Bedload transport resistance in rough open‐channel flows

During bedload movement by saltation, streamwise momentum is transferred from the ?ow to the saltating grains. When the grains collide with other grains on the bed or in the ?ow, streamwise momentum is reduced, and there is a decrease in streamwise ?ow velocity and an increase in ?ow resistance, herein termed bedload transport resistance f_bt. Based on experiments in two ?umes with ?xed and mobile plane beds and previously published data, an equation is developed that may be used to predict f_bt for both capacity and non‐capacity ?ows. The variables in this equation are identi?ed by dimensional analysis and the coef?cients are determined by non‐linear regression. This equation applies to rough turbulent open‐channel ?ows, where the relative submergence is between 1 and 20 and the entire sediment load moves by saltation. An investigation of the relative magnitudes of f_bt and grain resistance f_c suggests that where dimensionless shear stress θ is less than 1 and saltation is the dominant mode of bedload transport, f_bt/f_c increases with θ but never exceeds 1. Copyright © 2004 John Wiley & Sons, Ltd.     

Resistance to overland flow due to bed‐load transport on plane mobile beds

During bed‐load transport by overland ?ow, momentum is transferred from the ?ow to the bed via grain collisions, resulting in a decrease in ?ow velocity and an increase in ?ow resistance, herein termed bed‐load transport resistance. In overland ?ow on mobile plane beds, total ?ow resistance f consists of grain resistance f_g and bed‐load transport resistance f_bt. In order to identify and evaluate the relative importance of the factors controlling f_bt, 38 ?ume experiments were performed on slopes of 2·7 and 5·5° using sediment with median diameters of 0·74 and 1·16 mm. All ?ows were supercritical and turbulent. This study is an extension of a recent study by Gao and Abrahams (Earth Surface Processes and Landforms 2004, vol. 29, pp. 423–435). These authors found that f_bt is controlled by three factors: sediment concentration C, dimensionless sediment diameter D_*, and relative submergence h/D, where h is ?ow depth, D is median sediment diameter. However, a new dimensional analysis identi?es two additional factors: Froude number F and slope S. Multiple regression analyses reveal (1) that these ?ve factors together explain 97 per cent of the variance of f_bt, and (2) that S controls f_bt entirely through C. The variable C is therefore redundant, and a new functional equation relating f_bt to D_*, h/D, S and F is developed. This equation may be used to predict f_bt. An advantage of this equation is that it may be used to predict f_bt without measuring bed‐load transport rate. Copyright © 2004 John Wiley & Sons, Ltd.     

Rill flow resistance law under equilibrium bed‐load transport conditions

In this paper, a recently deduced flow resistance equation for open channel flow was tested under equilibrium bed‐load transport conditions in a rill. First, the flow resistance equation was deduced applying dimensional analysis and the incomplete self‐similarity condition for the flow velocity distribution. Then, the following steps were carried out for developing the analysis: (a) a relationship (Equation  13 ) between the Γ function of the velocity profile, the rill slope, and the Froude number was calibrated by the available measurements by Jiang et al.; (b) a relationship (Equation  17 ) between the Γ function, the rill slope, the Shields number, and the Froude number was calibrated by the same measurements; and (c) the Darcy–Weisbach friction factor values measured by Jiang et al. were compared with those calculated by the rill flow resistance equation with Γ estimated by Equations  13 and 17 . This last comparison demonstrated that the rill flow resistance equation, in which slope and Shields number, representative of sediment transport effects, are introduced, is characterized by the lowest values of the estimate errors.     

Influence of bed clusters and size gradation on operational time distribution for non‐uniform bed‐load transport

The operational time distribution (OTD) defines the time for bed‐load sediment spent in motion, which is needed to characterize the random nature of sediment transport. This study explores the influence of bed clusters and size gradation on OTD for non‐uniform bed‐loads. First, both static and mobile bed armouring experiments were conducted in laboratorial flumes to monitor the transport of mixed sand/gravel sediments. Only in the mobile armouring experiment did apparent bed clusters develop, because of stable feeding and a longer transport period. Second, a generalized subordinated advection (GSA) model was applied to quantify the observed dynamics of tracer particles. Results show that for the static armour layer (without sediment feed), the best‐fit OTD assigns more weight to the large displacement of small particles, likely because of the size‐selective entrainment process. The capacity coefficient in the GSA model, which affects the width of the OTD, is space dependent only for small particles whose dynamics can be significantly affected by larger particles and whose distribution is more likely to be space dependent in a mixed sand and gravel system. However, the OTD for the mobile armour layer (with sediment recirculation) exhibited longer tails for larger particles. This is because the trailing edge of larger particles is more resistant to erosion, and their leading front may not be easily trapped by self‐organized bed clusters. The strong interaction between particle–bed may cause the capacity coefficient to be space‐dependent for bed‐load transport along mobile armour layers. Therefore, the combined laboratory experiments and stochastic model analysis show that the OTD may be affected more by particle–bed interactions (such as clusters) than by particle–particle interactions (e.g. hiding and exposing), and that the GSA model can quantify mixed‐size sand/gravel transport along river beds within either static or mobile armour layers. Copyright © 2016 John Wiley & Sons, Ltd.     

Comparison of fractional bed‐material load ­computation methods in sand‐bed channels

This paper presents a comparison of different fractional bed‐material load computation methods in sand‐bed channels. These methods include the direct computation by size fraction approach of Einstein, Laursen and Toffaleti; the bed material fraction (BMF) approach using equations of Engelund and Hansen, Ackers and White, Yang, and Karim's modified BMF method; and the transport capacity fraction (TCF) approach using the transport capacity distribution functions of Karim and Kennedy, Li, and Wu and Molinas. Over 150 sets of flume and field data in the sand size range containing a total of 1007 data points are used to evaluate and compare the accuracy of these methods. Statistical analysis and graphical comparison are utilized to demonstrate the performance and variations in different methods. Overall, the Einstein method underpredicts the transport rate for finer sizes and overpredicts for the coarser sizes, while the other methods overestimate the finer fractions and underestimate the coarser fractions. The Wu and Molinas method, which was developed to account for these deficiencies, is shown to significantly improve fractional bed‐material load computations. The Karim and Kennedy method is also found to be applicable. Copyright © 2000 John Wiley & Sons, Ltd.     

A depth‐averaged two‐phase model for debris flows over erodible beds

Mass exchange between debris flow and the bed plays a vital role in debris flow dynamics. Here a depth‐averaged two‐phase model is proposed for debris flows over erodible beds. Compared to previous depth‐averaged two‐phase models, the present model features a physical step forward by explicitly incorporating the mass exchange between the flow and the bed. A widely used closure model in fluvial hydraulics is employed to estimate the mass exchange between the debris flow and the bed, and an existing relationship for bed entrainment rate is introduced for comparison. Also, two distinct closure models for the bed shear stresses are evaluated. One uses the Coulomb friction law and Manning's equation to determine the solid and fluid resistances respectively, while the other employs an analytically derived formula for the solid phase and the mixing length approach for the fluid phase. A well‐balanced numerical algorithm is applied to solve the governing equations of the model. The present model is first shown to reproduce average sediment concentrations in steady and uniform debris flows over saturated bed as compared to an existing formula underpinned by experimental datasets. Then, it is demonstrated to perform rather well as compared to the full set of USGS large‐scale experimental debris flows over erodible beds, in producing debris flow depth, front location and bed deformation. The effects of initial conditions on debris flow mass and momentum gain are resolved by the present model, which explicitly demonstrates the roles of the wetness, porosity and volume of bed sediments in affecting the flow. By virtue of extended modeling cases, the present model produces debris flow efficiency that, as revealed by existing observations and empirical relations, increases with initial volume, which is enhanced by mass gain from the bed. Copyright © 2017 John Wiley & Sons, Ltd.     

A non‐equilibrium sediment transport model for rill erosion

Sediment transport in rill flows exhibits the characteristics of non‐equilibrium transport, and the sediment transport rate of rill flow gradually recovers along the flow direction by erosion. By employing the concept of partial equilibrium sediment transport from open channel hydraulics, a dynamic model of rill erosion on hillslopes was developed. In the model, a parameter, called the restoration coefficient of sediment transport capacity, was used to express the recovery process of sediment transport rate, which was analysed by dimensional analysis and determined from laboratory experimental data. The values of soil loss simulated by the model were in agreement with observed values. The model results showed that the length and gradient of the hillslope and rainfall intensity had different influences on rill erosion. Copyright © 2006 John Wiley & Sons, Ltd.     

Patterns of grain‐size dependent sediment transport in low‐ordered,ephemeral channels

Sediment data were analyzed to determine grain‐size dependant factors affecting sediment transport in a low‐ordered, ephemeral watershed. Sediment and flow samples were collected during 22 flow events at the outlet of a 4·53 ha sub‐watershed within the Walnut Gulch Experimental Watershed in south‐eastern Arizona. Measured concentrations ranged from 4191 to 115 045 mg l^?1 and included grain sizes up to 8·0 mm in diameter. Two grain‐size dependent transport patterns were observed, that of the finer grain‐size fraction (approximately < 0·25 mm) and that of a coarser grain‐size fraction (approximately ≥ 0·25 mm). The concentration of the fine fraction decreased with flow duration, peaking near the beginning of a flow event and declining thereafter. The concentration of the fine fraction showed slight trends with season and recovery period. The concentration of the coarse fraction displayed a slight negative trend with instantaneous discharge and was not correlated with event duration. These patterns typically produced a condition where the majority of the fine fraction of the sediment yield was evacuated out of the watershed before the hydrograph peak while the majority of the coarser sediment was evacuated during the falling limb of the hydrograph. Each grain‐size dependent transport pattern was likely influenced by the source of the associated sediment. At the flow event time scale, the fines were primarily wash load, supplied from the hillslopes and the coarser grains were entrained from the channel bed. Because transport patterns differ based on grain size, attempts to define the total sediment concentration and sediment yield by the behavior of a single grain‐size fraction may lead to erroneous results, especially when a large range of sediment grain sizes are present. Copyright © 2010 John Wiley & Sons, Ltd.     

Shear velocity estimates in rough‐bed open‐channel flow

Shear velocity u_* is an important parameter in geophysical flows, in particular with respect to sediment transport dynamics. In this study, we investigate the feasibility of applying five standard methods [the logarithmic mean velocity profile, the Reynolds stress profile, the turbulent kinetic energy (TKE) profile, the wall similarity and spectral methods] that were initially developed to estimate shear velocity in smooth bed flow to turbulent flow over a loose bed of coarse gravel (D₅₀ = 1·5 cm) under sub‐threshold conditions. The analysis is based on quasi‐instantaneous three‐dimensional (3D) full depth velocity profiles with high spatial and temporal resolution that were measured with an Acoustic Doppler Velocity Profiler (ADVP) in an open channel. The results of the analysis confirm the importance of detailed velocity profile measurements for the determination of shear velocity in rough‐bed flows. Results from all methods fall into a range of ± 20% variability and no systematic trend between methods was observed. Local and temporal variation in the loose bed roughness may contribute to the variability of the logarithmic profile method results. Estimates obtained from the TKE and Reynolds stress methods reasonably agree. Most results from the wall similarity method are within 10% of those obtained by the TKE and Reynolds stress methods. The spectral method was difficult to use since the spectral energy of the vertical velocity component strongly increased with distance from the bed in the inner layer. This made the choice of the reference level problematic. Mean shear stress for all experiments follows a quadratic relationship with the mean velocity in the flow. The wall similarity method appears to be a promising tool for estimating shear velocity under rough‐bed flow conditions and in field studies where other methods may be difficult to apply. This method allows for the determination of u_* from a single point measurement at one level in the intermediate range (0·3 < h < 0·6). Copyright © 2013 John Wiley & Sons, Ltd.     

2D stream hydrodynamic,sediment transport and bed morphology model for engineering applications

A 2D depth‐averaged hydrodynamic, sediment transport and bed morphology model named STREMR HySeD is presented. The depth‐averaged sediment transport equations are derived from the 3D dilute, multiphase, flow equations and are incorporated into the hydrodynamic model STREMR. The hydrodynamic model includes a two‐equation turbulence model and a correction for the mean flow due to secondary flows. The suspended sediment load can be subdivided into different size classes using the continuum (two‐fluid) approach; however, only one bed sediment size is used herein. The validation of the model is presented by comparing the suspended sediment transport module against experimental measurements and analytical solutions for the case of equilibrium sediment‐laden in a transition from a rigid bed to a porous bed where re‐suspension of sediment is prevented. On the other hand, the bed‐load sediment transport and bed evolution numerical results are compared against bed equilibrium experimental results for the case of a meander bend. A sensitivity analysis based on the correction for secondary flow on the mean flow including the effect of secondary flow on bed shear stresses direction as well as the downward acceleration effect due to gravity on transverse bed slopes is performed and discussed. In general, acceptable agreement is found when comparing the numerical results obtained with STREMR HySeD against experimental measurements and analytical solutions. Copyright © 2007 John Wiley & Sons, Ltd.     

Enhanced bed load sediment transport by unsteady flows in a degrading channel

Laboratory flume experiments were done to investigate bed load sediment transport by both steady and unsteady flows in a degrading channel. The bed, respectively composed of uniform sand, uniform gravel, or sand-gravel mixtures, always undergoes bulk degradation. It is found that both uniform and non-uniform bed load transport is enhanced greatly by unsteady flows as compared to their volume-equivalent steady flows. This enhancement effect is evaluated by means of an enhancement factor, which is shown to be larger with a coarser bed and lower discharges. Also, the fractional transport rates of gravel and sand in non-uniform sand-gravel mixtures are compared with their uniform counterparts under both steady and unsteady flows. The sand is found to be able to greatly promote the transport of gravel, whilst the gravel considerably hinders the transport of sand. Particularly, the promoting and hindering impacts are more pronounced at lower discharges and tend to be weakened by flow unsteadiness.     

Coarse bed load transport in an alluvial gravel bed stream,Dupuyer Creek,Montana

Coarse bed load was sampled in a gravel/cobble bed stream during two major floods in the snowmelt runoff season. The channel is characterized by high rates of bank erosion and, therefore, high rates of sediment supply and bed load flux. Peak discharge reached four times bank‐full, and bed load was sampled at flows 0·7–1·7 times bank‐full. A large aperture bed load sampler (1 m by 0·45 m) captured the largest particles in motion, and specifically targeted the coarse bed load size distribution by using a relatively large mesh (32 mm or D₂₅ of streambed surface size distribution). Bed load flux was highly variable, with a peak value of 0·85 kg/s/m for the coarse fraction above 38 mm. Bed load size distribution and maximum particle size was related to flow strength. Entrainment was size selective for particles D₇₀ and larger (88–155 mm), while particles in the range D₃₀–D₇₀ (35–88 mm) ceased to move at essentially the same flow. Bed load flux was size selective in that coarse fractions of the streambed surface were under‐represented in or absent from the bed load. Painted tracer particles revealed that the streambed surface in the riffles could remain stable even during high rates of bed load transport. These observations suggest that a large proportion of bed load sediments was sourced from outside the riffles. Repeat surveys confirmed major scour and fill in pools (up to 0·75 m), and bank erosion (>2 m), which together contributed large volumes of sediment to the bed load. Copyright © 2007 John Wiley & Sons, Ltd.     

Sediment transport in high‐speed flows over a fixed bed: 1. Particle dynamics

Particle dynamics are investigated experimentally in supercritical high‐speed open channel flow over a fixed planar bed of low relative roughness height simulating flows in high‐gradient non‐alluvial mountain streams and hydraulic structures. Non‐dimensional equations were developed for transport mode, particle velocity, hop length and hop height accounting for a wide range of literature data encompassing sub‐ and supercritical flow conditions as well as planar and alluvial bed configurations. Particles were dominantly transported in saltation and particle trajectories on planar beds were rather flat and long compared with alluvial bed data due to (1) increased lift forces by spinning motion, (2) strongly downward directed secondary currents, and (3) a planar flume bed where variation in particle reflection and damping effects were minor. The analysis of particle saltation trajectories revealed that the rising and falling limbs were almost symmetrical contradicting alluvial bed data. Furthermore, no or negligible effect of particle size and shape on particle dynamics were found. Implications of experimental findings for mechanistic saltation‐abrasion models are briefly discussed. Copyright © 2017 John Wiley & Sons, Ltd.     

The effect of turbulent flow structures on saltation sand transport in the atmospheric boundary layer

The effect of turbulent flow structures on saltation sand transport was studied during two convective storms in Niger, West Africa. Continuous, synchronous measurements of saltation fluxes and turbulent velocity fluctuations were made with a sampling frequency of 1 Hz. The shear stress production was determined from the vertical and streamwise velocity fluctuations. The greatest stress-bearing events were classified as turbulent structures, with sweep, ejection, inward interaction, and outward interaction described according to the quadrant technique. The classified turbulent structures accounted for 63·5 per cent of the average shear stress during the first storm, and 56·0 per cent during the second storm. The percentage of active time was only 20·6 per cent and 15·8 per cent, respectively. High saltation fluxes were associated with sweeps and outward interactions. These two structures contribute positively (sweeps) and negatively (outward interactions) to the shear stress, but have in common that the streamwise velocity component is higher than average. Therefore, the horizontal drag force seems primarily responsible for saltation sand transport, and not the shear stress. This was also reflected by the low correlation coefficients (r) between shear stress and saltation flux (0·12 and 0·14, respectively), while the correlation coefficients between the streamwise velocity component and saltation flux were much higher (0·65 and 0·57, respectively). © 1998 John Wiley & Sons, Ltd.     

Implications of climate change in the twenty‐first century for simulated magnitude and frequency of bed‐material transport in tributaries of the Saint‐Lawrence River

More frequent extreme flood events are likely to occur in many areas in the twenty‐first century due to climate change. The impacts of these changes on sediment transport are examined at the event scale using a 1D morphodynamic model (SEDROUT4‐M) for three tributaries of the Saint‐Lawrence River (Québec, Canada) using daily discharge series generated with a hydrological model (HSAMI) from three global climate models (GCMs). For all tributaries, larger flood events occur in all future scenarios, leading to increases in bed‐material transport rates, number of transport events and number of days in the year where sediment transport occurs. The effective and half‐load discharges increase under all GCM simulations. Differences in flood timing within the tributaries, with a shift of peak annual discharge from the spring towards the winter, compared to the hydrograph of the Saint‐Lawrence River, generate higher sediment transport rates because of increased water surface slope and stream power. Previous research had shown that channel erosion is expected under all GCMs' discharge scenarios. This study shows that, despite lower bed elevations, flood risk is likely to increase as a result of higher flood magnitude, even with falling base level in the Saint‐Lawrence River. Copyright © 2010 John Wiley & Sons, Ltd.     

Transport of suspended sediment under the dam‐break flow on an inclined plane bed of arbitrary slope

The problem of transport of suspended sediment after the break of a dam on an inclined bed is considered. To that end we use the shallow‐water approximation for arbitrary, constant slopes of the bottom, taking into consideration the effect of friction. The numerical technique and the frictional model are validated by comparison with available experimental data and asymptotic analytical solutions, with special attention to the numerical solution near the wetting front. The transport of suspended sediment down the inclined bed is obtained and discussed as a function of the slope of the bed for different values of the parameters characterizing the sediment and its transport properties. For sufficiently large times we always find the formation of roll waves near the water front, which affects the transport of sediments significantly. These strong oscillations are accurately computed with the numerical method used. The relative importance of the bed load (to the suspended load) sediment transport is also discussed as a function of the size of the sediment particles and the slope of the bed for different models on the initiation of sediment suspension from bed load. We also check the dilute sediment approach and characterize the conditions for its failure. Finally, the results of the present simplified model are intended to be used as tests of more complex numerical models. Copyright © 2007 John Wiley & Sons, Ltd.     

Annual bed‐elevation regime in the alluvial channel of Squamish River,Southwestern British Columbia,Canada

The aim of this study is to examine the annual regime of channel scour and fill by monitoring bed‐elevation changes in a reach of Squamish River in southwestern British Columbia, Canada. Sonar surveys of 13 river cross‐sections in a sandy gravel‐bed single‐channel study reach were repeated biweekly over a full hydrologic year (1995/6). The survey results show that bedload movement occurs as waves or pulses forming bedwaves that appear to maintain an overall coherence with movement downstream. These bedwaves propagate downstream by a mode here termed pulse scour and pulse fill, a process distinguished from the conventional mode of scour and fill commonly associated with flood events (here termed local scour and local fill). Bedwave celerity was estimated to be about 15·5 m d⁻¹ corresponding to a bedwave residence time in the study reach of almost one hydrologic year. The total amount of local bed‐elevation change ranged between 0·22 m and 2·41 m during the period of study. Analysis of the bed‐elevation and flow data reveals that, because of the bedwave phenomenon, there is no simple relation between the mean bed‐elevation and discharge nor any strong linear correlation among cross‐sectional behaviour. The bed‐elevation data also suggest that complex changes to the bed within a cross‐section are masked when the bed is viewed in one dimension, although no definitive trends in bed behaviour were found in the two‐dimensional analysis. Although a weak seasonal effect is evident in this study, the bed‐elevation regime is dominated by sediment supply‐driven fluctuations in bedload transport occurring at timescales shorter than the seasonal fluctuation in discharge. The study also indicates that bed‐elevation monitoring on Squamish River, and others like it, for purposes of detecting and measuring aggradation/degradation must take into account very considerable and normal channel‐bed variability operating at timescales from hours to months. Copyright © 2000 John Wiley & Sons, Ltd.     

Suspended load in flows on erodible bed

Steady state suspended-load of sediment transported in flow over erodible beds usually is treated by the advection-diffusion approach, though in recent years, it is being treated as a two-phase flow phenomenon incorporating kinetics of sediment particles. Among the advection-diffusion approaches, Rouse＇s equation is the well-known, although a number of researchers in later periods have attempted to improve it by modifying the mixing length concept taking into account other aspects. In this paper, the advection-diffusion approach and associated logarithmic law of flow velocity are revisited. It is concluded from the logarithmic law that the Reynolds shear stress is a linear function of height above the bed, which reduces to bed shear stress in the case of a long horizontal channel. As a consequence, it is shown that the volumetric concentration of sediment is best approximated by the sum of two power laws of height above the bed. An equation is derived for the suspended-load transport rate in terms of elementary functions.     

Predicting sediment transport by interrill overland flow on rough surfaces

Modelling soil erosion requires an equation for predicting the sediment transport capacity by interrill overland flow on rough surfaces. The conventional practice of partitioning total shear stress into grain and form shear stress and predicting transport capacity using grain shear stress lacks rigour and is prone to underestimation. This study therefore explores the possibility that inasmuch as surface roughness affects flow hydraulic variables which, in turn, determine transport capacity, there may be one or more hydraulic variables which capture the effect of surface roughness on transport capacity suffciently well for good predictions of transport capacity to be achieved from data on these variables alone. To investigate this possibility, regression analyses were performed on data from 1506 flume experiments in which discharge, slope, water temperature, rainfall intensity, and roughness size, shape and concentration were varied. The analyses reveal that 89·8 per cent of the variance in transport capacity can be accounted for by excess flow power and flow depth. Including roughness size and concentration in the regression improves that explained variance by only 3·5 per cent. Evidently, flow depth, when used in combination with excess flow power, largely captures the effect of surface roughness on transport capacity. This finding promises to simplify greatly the task of developing a general sediment equation for interrill overland flow on rough surfaces. Copyright © 1998 John Wiley & Sons, Ltd.