Sediment Continuity Research Articles

3D numerical simulation of local scouring under hydrographs

Owing to the interaction between three-dimensional (3D) flow pattern and bed material, the process of local scouring around bridge piers is complex. Simply using the empirical scour formula may be insufficient for the evaluation of pier scour under the unsteady flow condition. In the present study, the evolution of scour depth under unsteady flow has been simulated using a 3D numerical model. The model solves 3D Navier–Stokes equations incorporated with the sediment continuity equation to take into account the interaction between flow and sediment. The simulated scour-depth evolution coincides with the measured one quite well under the steady flow condition. For the unsteady hydrograph, a compounded method is proposed for simulations of scour-depth evolution as well as for scour hole development. The results show the simulated bed elevation contours are in good agreement in front of the pier, while the simulated final scour depth is slightly lower than the measured data by 15%. In addition, it is found that the simulated scour depth at the end of the rising limb is 74–79% of the final scour depth, which implies that the recession period of the hydrograph plays a less effective role than the rising limb in the unsteady scouring process.

A numerical shoreline model for shorelines with large curvature

This paper presents a new numerical model for shoreline change which can be used to model the evolution of shorelines with large curvature. The model is based on a one-line formulation in terms of coordinates which follow the shape of the shoreline, instead of the more common approach where the two orthogonal horizontal directions are used. The volume error in the sediment continuity equation which is thereby introduced is removed through an iterative procedure. The model treats the shoreline changes by computing the sediment transport in a 2D coastal area model, and then integrating the sediment transport field across the coastal profile to obtain the longshore sediment transport variation along the shoreline. The model is used to compute the evolution of a shoreline with a 90° change in shoreline orientation; due to this drastic change in orientation a migrating shoreline spit develops in the model. The dimensions of the spits evolving in the model compare favorably to previous model results and to field observation of the Skaw Spit in the north of Denmark.

NUMERICAL SIMULATION OF FLOW AND LOCAL SCOUR AT TWO SUBMERGED-EMERGENT TANDEM CYLINDRICAL PIERS

In this paper, the flow and local scour variation around two submerged and un-submerged tandem piers are studied using 3D flow model where the upstream pier is submerged while the downstream pier is emergent. The model uses a finite-volume method to solve the non-transi ent Navier-Stokes equations for three dimensions on a general non-orthogonal grid. The   k turbulence model is used to solve the Reynolds-stress term. The numerical model solves the sediment continuity equation in conjunction with van-Rijn’s bed-load sediment transport formula to simulate the bed evolution. The 3D flow model is verified through experimental study in a non cohesive bed material in an experimental flume. The different causes of local scour around two submerged and unsubmerged piers are simulated well, such as bow flow, down flow, horseshoe vortex, pressure variation and lee-wake vortex. It is found from this study that the maximum local scour depth by interaction between two tandem submerged unsubmerged piers depends on submersion ratio of upstream pier, the densimetric Froude number, the longitudinal distance between piers and the ratio of pier diameter to channel bed width. The maximum scour depth decreases by increasing the submerged pier height then begin to increase by increasing the submerged pier to a height larger than half the water depth and in general the maximum scour depth is less than that of two unsubmerged piers. The results show good agreement between simulation and experimental results. Also, empirical equations are developed for computing the maximum scour depth due to the interaction between two submerged unsubmerged piers with circular shapes as a function of submergence ratio, piers spacing, densimetric Froude number and channel width to pier diameter ratio.

Control of shallow water and sediment continuity coupled system

This paper presents an algebraic method to design a linear feedback control for regulating the water flow in open channels. We deal with a hyperbolic system of partial differential equations describing the behavior of the water flow and the sediment transport. By using an a priori estimation techniques and the Faedo–Galerkin method, we build a stabilizing boundary control. This control law ensures a decrease of the energy and convergence of the controlled system.

Bed load transport by bed form migration

A theoretically-based methodology is presented for the determination of bed load transport from high-resolution measurements of bed surface elevations for steady-state or developing dunes. The methodology is based on the general form of the Exner equation for sediment continuity and requires information on the distribution of sediment volume concentration as well as the migration velocity of bed layers. In order to determine layer speeds, a new method based on cross-correlation analysis of elevation slices is proposed. The methodology is tested using artificially-created data as well as data from a physical model and from a flume study of developing bed forms. The analyses show the applicability of the method to determine bed load transport without the need to introduce assumptions about the form of the migrating surface. It is shown that predicted transport rates match measured or theoretical transport rates for steadily moving bed forms of an arbitrary shape. The method can also be used to predict transport rates over deforming bed forms, with the reasons for potential deviations between predicted and measured or theoretical transport rates for deforming bed forms identified and discussed. It is further shown that a simplified bulk-surface approach, that is relatively straightforward to apply and in which it is assumed that bed-layer velocity is constant with depth, gives results that are comparable to analyses based on determined bed-layer velocity variation with depth.

Influence of Suspended Load on 3D Numerical Simulation of Flow and Bed Evolution in a Meandering Channel Bend

AbstractA three-dimensional (3D) numerical model based on unstructured grids has been used to study flow and bed evolution in a laboratory meandering channel bend. The model employs the Reynolds-averaged Navier-Stokes equations and the low-Reynolds-number k−ω turbulence model for flow simulation. The model incorporates the suspended-load transport module and the bed-load transport module to simulate sediment transport and employs the sediment continuity equation to calculate channel bed evolution. The numerical simulation is performed in a meandering channel with a movable bed, in which the suspended load is comparable to the bed load. The model captures the main features of the bathymetry at equilibrium conditions. The streamwise velocity profiles and the suspended sediment concentration profiles at equilibrium conditions are also predicted by this simulation, and the agreement with the measured data is generally reasonable. The influence of including the suspended load is revealed by the comparison betw...

Grain-Scale Nonequilibrium Sediment-Transport Model for Unsteady Flow

AbstractA one-dimensional (1D) finite-volume model is developed for simulating nonequilibrium sediment transport in unsteady flow. The governing equations are the 1D mass and momentum conservation equations for sediment-laden flow and the sediment continuity equation for both bed load and suspended-load transport. The Rouse profile is modified to consider the nonequilibrium transport of suspended sediment. The spatial lag between the instantaneous flow properties (e.g., velocity, bed shear stress) and the rate of bed load transport in unsteady flow is quantified by using an adaptation length, which is derived theoretically by applying the momentum principle in the bed load layer. This new method for calculating the adaptation length is verified using data from several experiments and yields better results than other empirical formulas for a wide range of shear stress. The nonequilibrium model is applied to simulate a series of laboratory dam-break flows over erodible beds, and the simulated results agree ...

A theoretical framework for the morphodynamics of bedrock channels

Bedrock rivers are characterized by conditions of insufficient sediment supply, wherein the amount of sediment supplied to the channel is less than the channel's sediment transport capacity. Consequently, bedrock channels generally exhibit discontinuous sediment cover, which current approaches to the morphodynamics of alluvial rivers are unable to handle. To fill this gap, we present a theoretical framework in which local sediment transport rates are proportional to the areal concentration of sediment available for transport on the bed and the sediment continuity equation is reformulated to account for temporal changes in areal concentration of sediment on nonalluviated surfaces. We then perform a linear stability analysis that shows that an initially uniform distribution of the areal concentration of sediment on the bed is unstable to small perturbations. This suggests that the sediment cover in bedrock channels tends to concentrate into regions which may eventually be alluviated, in general agreement with experimental observations.

Instability Theory of Sand Ripples Formed by Turbulent Shear Flows

AbstractA theory of turbulent shear flow over a sand bed is developed, addressing the instability principle of the fluid-granular bed interface leading to the formation of ripples. The Reynolds-averaged Navier-Stokes (RANS) equations and the time-averaged continuity equation are analyzed using a 1/7-power law of the time-averaged streamwise velocity and treating the curvilinear streamlines by the Boussinesq approximation. The integration of the RANS equations leads to a governing dynamical equation of flow over a mobile bed. A near-bed flow layer of 3.5 times the ripple height is considered being affected by the ripples. The dynamical equation of the mobile sand bed is based on the Exner’s sediment continuity equation in conjunction with the Meyer-Peter and Muller bed-load transport formula as modified to account for the effect of local bed slope attributable to bed forms. The coupled dynamical equations are then analyzed to estimate the parameters for the instability that results in the formation of ripp...

Bed load transport in bedrock rivers: The role of sediment cover in grain entrainment, translation, and deposition

[1] Bedrock rivers exert a critical control over landscape evolution, yet little is known about the sediment transport processes that affect their incision. We present theoretical analyses and field data that demonstrate how grain entrainment, translation and deposition are affected by the degree of sediment cover in a bedrock channel. Theoretical considerations of grain entrainment mechanics and sediment continuity each demonstrate that areas of exposed bedrock and thin sediment depths cause sediment transport to be size-independent, albeit excluding extreme grain sizes. We report gravel and cobble magnetic tracer data from three rivers with contrasting sediment cover: the bedrock River Calder (20% cover), the bedrock South Fork Eel River (80%) and the alluvial Allt Dubhaig (100%). These data sets show that: 1) transport distances in the River Calder are controlled by sediment patch location, whereas in the other rivers transport distances are described by gamma distributions representing local dispersion; 2) River Calder transport distances are size-independent across all recorded shear stresses, whereas the other rivers display size-selectivity; 3) River Calder tracers are entrained at a dimensionless shear stress of 0.038, which is relatively low compared to alluvial rivers; and, 4) virtual grain velocities in the River Calder are higher than in a comparable reach of the Allt Dubhaig. These contrasts result from differences in the thicknesses and spatial distribution of sediment in the three rivers, and support the theoretical analysis. Sediment processes in bedrock rivers systematically vary along a continuum between bedrock and alluvial end-members. Citation: Hodge, R. A., T. B. Hoey, and L. S. Sklar (2011), Bed load transport in bedrock rivers: The role of sediment cover in grain entrainment, translation, and deposition, J. Geophys. Res., 116, F04028, doi:10.1029/2011JF002032.

Experimental and computational investigation of local scour around bridge piers

Experiments and numerical simulations are carried out to study clear-water scour around three bridge piers with cylindrical, square, and diamond cross-sectional shape, respectively. To handle movable-bed channels with embedded hydraulic structures, the fluid–structure interaction curvilinear immersed boundary (FSI-CURVIB) method is employed. The hydrodynamic model solves the unsteady Reynolds-averaged Navier–Stokes (URANS) equations closed with the k-ω turbulence model using a second-order accurate fractional step method. Bed erosion is simulated by solving the sediment continuity equation in the bed-load layer using a second-order accurate unstructured, finite-volume formulation with a sand-slide, bed-slope-limiting algorithm. Grid sensitivity studies are carried out to investigate the effect of grid resolution on the predictive capability of the model. Comparisons of the simulations with the experimental data show that for all three cases the agreement is reasonable. A major finding of this work, however, is that the predictive capability of the URANS morphodynamic model improves dramatically for the diamond shape pier for which sediment transport is driven primarily by the shear layers shed from the pier sharp edges. For piers with blunt leading edge, on the other hand, as the circular and square shapes, the URANS model cannot resolve the energetic horseshoe vortex system at the pier/bed junction and thus significantly underpredicts both the scour depth at the nose of the pier and the rate of scour growth. It is also shown that ad hoc empirical corrections that modify the calculated critical bed shear stress to enhance scour rate in the pier leading edge need to be applied with caution as their predictive capabilities are not universal but rather depend on the pier shape and the region of the flow.

Curvilinear immersed boundary method for simulating coupled flow and bed morphodynamic interactions due to sediment transport phenomena

The fluid–structure interaction curvilinear immersed boundary (FSI-CURVIB) numerical method of Borazjani et al. [3] is extended to simulate coupled flow and sediment transport phenomena in turbulent open-channel flows. The mobile channel bed is discretized with an unstructured triangular mesh and is treated as a sharp-interface immersed boundary embedded in a background curvilinear mesh used to discretize the general channel outline. The unsteady Reynolds-averaged Navier–Stokes (URANS) equations closed with the k − ω turbulence model are solved numerically on a hybrid staggered/non-staggered grid using a second-order accurate fractional step method. The bed deformation is calculated by solving the sediment continuity equation in the bed-load layer using an unstructured, finite-volume formulation that is consistent with the CURVIB framework. Both the first-order upwind and the higher-order hybrid GAMMA schemes [12] are implemented to discretize the bed-load flux gradients and their relative accuracy is evaluated through a systematic grid refinement study. The GAMMA scheme is employed in conjunction with a sand-slide algorithm for limiting the bed slope at locations where the material angle of repose condition is violated. The flow and bed deformation equations are coupled using the partitioned loose-coupling FSI-CURVIB approach [3]. The hydrodynamic module of the method is validated by applying it to simulate the flow in an 180° open-channel bend with fixed bed. To demonstrate the ability of the model to simulate bed morphodynamics and evaluate its accuracy, we apply it to calculate turbulent flow through two mobile-bed open channels, with 90° and 135° bends, respectively, for which experimental measurements are available.

Numerical Modeling of Abutment Scour with the Focus on the Incipient Motion on Sloping Beds

A three-dimensional computational fluid dynamics model is applied to predict local scour around an abutment in a rectangular laboratory flume. When modeling local scour, steep bed slopes up to the angle of repose occur. To predict the depth and the shape of the local scour correctly, the reduction of the critical shear stress due to the sloping bed must be taken into account. The focus of this study is to investigate different formulas for the threshold of noncohesive sediment motion on sloping beds. Some formulas only take the transversal angle (perpendicular to the flow direction) into account, but others also consider the longitudinal angle (streamwise direction). The numerical model solves the transient Reynolds-averaged Navier-Stokes equations in all three dimensions to compute the water flow. Sediment continuity in combination with an empirical formula is used to capture the bed load transport and the resulting bed changes. When the sloping bed exceeds the angle of repose, the bed slope is corrected with a sand-slide algorithm. The results from the numerical simulations are compared with data from physical experiments. The reduction of the bed shear stress on the sloping bed improves the results of the numerical simulation distinctly. The best results are obtained with the formulas that use both the transversal and the longitudinal angle for the reduction of the critical bed shear stress.

Theoretical and Analytical Approaches for Investigating the Relations between Sediment Transport and Channel Shape

Abstract — This study investigated the effect of cross sectional geometry on sediment transport rate. The processes of sediment transport are generally associated to environmental management, such as pollution caused by the forming of suspended sediment in the channel network of a watershed and preserving physical habitats and native vegetations, and engineering applications, such as the influence of sediment transport on hydraulic structures and flood control design. Many equations have been proposed for computing the sediment transport, the influence of many variables on sediment transport has been understood; however, the effect of other variables still requires further research. For open channel flow, sediment transport capacity is recognized to be a function of friction slope, flow velocity, grain size, grain roughness and form roughness, the hydraulic radius of the bed section and the type and quantity of vegetation cover. The effect of cross sectional geometry of the channel on sediment transport is one of the variables that need additional investigation. The width-depth ratio (W/d) is a comparative indicator of the channel shape. The width is the total distance across the channel and the depth is the mean depth of the channel. The mean depth is best calculated as total cross-sectional area divided by the top width. Channels with high W/d ratios tend to be shallow and wide, while channels with low (W/d) ratios tend to be narrow and deep. In this study, the effects of the width-depth ratio on sediment transport was demonstrated theoretically by inserting the shape factor in sediment continuity equation and analytically by utilizing the field data sets for Yalobusha River. It was found by utilizing the two approaches as a width-depth ratio increases the sediment transport decreases.

Contrasting stream stability characteristics in adjacent urban watersheds: Santa Clara Valley, California

AbstractA comparative study of two adjacent stream channels in the Santa Clara Valley region of California provided an opportunity to study the relative effects of multi‐faceted watershed‐urbanization impacts on channel evolution and stability. Berryessa Creek (15.5 km2) and Upper Penitencia Creek (61.3 km2) have similar intrinsic watershed characteristics; however, urbanization processes have imposed distinctly different evolutionary trends in each watershed. The influences of drainage network manipulation, hydrologic routing and engineering infrastructure has resulted in Upper Penitencia Creek remaining relatively stable throughout the course of urbanization, while Berryessa Creek has experienced system‐wide channel instability problems. This study enumerates the many anthropogenic impacts and provides insight into basin alterations that can have either positive or negative feedbacks in maintaining or degrading channel stability throughout the course of urbanization.Results show that infrastructure that disrupts the bed material sediment continuity (such as large drop structures or sedimentation ponds) generate long‐term downstream channel instabilities leading to channel degradation and continued maintenance. Off‐line flow diversions (in this study percolation ponds) that do not disrupt bed material transport can emulate pre‐urbanization conditions offsetting channel degradation resulting from changes in hydrology. This study also demonstrates the degradational responses of a stream due to losses in riparian vegetation from water table lowering transforming a perennial stream into an ephemeral stream resulting in increased bank instability. The importance of maintaining floodplains for flood access and channel stability has also been identified and compared to conditions of channel encroachment to facilitate maintenance, which have further exacerbated downstream channel degradation, long‐term channel maintenance and dredging. Copyright © 2009 John Wiley & Sons, Ltd.

Implications of flow control by the Three Gorges Dam on sediment and channel dynamics of the middle Yangtze (Changjiang) River, China

The impacts of a dam on the river downstream in terms of hydrology and morphology are determined by a complex mix of variables that includes the patterns of release of water through the dam and the characteristics of the downstream channel. Scour of the downstream channel is a common response because large dams cause a significant interruption to sediment continuity. Here we show that in the case of China9s Three Gorges Dam on the Yangtze River the outcome is complicated, as is commonly the case in large rivers. The downstream channel and floodplain system compose an area of long-term sediment accumulation and unstable channels with seasonally contrasting erosion and deposition patterns related to the migrating seasonal monsoon rainfall zones. In achieving one of the main purposes of this dam, that of flood control in the middle and lower basins, the pattern of flows released from the dam will closely resemble those seasonal flows that are responsible for channel instability in the middle catchment, thus effectively making erosive conditions the most common during a year. There is obviously concern about the ultimate impact of sediment storage in the dam on the dynamics of the delta and adjacent coast, and we show that this depends on the trajectory and duration of the erosive responses in the middle Yangtze basin. In this particular case, the outcome is of great significance to the well being of the densely populated riparian areas of the river.

Modeling Shoreline Evolution at Hai Hau Beach, Vietnam

Abstract The coastline of Hai Hau District, located on the northeast coast of Vietnam with about 30 km of shoreline, is chronically eroding. Previous studies have tried to highlight the main causes of the erosion along this coastline, and several hypotheses exist. To examine the hypothesis that gradients in the longshore sediment transport rate and cross-shore fine sediment lost offshore are the main causes generating the serius erosion at Hai Hau Beach, a newly developed numerical model of shoreline change based on the one-line theory was applied and compared with data. Sea dike segments, reinforced by stones and mortar, were modeled using a seawall boundary condition, and the sediment continuity equation was modified to take into account the offshore transport of fine-grained sediment. The simulated shorelines agreed well with the measured shorelines, both for the calibration and validation periods. The calculated sediment budget shows that the net sediment transport is in the southward direction and th...

Exner equation: A continuum approximation of a discrete granular system

In contrast to using a standard control volume approach, general statements of sediment mass balance are derived herein from spatial averaging of the sub‐particle‐scale differential equation of solid mass conservation. The general form of the Exner equation for sediment continuity that is obtained enables analyses in terms of size fractions and also in terms of individual or successive layers, where layer interfaces (e.g., for the bed surface and for bed and suspended loads) are defined on the basis of isosurfaces of sediment concentration (volume fraction) or other sediment properties (e.g., densities or transport rates) within regions of constant concentration. The presented expressions highlight the averaged nature of variables and also the effects of the scales of consideration on definition and interpretation of the macroscopic (mixture‐scale) sediment and layer properties (e.g., averaged densities, volume concentrations or fractions, velocities, transport modes and rates, interfaces, and bed layers). For appropriate simplifications, the general form of the Exner equation is shown to reduce to give more specific conventional expressions, revealing the assumptions implicit in these equations.

A semi-empirical model for clear-water scour evolution at bridge abutments

The computation of temporal variation of clear-water scour is important for the design of bridge foundations. Previous studies implied that a very long flow duration is needed to achieve equilibrium scour at bridge abutments. However, the corresponding durations in the prototype conditions may yield considerably greater values than the time to peak of most of the design floods of small to medium sized catchment basins. Therefore, there is a need to estimate the temporal variation of scour depth. This study deals with development of a semi-empirical model for determining the time-dependent variation of clear-water scour depth at vertical-wall abutments. This approach applies the sediment continuity equation to a scour hole around a vertical-wall abutment. A sediment pickup function was used to formulate the rate of sediment transport from the scour hole. The results of the proposed model were compared with those of empirical models. The model agreed well with the test results.

Measurement of wave-by-wave bed-levels in the swash zone

A technique is described to observe and quantify wave-by-wave bed-level changes in the swash zone. The ultrasonic instrument system is non-contact with the beach face surface being measured and the sensors remain outside of the fluid flows causing sediment movement. Sensor resolution combined with the electronic noise inherent within a digital network data-logging system results in a (conservative) measurement accuracy of ± 1 mm, equating to a couple of sand grain diameters in height. Illustrative field results demonstrate the practical use of the instrumentation, and a simple data pre-processing method to separate swashes and intervening bed-level ‘events’ is discussed. These example data reveal rather complex fluctuations of the bed observed over time periods of minutes to hours. Rather strikingly, gross bed-level changes per wave are revealed to be up to many orders of magnitude larger than the observed net rate of beach face evolution. It is outlined how observations of successive bed-level changes at multiple locations within a dense grid, combined with a consideration of sediment continuity, will now enable the total net sediment transported per uprush–backwash to be quantified.