Movable Bed Research Articles

A depth-averaged non-cohesive sediment transport model with improved discretization of flux and source terms

This paper presents novel flux and source term treatments within a Godunov-type finite volume framework for predicting the depth-averaged shallow water flow and sediment transport with enhanced the accuracy and stability. The suspended load ratio is introduced to differentiate between the advection of the suspended load and the advection of water. A modified Harten, Lax and van Leer Riemann solver with the contact wave restored (HLLC) is derived for the flux calculation based on the new wave pattern involving the suspended load ratio. The source term calculation is enhanced by means of a novel splitting-point implicit discretization. The slope effect is introduced by modifying the critical shear stress, with two treatments being discussed. The numerical scheme is tested in five examples that comprise both fixed and movable beds. The model predictions show good agreement with measurement, except for cases where local three-dimensional effects dominate.

Observing the Laboratory Interaction of Undertow and Nonlinear Wave Motion over Barred and Nonbarred Beaches to Determine Beach Profile Evolution in the Surf Zone

ABSTRACT Choi, J.; Roh, M., and Hwang, H., 2018. Observing the laboratory interaction of undertow and nonlinear wave motion over barred and nonbarred beaches to determine beach profile evolution in the surf zone. A vertically two-dimensional laboratory experiment was performed with a movable bed to investigate the interaction of undertow and sawtooth-shaped nonlinear wave motion over the cross-shore evolution of barred (storm) and nonbarred (normal) beach profiles. The bottom elevations, free-surface motion, and flow velocity were measured under regular wave conditions, excluding infragravity waves, over a movable bed. The observations were conducted in the surf zone during alternate repeats of the two wave conditions until each quasiequilibrium state was reached. From the net sediment transport of the observation area, it was shown that the storm case was in an erosion state and that the normal case was in an accretion state. The measurements confirmed that the strong undertow, which is a dominant factor...

Flow variability along a vegetated natural stream under various sediment transport rates

The influence of vegetation and sediment on flow characteristics in open channels cannot be neglected. To study the flow variability under the effects of the instream natural vegetation and sediment supply, experiments were conducted with varied water and sediment supply in a movable bed of a river prototype. The instantaneous three-dimensional velocities near two types of vegetation patches (the shrub and the weed) and along the centerline of the main channel with vegetation belts were measured using a 3-D side-looking acoustic Doppler velocimetry. The experimental results show that both the instream vegetation and sediment supply strongly affect the flow and turbulence characteristics. In the case of vegetation patches, both the shrub and weed have a considerable influence on the distribution of the streamwise velocity and turbulence intensity of their surrounding water. The streamwise velocity distribution followed as J-shape and linear shape around the weed and shrub under different experimental conditions. The turbulence intensity was large at the top of the weed and shrub; the shrub had its greatest influence on the downstream water flow. In the case of vegetation belts, the streamwise velocity along the centerline of the main channel exhibited an S-shape, J-shape and linear shape at different locations under varied water, vegetation structures and riverbed configurations. The turbulence intensity along the centerline of the main channel ranged from 0.0 to 0.1. The upstream turbulence intensity was affected considerably by a sediment supply, while the downstream turbulence intensity changed with the varied vegetation characteristics and riverbed topography. The second flow coefficient M-value increased longitudinally and was almost positive along the centerline of the main channel, implying that the rotational direction of the secondary current cell was clockwise.

Performance evaluation of several sequencing batch biofilm reactors with movable bed in treatment of linear alkyl benzene sulfonate in urban wastewater

Detergents are one of the major environmental pollutants whose consumption will increase by increasing the level of health of countries, which can cause many problems if they are not unfiltered and exposed to the environment. After soap, linear benzene sulfonate is the most common household detergent and it is used in more than 100 countries around the world as a raw material for the production of surfactants such as washing powders, dishwashing liquids and other detergents. Among the various methods of treatment, biological processes are the most promising ones. The aim of this study is to evaluate the performance of a moving bed sequencing continuous-inflow reactor (MSCR) for linear alkyl benzene sulfonate (LAS) removal from municipal wastewater at different operating conditions. In this research study, a Plexiglass pilot with dimensions of 54 × 25 × 25 cm, and total volume of about 35 L and used volume of 30 L was used. The reactor contained 70% of K3 (Kaldnes) media, and the remaining 30% was considered as the functional volume. Results showed that the MSCR has a high capability in the treatment of municipal wastewater polluted by LAS and a good flexibility to input variation of both LAS and organic load. The maximum removal efficiency obtained at hydraulic retention time of 2.5 h, with input organic load of 300 mg/L and input LAS of 15 mg/L, was 96.4%. The maximum efficiencies obtained at hydraulic retention time of 2.5 h, with input organic load of 500 mg/L and input LAS of 15 mg/L and 25 mg/L, were 88.7%, and 92.2%, respectively.

Relevance of erosion processes when modelling in-channel gravel debris flows for efficient hazard assessment

A storm, composed of two delayed cells, hit the Monte Antelao slopes (Dolomites, North Eastern Italy) in the early morning of July 18th, 2009. The resulting runoff triggered two consecutive debris flows along the Rovina di Cancia channel. The detailed topographic data collected before and just after this event allowed an accurate reconstruction of the morphological changes experienced by the channel bed. These data are here used as benchmark to test the ability of numerical models to reproduce the dynamics of a real event, taking into account the morphology changes of the channel bed. The aim is to provide an efficient model for engineering applications on large scales, such as those required by debris flow hazard assessment. A rainfall-runoff transformation is applied to reconstruct the solid-liquid hydrograph needed for computing the debris flow propagation. Two routing models are used: a GIS-based movable bed model, and a widely used fixed bed model (FLO-2D). Although similar results are obtained in terms of areas subjected to deposition, significant differences emerge in terms of mobilized volumes. Only the simulation of both the deposition and entrainment processes allows to reliably reproduce the sediment volumes estimated from the pre- and post-event topographic data. This information is fundamental in any hazard assessment because the volume of sediment mobilized by debris flow events exerts a fundamental control on the extension of areas subjected to inundation and on the thickness of sediment deposits. The capability to reproduce correctly the mobilized volumes also entails a more reliable simulation of the evolution of the peak and volume of the solid-liquid hydrograph as the debris flow propagates downstream, allowing the identification of the channel reach where banks could be overflowed. Conversely, adopting a fixed bed model leads mainly to an underestimation of the both the transported sediments volumes and the area subjected to deposition. As a consequence, the maximum debris flow depth in the portion of the channel subjected to erosion is underestimated and that in the portion of the channel subjected to deposition is overestimated. All these types of information are of great importance for an effective hazard assessment.

Bottom‐Slope‐Induced Net Sediment Transport Rate Under Oscillatory Flows in the Rippled‐Bed Regime

AbstractFull‐scale experiments in the rippled‐bed regime were conducted in an oscillatory water tunnel to study the net sediment transport rate due to oscillatory flows on sloping bottoms (up to 2.6°). The tests cover a variety of sinusoidal flows, under which uniform two‐dimensional ripples are generated from a coarse sand movable bed. A laser‐based bottom profiler was developed to measure ripple geometry and net sediment transport rate. Under the same flow condition, a small bottom slope can slightly change the shape of the equilibrium ripples; for example, ripples become upslope leaning, but the ripple dimensions remain almost unchanged. Ripples are also found to migrate in the downslope direction with uniform speed and permanent shape, which is due to the spatial variation of net bedload transport rate. For a given flow condition, the slope‐induced net sediment transport rates are in the downslope direction and increase linearly with the bottom slope. A conceptual model, which is an extension of a sheet flow model (Yuan, Li, & Madsen, 2017, https://doi.org/10.1002/2016JC011996), was also developed. This calibration‐free model can reasonably predict the net transport rate, despite that a moderate underestimate (a factor slightly less than 2) is observed. Both our experiments and model suggest that the presence of ripples significantly enhances sediment mixing and leads to a large net suspended‐load transport rate, which will not occur under sheet flow conditions. Therefore, net transport rate in the ripple‐bed regime can be comparable to that in the sheet flow regime, although the flow condition is much weaker.

Numerical modeling of sediment transport based on unsteady and steady flows by incompressible smoothed particle hydrodynamics method

The purpose of the present paper is to introduce a simple two-part multi-phase model for the sediment transport problems based on the incompressible smoothed particle hydrodynamics (ISPH) method. The proposed model simulates the movement of sediment particles in two parts. The sediment particles are classified into three categories, including the motionless particles, moving particles behave like a rigid body, and moving particles with a pseudo fluid behavior. The criterion for the classification of sediment particles is the Bingham rheological model. Verification of the present model is performed by simulation of the dam break waves on movable beds with different conditions and the bed scouring under steady flow condition. Comparison of the present model results, the experimental data and available numerical results show that it has good ability to simulate flow pattern and sediment transport.

Experimental Investigation of Total Bottom Shear Stress for Oscillatory Flows Over Sand Ripples

AbstractShoaling waves often produce vortex ripples on a sandy seabed, which significantly increases the local bottom shear stress. To improve the quantitative understanding of this phenomenon, a full‐scale experimental study is conducted using an oscillatory water tunnel. In the tests, sinusoidal oscillatory flows generate two‐dimensional uniform sand ripples from a 9‐m‐long movable bed made of coarse sand. The total bottom shear stress is estimated from the change of water pressure for driving the oscillatory flow. Flow around individual ripples is also measured using particle image velocimetry. After correction for imperfect flow generation and facility vibration, the leading three odd harmonics of total bottom shear stress are kept in the final measurements. The first harmonic is the dominant one and is generally in phase with the free‐stream velocity. Its amplitude decreases as ripples are washed‐off by increasing flow intensity. The third and the fifth harmonics are about 10–20% of the first harmonic in amplitude. Their presence makes the intraperiod variation of total bottom shear stress quite wavy with three peaks within one half period. Flow measurements suggest that these peaks are closely related to coherent vortex motions. For two selected tests, total bottom shear stress is estimated from velocity measurements via a control volume analysis. The results are in good agreement with those from the pressure‐based technique, which verifies both approaches. A new predictor for the equivalent sand grain roughness in Humbyrd's (2012, http://hdl.handle.net/1721.1/78234) formula for wave friction factor is calibrated based on the obtained measurements of maximum total bottom shear stress.

Free-Flow Sediment Flushing: Insights from Prototype-Scale Studies

Free-flow sediment flushing operation offers viable means to preserve the storage capacity of dam reservoirs as the incoming flood erodes the flushing channel, and the deposited sediment is flushed from the reservoir. This method involves complex flow patterns and flushing channel formation procedures owing to the dynamic interaction between varying flow conditions (e.g., shallow and deep flows) and moveable bed variations notably when the non-uniform sediments exist in the complex geometry of reservoirs. In the present study, first, the numerical simulation of a previously conducted free-flow sediment flushing operation in the Dashidaira and the target segment of Unazuki reservoirs using the available field-measured data were presented. Then, to improve the flushing efficiency in the Dashidaira reservoir, the effects of using a groyne were studied. A fully 3D numerical model using the finite volume method in combination with a wetting/draying algorithm was utilized to reproduce the flow velocity field and morphological bed changes. While the characteristics of the flow field can be captured by the numerical model in Dashidaira and Unazuki reservoirs, simulated bed changes in upstream areas covered with the coarser materials (e.g., study zone of Unazuki reservoir) showed some discrepancies. The outcomes also revealed that implementing a groyne at the entrance of the wide midstream of Dashidaira reservoir can locally increase the sediment erosion chance from this area and thereby can improve the flushing efficiency by approximately 10%. Therefore, the risks associated with the accumulation of distorted sediments in the wide midstream of Dashidaira reservoir within a long-term period could be reduced.

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 and physical modelling of future Rhône Delta (Switzerland)

The Rhône River on its Swiss course flows through the Lake of Geneva before traversing Geneva and continuing towards France. The river is entirely canalized upstream of the Lake of Geneva, over a length of about 160 km. Hence, a large river restoration project, the Third Rhône River Correction, is being planned for the upcoming 20-30 years. One of the first works to be realized will be the restoration of a delta estuary of the Rhône River into the lake. This delta will propose morphological diversity over a length of about 1.5 km, for a width of about 0.8 km, and will consist of a terrestrial part and a lake part. Both numerical and physical modelling have been performed to assess the morpho-dynamic potential of this delta. The morphological numerical modelling predicts evolution of the delta within a time frame of 30 years. The maritime numerical modelling shows the deformation of the delta head due to storm events on the lake, as well as the related littoral transport. The computations allowed assessing the progressive development of the delta into the lake, as well as the evolution of the terrestrial part and of a secondary river stretch. This allowed determining 3 interesting geometries to be tested on a physical model. The physical model has been constructed at an undistorted 1: 75 scale and reproduces morphology of the Rhône River and its delta with a movable bed and a movable delta. Two different materials have been mixed to simulate the sand and gravel parts of the sediment transport. Also, a wave generator has been used to reproduce storm events on the lake. This paper presents a comparison of numerical and physical model predictions of the morpho-dynamic behavior of the delta, including the influence of coastal events on the estuary dynamics.

Application of a Line Laser Scanner for Bed Form Tracking in a Laboratory Flume

AbstractA new measurement method for continuous detection of bed forms in movable bed laboratory experiments is presented and tested. The device consists of a line laser coupled to a 3‐D camera, which makes use of triangulation. This allows to measure bed forms during morphodynamic experiments, without removing the water from the flume. A correction is applied for the effect of laser refraction at the air‐water interface. We conclude that the absolute measurement error increases with increasing flow velocity, its standard deviation increases with water depth and flow velocity, and the percentage of missing values increases with water depth. Although 71% of the data is lost in a pilot moving bed experiment with sand, still high agreement between flowing water and dry bed measurements is found when a robust LOcally weighted regrESSion (LOESS) procedure is applied. This is promising for bed form tracking applications in laboratory experiments, especially when lightweight sediments like polystyrene are used, which require smaller flow velocities to achieve dynamic similarity to the prototype. This is confirmed in a moving bed experiment with polystyrene.

Effects of morphological change on fluvial flood patterns evaluated by a hydro-geomorphological model

Abstract High aggradation and degradation in a river induced by the last flood event will raise and decrease the risk of an upcoming flood event, respectively. To quantitatively investigate this effect, a two-dimensional (2D) hydrodynamic model coupled with a sediment transport the river-bed evolution models is developed. After being validated against two experimental benchmark tests, the model is applied to simulate the effects of the morphological change on flood patterns. It is found in two experimental scale tests that bed evolution may have substantial influence on water level, which is directly related to flood risk extent. In the application of the model computing a realistic flood event in Bayangaole Reach of Yellow River, the results show that the water surface level becomes lower for an upcoming flood event with the same hydrograph, indicating the flood risk considerably decreases in the next flood event. The effect of a perturbed bed therefore could be of significance for fluvial flood over a movable bed and therefore to flood risk management.

Efficient analytical implementation of the DOT Riemann solver for the de Saint Venant–Exner morphodynamic model

Within the framework of the de Saint Venant equations coupled with the Exner equation for morphodynamic evolution, this work presents a new efficient implementation of the Dumbser-Osher-Toro (DOT) scheme for non-conservative problems. The DOT path-conservative scheme is a robust upwind method based on a complete Riemann solver, but it has the drawback of requiring expensive numerical computations. Indeed, to compute the non-linear time evolution in each time step, the DOT scheme requires numerical computation of the flux matrix eigenstructure (the totality of eigenvalues and eigenvectors) several times at each cell edge. In this work, an analytical and compact formulation of the eigenstructure for the de Saint Venant–Exner (dSVE) model is introduced and tested in terms of numerical efficiency and stability. Using the original DOT and PRICE-C (a very efficient FORCE-type method) as reference methods, we present a convergence analysis (error against CPU time) to study the performance of the DOT method with our new analytical implementation of eigenstructure calculations (A-DOT). In particular, the numerical performance of the three methods is tested in three test cases: a movable bed Riemann problem with analytical solution; a problem with smooth analytical solution; a test in which the water flow is characterised by subcritical and supercritical regions. For a given target error, the A-DOT method is always the most efficient choice. Finally, two experimental data sets and different transport formulae are considered to test the A-DOT model in more practical case studies.

Hazards due to large wood accumulations: Local scour and backwater rise

Large wood (LW) in rivers increases the flow variability and provides habitats for various species. During flood events, transported logs can accumulate at river infrastructures and increase the flood hazard. LW accumulations result in an upstream backwater rise and may increase local scour, for instance at bridge piers. Consequently, estimates of the resulting backwater rise and local scour are necessary to improve the flood hazard assessment. This study presents the findings of flume experiments with a movable bed on local scour and backwater rise due to LW accumulations. The approach flow conditions and the bed material were varied systematically for a specific LW accumulation volume. For all experiments, the initial condition for the bed material was defined as weak transport, since the bed shear stress was slightly below the critical bed shear stress for incipient motion. The inflow Froude number was identified as the governing parameter for backwater rise due to LW accumulations. The present study confirms the hypothesis that the resulting local scour reduces backwater rise. For the local scour, the unit discharge and the grain size diameter are the decisive parameters.

Laboratory Study on Cross Shore Sediment Budget over Submerged Breakwaters

The objective of this study is to understand the characteristics of the cross-shore sediment transport over the submerged breakwater through quantitative observations of wave breaking, undertow, and the characteristics of near bottom velocity profiles such as skewness, asymmetry around the permeable or impermeable submerged breakwaters. A series of laboratory experiments were conducted in a 2D wave flume with uniformly sloping 1/20 movable bed of uniform sand grains (D50 =0.15 mm). Either permeable or impermeable breakwaters was installed and four regular incident wave conditions were selected so that generated waves cover both daily or stormy wave conditions. Boundary detection technique was used to obtain the temporal and spatial variation of bed profile and then to calculate cross shore sediment transport rate, CTR, from the images captured by multiple high speed and normal video cameras. Tracer particles were used in the experiment and PIV was applied to capture the velocity field around the submerged breakwater. The experimental results indicate that the impermeable breakwater is generally more effective than the permeable breakwater in terms of the reduction of the seaward CTR over the submerged breakwater but the amount of CTR was very sensitive to the breaking point especially in the case of impermeable breakwater. Increase in acceleration skewness caused low CTR in impermeable breakwater case even with a relatively high wave action on the lee of the breakwater.

Effect of vegetation on flows and sediment transport

Vegetation is a common feature in natural coastal and riverine waters, interacting with both water flow and sediment transport. However, the physical processes governing these interactions are still poorly understood, which makes it difficult to predict sediment transport and associated morphodynamics in a vegetated environment. In this context, an experimental study was conducted in laboratory with a movable bed trapped in artificial vegetation. The experimental flume is a rectangular open channel 5.75 m long and 0.29 m wide. For flow measurements, the channel is equipped with a fast camera and ADV probe. This work focuses on identifying the vegetation effects on flows and sediment transport. In fact, it was shown that the vegetation presence in a watercourse promotes deposition and sediment accumulation. This is explained by a reduction of the bed shear stress, since the friction occurs mainly by the drag force effect exerted by the vegetation. It was shown too that the vegetation reduced the bedload transport. Thanks to the partitioning of shear stress, it was possible to predict the bedload transport using standard formulas with a reasonable accuracy.

Self-Adjustment Process of Flow Pathway in a Narrow Curved Channel

This study focuses on river bed fluctuation of the curved channel with channel width narrowing, where is located in the inlet of the old meandering river with 30 (m) width from straightened one with 80 (m) in the Kushiro Wetland. From field survey, in response to change in water and sediment discharges, significant streamwise variation in water flow width in the curved channel adjusts in order to establish the dynamic equilibrium. Along the outer bank of curved channel, the secular bed deposit beside the outer bank is increasing, and as a result, the main streamline flows into the old river along the inner bank as left bank. Moreover, this narrowing curved channel easily leads to overspill some flood water including rich suspended sediment and to deposit some fine sand near channel side flood plain. We intend to explain above significant bed variations by using movable bed experiments with the distorted model. As a result, we suggest, though qualitatively, that the existence of the sandbar upstream of the curved channel causes the autonomous specification of the flow path width in the curved channel with a narrowing width, and that this flow path is formed.

Limiting the development of riparian vegetation in the Isère River: A physical modelling study

Physical modelling experiments are conducted to investigate if a modification of the Isère River (French Alps) hydrology by changing dams management is able to foster riverbed morphodynamic and, thus limiting riparian plant development. The experimental setup is a 1:35 scale, undistorted movable bed designed to ensure the Froude number similarity and initial conditions for sediment particle motion. The physical model is 35 m long, 2.6 m wide, with a sand mixture composed of three grain size classes. Two runs with different flow and bed load conditions are simulated. Preliminary results show an intense riverbed activity when the system reaches a dynamic equilibrium state. Under these conditions, bar mobility is strong enough to limit vegetation encroachment only when water discharges are higher than the discharge of a 5-years flood during more than 10 days. These results indicate that the hydrological characteristics of the Isère River and the actual configuration of the hydropower structures could be not able to release annually the flow conditions needed to control riparian plant development.

Sediment incipient motion on movable bed in rigid vegetation environment

Vegetation in open channels has a significant influence on the characteristics of bed load movement. To date, studies of incipient motion of sediment in open channels with submerged vegetation have been restricted by limitations in statistical approaches and measuring equipment. Researchers have also neglected incipient motion of sediment in the presence of vegetation when deriving semi-empirical equations for the rates of bed load transport, and have generally considered it the same as that without vegetation, which is clearly inconsistent with, and does not represent, the actual conditions. In this study, we therefore studied the vegetation and sandy bed in a natural river to determine the characteristics of incipient motion of sediment within rigid vegetation on a movable bed. From the spatially averaged velocity, we then described the incipient motion of sediment under the water-vegetation interface. We found that there were three phases of incipient motion of sediment, namely static, partially in motion, and entirely in motion. We defined the incipient motion of sediment from the conditions for the third process. We derived a semi-empirical equation for the sediment incipient velocity in the presence of submerged vegetation from our experimental results, and found that, of the factors explored, the vegetation factor Fv had most influence on the incipient motion velocity of sediment with vegetation. For a given vegetation density, the average depth of the scour holes around the vegetation elements were linearly related with the spatially averaged velocity of the flow under the water-vegetation interface. These results demonstrate that our method gave reasonable estimates of the spatially averaged velocity for incipient motion of sediment.