show reasonable agreement with the measured data at Zhicheng. Accordingly, the probabilistic model can be used to predict the riverbed armoring and to investigate the non-equilibrium transport of non-uniform sediment in a sand–gravel bed river.

Hydrologic-hydraulic modeling of sediment transport along the main stem of a watershed: role of tributaries and channel geometry

ABSTRACTCurrent estimations of sediment transport at the watershed scale are limited by the difficulty of accurately simulating the sediment transfer along the main stem. The typical approach to simulating watershed sediment transport involves the adoption of hydrologic sediment routing schemes that do not fully capture the contribution and timing of side tributaries, and the inclusion of a simplified channel geometry that does not include its hydraulic feedback. In this paper, we present the results of a coupled hydrologic-hydraulic model of sediment transport applied to a small watershed of Iowa. The model was developed to simulate both the hydrologic network and non-equilibrium sediment transport that occur during a flood. The model results highlight the importance of including side tributaries in order to capture a realistic duration of shear stress that ultimately affects sediment transport. Comparisons with bank erosion measurements indicate that the presented approach is also promising to estimate sediment sources along the main stem.

Morphological Computation of Dune Evolution with Equilibrium and Non-Equilibrium Sediment Transport Models

Morphological Computation of Dune Evolution with Equilibrium and Non-Equilibrium Sediment Transport Models

Morphological Computation of Dune Evolution with Equilibrium and Non-Equilibrium Sediment Transport Models

Morphological Computation of Dune Evolution with Equilibrium and Non-Equilibrium Sediment Transport Models

Effects of initial stage of dam-break flows on sediment transport

Experimental and numerical studies of dam-break flows over sediment bed under dry and wet downstream conditions are investigated and their effects on sediment transport and bed change on flow are illustrated. Dam-break waves are generated by suddenly lifting a gate inside the flume for three different upstream reservoir heads. The flow characteristics are detected by employing simple and economical measuring technique. The numerical model solves the two-dimensional Reynolds-Averaged Navier–Stokes (RANS) equations with k-ε turbulence closure using the explicit finite volume method on adaptive, non-staggered grid. The model is validated with laboratory data and is extended for simulating non-equilibrium sediment transport and bed evolution process. The volume of fluid technique is used to track the evolution of the free surface, satisfying the advection equation. The comparison study reveals that the current model is capable of defining the dam-break flow and improves the accuracy of determining morphological changes at the initial stages of the dam-break flow. A good agreement between the model solutions and the experimental data is observed.

Effects of concentration-dependent settling velocity on non-equilibrium transport of suspended sediment

In this study, non-equilibrium transport of suspended sediment from one equilibrium state to another is investigated. Based on a convective-diffusion equation, a numerical model for flow with suspended sediment is developed by considering the effect of concentration-dependent settling velocity. The numerical model is validated by comparing analytical solutions and experimental results. The concentration profiles, mean concentrations and distance necessary to reach a new equilibrium state are examined by comparing them with the results of constant settling velocity. For a high concentration flow, the results indicate that evident differences between the above three indicators can be determined with and without concentration-dependent settling velocity. Additionally, the effects of concentration-dependent settling velocity are sensitive to the sediment mobility parameter (or Rouse number), although they are nearly independent of the diffusion Reynolds number.

A Non-Equilibrium Sediment Transport Model for Dam Break Flow over Moveable Bed Based on Non-Uniform Rectangular Mesh

The use of multiple-level non-uniform rectangular mesh in coupled flow and sediment transport modeling is preferred to achieve high accuracy in important region without increasing computational cost greatly. Here, a robust coupled hydrodynamic and non-equilibrium sediment transport model is developed on non-uniform rectangular mesh to simulate dam break flow over movable beds. The enhanced shallow water and sediment transport equations are adopted to consider the mass and momentum exchange between the flow phase and sediment phase. The flux at the interface is calculated by the positivity preserving central upwind scheme, which belongs to Godunov-type Riemann-problem-solver-free central schemes and is less expensive than other popular Riemann solvers while still capable of tracking wet/dry fronts accurately. The nonnegative water depth reconstruction method is used to achieve second-order accuracy in space. The model was first verified against two laboratory experiments of dam break flow over irregular fixed bed. Then the quantitative performance of the model was further investigated by comparing the computational results with measurement data of dam break flow over movable bed. The good agreements between the measurements and the numerical simulations are found for the flow depth, velocity and bed changes.

Numerical modelling of simultaneous overtopping and seepage flows with application to dike breaching

Dike failures due to overtopping frequently occur during floods, causing serious damage to settlements and the environment. For risk management, it is of great importance to understand the mechanisms of dike failure and predict this process accurately. In this study, a three-dimensional numerical model is developed to simulate both overtopping and seepage flows during dike breaching. The governing equations describing the free water flow are extended and applied to simulate also the filtration through porous media. A non-equilibrium sediment transport model is utilized for simulation of the bed deformation. The numerical model is firstly applied to flows over a solid embankment in order to validate the flow part of the model, and then the dike breaching is simulated such that the bed deformation model is also incorporated. By comparison with the experimental results, it is shown that the developed model reproduces overflow and the dike failure processes reasonably well.

Modelling of hyperconcentrated flood and channel evolution in a braided reach using a dynamically coupled one-dimensional approach

Hyperconcentrated sediment-laden floods often occur in a braided reach of the Lower Yellow River, usually leading to significant channel evolution. A one-dimensional (1D) morphodynamic model using a dynamically coupled solution approach is developed to simulate hyperconcentrated flood and channel evolution in the braided reach with an extremely irregular cross-sectional geometry. In the model, the improved equations for hydrodynamics account for the effects of sediment concentration and bed evolution, which are coupled with the equations of non-equilibrium sediment transport and bed evolution. The model was validated using measurements from the 1977 and 2004 hyperconcentrated floods. Furthermore, the effects were investigated of different cross-sectional spacings and allocation modes of channel deformation area on the model results. It was found that a suitable cross-sectional distance of less than 3 km should be adopted when simulating hyperconcentrated floods, and the results using the uniform allocation mode can agree better with measurements than other two allocation modes.

Depth-averaged modelling of granular dike overtopping

Failure of river dikes due to overtopping is a dangerous phenomenon to be avoided, and a complex unsteady sediment transport problem that is under intense scientific consideration. Mathematical modelling of these flows is conducted using one-dimensional families of models based on different conceptual approximations, including (i) a clear-water layer and bed-load layer approach; (ii) a mixture flow approach dividing the sediment transport into bed and suspended load transport modes; and (iii) a two-phase approach formulating the mass and momentum conservation equations for the water and sediment phases separately. These families of conceptual models involve a vertical momentum balance reducing to hydrostatic pressure distribution. As discussed in previous works, numerical results might be improved by relaxing this closure hypothesis. Herein, a vertically-averaged RANS model is presented for a water–sediment mixture, conceptually divided into suspended/bed-load layers, overtopping the erodible dike surface under non-equilibrium sediment transport and non-hydrostatic fluid pressure conditions. The model is critically compared with experimental data and Saint-Venant type simulations, resulting in improved predictions of the dike crest reach. However, the erosion at the dike toe is overpredicted, stating a limitation of depth-averaged modelling.

A simple non-equilibrium bedload transport equation for the formation of dune in a shallowwater flow over an erodible bed

In this work, we consider the long-standing problem of capturing dune formation in an erodible-bed channel at subcritical speed by using a reduced order model of depth-averaged equations. The pioneering study by Reynolds [1] showed that the standard Saint-Venant-Exner equations are unconditionally stable at subcritical Froude number. Hence, the use of depthaveraged flow equations, which are commonly used by the hydraulic community, prevents the formation of bedforms as dunes. Recently, Cañada-Pereira &amp; Bohorquez [2] have proposed a simple sediment transport formulation able to capture the formation of dune when coupled with the Saint-Venant equations. We replace the standard Exner equation with a non-equilibrium sediment transport equation that includes the following necessary ingredients: first, a phase shift in the particle entrainment rate; second, a particle diffusivity and an eddy viscosity. Subsequently, we solve the linear stability problem of an erodiblebed channel and show that the neutral curve properly captures the bed instability both in subcritical regime (i.e. dune) and supercritical flow (i.e. antidune and roll wave). Finally, we corroborate the capabilities of the model by means of non-linear numerical simulations which reproduce the growth of dune and antidune in agreement with experiments.