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.     

Bedform development and its effect on bed stabilization and sediment transport based on a flume experiment with non-uniform sediment

Non-uniform sediment deposited in a confined, steep mountain channel can alter the bed surface composition. This study evaluates the contribution of geometric and resistance parameters to bed sta-bilization and the reduction in sediment transport. Flume experiments were done under various hydraulic conditions with non-uniform bed material and no sediment supply from upstream. Results indicate that flume channels respond in a sequence of coarsening and with the formation of bedform-roughness features such as rapids, cascades, and steps. A bedform development coefficient is introduced and is shown to increase (i.e. vertical sinuosity develops) in response to increasing shear stress during the organization process. The bedform development coefficient also is positively correlated with the critical Shields number and Manning's roughness coefficient, suggesting the evolution of flow resistance with increasing bedform development. The sediment transport rate decreases with increasing bed shear stress and bedform development, further illustrating the effect of bed stabilization. An empirical sedi-ment transport model for an equilibrium condition is proposed that uses the bedform development coefficient, relative particle submergence (i.e. the ratio of mean water depth and maximum sediment diameter), modified bed slope, and discharge. The model suggests bedform development can play a primary role in reducing sediment transport (increasing bed stabilization). The model is an extension of Lane's (1955) relation specifically adapted for mountain streams. These results explain the significance of bedform development in heightening flow resistance, stabilizing the bed, and reducing sediment transport in coarse, steep channels.     

Graded and uniform bed load sediment transport in a degrading channel

Twenty runs of experiments are carried out to investigate non-equilibrium transport of graded and uniform bed load sediment in a degrading channel. Well-sorted gravel and sand are employed to compose four kinds of sediment beds with different gravel/sand contents, i.e., uniform 100%gravel bed, uniform 100% sand bed, and two graded sediment beds respectively with 53% gravel and 47% sand as well as 22%gravel and 78%sand. For different sediment beds, the experiments are conducted under the same discharges, thereby allowing for the role of sediment composition in dictating the bed load transport rate to be identified. A new observed dataset is generated concerning the flow, sediment transport and evolution of bed elevation and composition, which can be exploited to underpin devel-opments of mathematical river models. The data shows that in a degrading channel, the sand greatly promotes the transport of gravel, whilst the gravel considerably hinders the transport of sand. The promoting and hindering effects are evaluated by means of impact factors defined based on sediment transport rates. The impact factors are shown to vary with flow discharge by orders of magnitude, being most pronounced at the lowest discharge. It is characterized that variations in sand or gravel inputs as a result of human activities and climate change may lead to severe morphological changes in degrading channels.     

Measurements of coupled fluid and sediment motion over mobile sand dunes in a laboratory flume

The relationship between turbulent fluid motions and sediment particle motions over mobile sand dunes was investigated by using a laser Doppler velocimeter and an acoustic backscatter system in laboratory experiments performed at the USDA-ARS-National Sedimentation Laboratory. Profiles of acoustic backscatter from particles and at-a-point turbulence data were collected while translating both measurement devices downstream at the speed of mobile dune bedforms. The resulting data set was used to examine the frequency （recurrence frequency） at which the fluctuating backscatter and fluid velocity signals exceeded magnitude thresholds based on the standard deviation （σ） of the local velocity and the magnitude the acoustic signal resulting from backscatter from suspended particles. The slope of the downstream and vertical velocity recurrence frequencies generally indicated a gradually increasing recurrence time with increasing elevation. The recurrence frequency for acoustic backscatter data was not strongly variable with elevation. The closest correspondence between the recurrence frequencies of sediment backscatter and vertical velocities at the 1σ magnitude threshold was in a region defined by X/L〈0.4 and y〈6 cm. The downstream velocity was most closely related to backscatter in a small region at 0.4〈X/L〈0.8 and less than 3-4 cm from the bed.     

Evaluation of a gravel transport sensor for bed load measurements in natural flows

A recent acoustic instrument （Gravel Transport Sensor, GTS） was tested for predicting sediment transport rate （bed load rate） in gravel bed streams. The GTS operation is based on the particle collision theory of submerged obstacles in fluids. When particles collide with the GTS cylinder their momentum is recorded in the form of ping rates. The GTS is attractive for further consideration here because of its potential to provide continuous unattended local bed load measurements, especially in areas found in streams that access may be difficult under extreme conditions. Laboratory experiments coupled with numerical simulations for the same flow conditions were performed in order to determine the conditions under which particles of different size will hit the GTS cylinder and be able to register a ping rate. The GTS was able to detect the number of particles with diameter in the range of 15.9 to 25.4 mm, with reasonable accuracy, if the applied Shields effective stress τ＊e = τ＊ - τ＊cr was in the range of 0.006 to 0.015. A drawback of the tested prototype GTS, however, was that it exerted increased resistance on the incoming particles. The added drag effects increased the overall resistance that was exerted by the flow on particles and thus increased the likelihood that particles will rest in the ambient region of the cylinder instead of hitting it. Numerical simulation of the flow around the GTS cylinder revealed that changing the prototype geometry from cylindrical to ellipsoid or rhomboid will increase the likelihood of the particles hitting the instrument under the same flow conditions failed by the original tested GTS cylinder.     

Effect of incoming sediment on the transport rate of bed load in mountain streams

Field experiments were conducted on bed load transport in the Diaoga River, a mountain stream in southwest China, to study the variation of bed load transport with varying sediment supply. The rate of bed load transport is greatly affected by incoming sediment （load and size）. Under the same flow conditions, bed load transport rates may differ by three orders of magnitude depending on whether measurements were taken before or after the first flood of the year. The relation of the ＂bed load transport rate versus flow intensity＂ appears to have similar characteristics as a clockwise looped-rating curve. Experiments also were conducted during the non-flood season to study bed load transport processes with different incoming load from an upstream section. Bed load with different sizes can be grouped into two types： traveling bed load and structural bed load. Traveling bed load is composed of sediment finer than a critical size, De, and its transport rate depends mainly on the incoming sediment rate. The incoming sediment rate can alter the rate of bed load transport by three orders of magnitude. Structural bed load is composed of coarser sediment and its transport rate closely relies on the flow intensity.     

Detecting significant sediment motion in a laboratory flume using digital video image analysis

A video analysis method for monitoring sediment transport and sorting processes in a laboratory flume is presented. Video taken through the glass side‐wall of a laboratory flume is captured using a digital CCD (charge‐coupled device) camera and significant movements between individual frames are detected using image analysis. This method involves direct subtraction of the brightness numbers of pixels in sequential video frames, followed by thresholding to produce binarized images of significant change, above the inherent level of system noise. Experimental results showing dilation of a gravel framework and rapid infiltration of fines just prior to entrainment are discussed. Copyright © 2000 John Wiley & Sons, Ltd.     

Formation of stationary alternate bars in a steep channel with mixed-size sediment: A flume experiment

Alternate bars were formed by sediment transport in a flume with Froude-modelled flow and relative roughness characteristic of gravel-boulder channels with steep slopes. The flume (0.3 m wide × 7.5 m long) was filled with a sand-gravel mixture, which was also fed into the top of the flume at a constant rate under constant discharge. Channel slope was set at 0.03. Initially, coarse particles accumulated on incipient bar heads near one side of the flume and diverted flow and bedload transport across the flume toward a pool scoured against the opposite flume wall downstream. Sorting in the pool directed coarse particles onto the next bar head downstream. Alternate sequences of pools and coarse bar heads were thereby linked down the entire flume by interactions of sediment sorting, flow, and channel morphology. During episodes of bar construction, unsorted bedload invaded interior bar surfaces and was deposited. Persistent deposition of coarse particles on bar heads prevented downstream migration of bars by inhibiting bar-head erosion and bedload transport over bars. Likely factors leading to bar-head stabilization in modelled gravel-bed channels are coarse mixed-size sediment, steep channel gradients, and shallow depths.     

Developing a Lagrangian sediment transport model for open channel flows

A three-dimensional stochastic Lagrangian particle tracking sediment transport model is developed to solve the discrete advection-dispersion equation using a combination of empirical dispersion equations.The performance of three widely-used longitudinal dispersion coefficient equations was examined to select one of them as the primary dispersion equation term in the developed model. Also, a conditional empirical equation was used to consider the effect of vertical dispersion term in top layers n...     

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.     

Bedload transport and sediment yield in the Onyx River,Antarctica

Bedload transport measurements were made in a braided reach of the Onyx River, Wright Valley, Antarctica, during summer 1984/85. Transport was predominantly of sand in the form of dunes, which moved in a band down the centre of the channels, the perimeters of which were composed of a gravel pavement created during short duration high flows in earlier years. Transport rates at-a-point and past-a-cross-section were highly variable in space and time, even under conditions of constant discharge, and it was inferred that many factors other than hydraulic conditions—particularly sediment supply—control transport rates. An empirical power function relationship between sediment discharge and water discharge was used to predict an average annual total sediment discharge of 3400 t y^?1 past the study reach. This gives a specific sediment yield of 5.9 t km^?2 · y^?1, which is two orders of magnitude less than values for Arctic and Alpine proglacial rivers, and confirms earlier conclusions that sedimentation rates on Antarctic sandur are much lower than in the arctic.     

Fine sediment carrying capacity of combined wave and current flows

The so-called fine sediment in many coastal areas and estuaries in China is mostly referred to the mixture of cohesive sediment and non-cohesive sediment. To predict the mixed type time sediment transport, sediment carrying capacity formulae combined with the 2-D suspended sediment transport equation and morphologic equation have been widely used in China. In the present study, the sediment carrying capacity formula suggested by Dou et al. （1995） for wave conditions has been improved and implemented for the prediction of sediment transport in nearshore regions where wave activities are significant. The improvement is based on the wave energy dissipation principle inside and outside the surf zone. In the improved formula, sediment in suspension increases with the magnitude of the wave period and this feature complies with general observations. More than 300 laboratory and field measured data sets have been reviewed and 12 of them have been used to verify and determine the major coefficients in the improved formula. The application of the sediment carrying capacity model in combined wave and current situations shows that the model can faithfully reproduce the cross-shore sediment concentration distributions at the southwest coast of Bohai Bay.     

Multigene genetic programming for sediment transport modeling in sewers for conditions of non-deposition with a bed deposit

It is known that construction of large sewers based on consideration of flow with non-deposition without a bed deposit is not economical. Sewer design based on consideration of flow with non-deposition with a bed deposit reduces channel bed slope and construction cost in which the presence of a small depth of sediment deposition on the bed increases the sediment transport capacity of the flow. This paper suggests a new Pareto-optimal model developed by the multigene genetic programming (MGGP) technique to estimate particle Froude number (Fr_p) in large sewers with conditions of sediment deposition on the bed. To this end, four data sets including wide ranges of sediment size and concentration, deposit thickness, and pipe size are used. On the basis of different statistical performance indices, the efficiency of the proposed Pareto-optimal MGGP model is compared to those of the best MGGP model developed in the current study as well as the conventional regression models available in the literature. The results indicate the higher efficiency of the MGGP-based models for Fr_p estimation in the case of no additional deposition onto a bed with a sediment deposit. Inasmuch as the Pareto-optimal MGGP model utilizes a lower number of input parameters to yield comparatively higher performance than the conventional regression models, it can be used as a parsimonious model for self-cleansing design of large sewers in practice.     

Influence of the biomass content in sediment on the sediment nutrient flux for a pulsed organic load

A laboratory study was carried out to investigate the influence of the biomass content in the sediment on the rate of diagenesis of particulate organic materials (POM) and the consequent sediment oxygen demand (SOD) and nutrient fluxes. Fish food pellets were loaded into the sediment to simulate a sudden POM input. Three types of sediments with different biomass contents were tested, including a raw marine sediment, the marine sediment after one month of cultivation and an artificial sediment of sand and clay without any biomass. There was little difference in organic flux from the three different sediments. However, compared to the artificial sediment, the marine sediments had much higher SOD and ammonia flux. A mathematical model also has been developed for the SOD dynamics and nutrient fluxes. Both the experimental and simulation results indicate the important role of the biomass in the sediment in POM diagenesis, SOD and nutrient fluxes.     

Developing a sediment budget for a small drainage basin in Australia

A sediment budget was developed for the 1.7 km² Maluna Creek drainage basin located in the Hunter Valley, New South Wales, Australia, for the period 1971-86. the impact of viticulture, which commenced at Maluna in 1971, was studied using erosion plots, with caesium-137 as an indicator of both soil erosion and sedimentation. Two methods were used to estimate vineyard soil losses from caesium-137 measurements. Sediment output from the catchment was measured for three years, and extrapolated from readings taken at a nearby long-term stream flow gauging station for the remaining 13 years. Relative amounts of soil loss from forest (60 per cent basin area), grazing land (30 per cent) and vineyards (10 per cent) were calculated. Soil losses by rain splash detachment were ten times greater from bare/cultivated sufaces than from the forest. Erosion plots of area 2 m² showed no significant differences in soil loss between forest and grassland but, under bare soil, losses were 100 times greater. the ¹³⁷Cs method was employed to calculate net soil loss from all vineyard blocks using both a previously established calibration curve and a proportional model. the latter method gave estimates of soil loss which were 3-9 times greater than by the calibration curve, and indicated that average soil losses from the vineyard were equivalent to 62 t ha^?1 y^?1 (1971-86). It was estimated that the forest contributed 1-8 per cent, the grazing land 1.6 per cent, and the vineyard 96.6 per cent of the total soil loss during that period. Sediment storages within the fluvial system adjacent to the vineyard ws 9460 t for the period, whereas sediment output was equivalent to 215 t km^?1 y^?1. Independent measurements of soil erosion, storage, and output showed that 56 per cent of the eroded sediment remained in the catchment, and 34 per cent was transported out by Maluna Creek. the budget was able to be balanced to within 10 per cent.     

Effect of bed load supply on sediment transport in mountain streams

Mountain streams with their tributary torrents build the upper part of the fluvial network. They are important regarding the transfer of sediment from headwaters to lower basins. Channels are typically steep with wide grain size distributions, ranging from fine sand up to large boulders, and a stabilized bed surface. Mountain streams often are supply-limited with respect to mobile bed load, which needs to be addressed when bed load transport equations are applied to such streams. To better understand supply limitation, laboratory experiments highlighting the effect of bed load supply on incipient motion and bed load transport rate are discussed. Experimental tests were done in which fine bed load was supplied to a previously armored channel bed, with flow conditions ranging from one-third to twice the critical dis-charge for the bed surface. At flows not exceeding the critical discharge, the time series of the bed load transport rate at the downstream model boundary featured consistent patterns which are attributed to distinct phases: (i) a temporal lag, (ii) an equilibrium state, and (iii) a post-supply phase. Bed load transport occurred even at flows distinctly below that for incipient motion of the bed surface. But, with the mass of total bed load outflow approaching the supply amount, the mass did not exclusively consist of supplied grains. The coarser the supplied bed load, the more sediment was mobilized from the bed surface. At higher flows, processes differed. Total bed load outflow exceeded the supply amount and the break-up of the armor layer caused a refining of the bed surface.     

Bed load transport during rising and falling stages on two small streams

Bed load transport rates were measured with continuously recording pit samplers on two small gravel-bed streams in the Goodwin Creek Research Watershed, northern Mississippi, U.S.A. When transport samples were grouped according to whether the stage was rising or falling, significant differences in mean bed load transport rates were found at nearly all flow strengths. At higher flow strengths, mean bed load transport rates were greater during rising stages than during falling stages. The greater transport rates measured during rising stages may be caused by a lag in the formation and destruction of bed roughness elements. One of the streams also showed evidence for greater transport rates for low flows as the stage declined. This may be caused by differences in the stability of the bed material at the beginning and at the end of a transport event.     

The LHLLC scheme for Two-Layer and Two-Phase transcritical flows over a mobile bed with avalanching,wetting and drying

A numerical method of the Godunov type is presented for solving either Two-Phase or Two-Layer forms of Debris Flow Models (DFMs) describing shallow-water flow and sediment dynamics. DFMs explicitly link sediment concentrations to the momentum balance, and thus can be applied to cases involving high sediment concentrations, as in debris flows, in addition to low concentration test cases typically found in surface waters. In this paper, Two-Phase and Two-Layer DFMs are presented in a common mathematical framework to illuminate key similarities and differences and lay a foundation for a general purpose DFM solver. The proposed solver termed LHLLC is shown to achieve good accuracy over a wide range of test cases. Importantly, numerical diffusion of sediment profiles is minimized, particularly on steep slopes, the scheme is shown to preserve stationary solutions involving wet/dry interfaces, and the scheme accounts for gravity-driven slumping (avalanching) which cannot be resolved by classical DFMs.     

ADV measurements of velocity distributions in a gravel‐bed flume

Velocity measurements carried out by an acoustic doppler velocimeter (ADV) in a rectangular laboratory ?ume having a gravel bed are presented. The velocity pro?les are measured in six verticals of the channel cross‐section having an increasing distance (from 4 to 38·5 cm) from the ?ume wall. The experimental runs are carried out for ?ve different bed arrangements, characterized by different concentrations of coarser elements, and for the two conditions of small‐ and large‐scale roughness. For both hydraulic conditions, the velocity measurements are ?rst used to test the applicability of the Dean pro?le and of the logarithmic pro?le corrected by a divergence function proposed in this paper. Then, for each value of the depth sediment ratio h/d₈₄, the non‐dimensional friction factor parameter is calculated by integration of the measured velocity distributions in the different verticals of the cross‐section. Finally a semi‐logarithmic ?ow resistance equation is empirically deduced. Copyright © 2003 John Wiley & Sons, Ltd.