The variability of critical shear stress, friction angle, and grain protrusion in water-worked sediments

The erodibility of a grain on a rough bed is controlled by, among other factors, its relative projection above the mean bed, its exposure relative to upstream grains, and its friction angle. Here we report direct measurements of friction angles, grain projection and exposure, and small-scale topographic structure on a variety of water-worked mixed-grain sediment surfaces. Using a simple analytical model of the force balance on individual grains, we calculate the distribution of critical shear stress for idealized spherical grains on the measured bed topography. The friction angle, projection, and exposure of single grain sizes vary widely from point to point within a given bed surface; the variability within a single surface often exceeds the difference between the mean values of disparate surfaces. As a result, the critical shear stress for a given grain size on a sediment surface is characterized by a probability distribution, rather than a single value. On a given bed, the crtitical shear stress distributions of different grain sizes have similar lower bounds, but above their lower tails they diverge rapidly, with smaller grains having substantially higher median critical shear stresses. Large numbers of fines, trapp.ed within pockets on the bed or shielded by upstream grains, are effectively lost to the flow. Our calculations suggest that critical shear stress, as conventionally measured, is defined by the most erodible grains, entrained during transient shear stress excursions associated with the turbulent flow; this implies a physical basis for the indeterminacy of initial motion. These observations suggest that transport rate/shear stress relationships may be controlled, in part, by the increasing numbers of grains that become available for entrainment as mean shear stress increases. They also suggest that bed textures and grain size distributions may be controlled, within the constraints of an imposed shear stress and sediment supply regime, by the influence of each size fraction on the erodibility of other grain sizes present on the bed.     

The motion of sediment-water mixtures during intense bedload transport: computer simulations

A new model, which couples fluid and particle dynamics, has been developed to study the motion of the sediment-water mixture during intense bedload transport, including the velocity profiles of both sediment and water, the roughness length of an upper plane bed and the thickness of moving sediment layers. Standard mixing length theory is used to model the motion of water above the boundary between the overlying water and the sediment-water mixture. The turbulent flow within the moving sediment layers is described by a shear stress model, in which the effective viscosity of the flowing water is proportional to the velocity difference between the fluid and the sediment. The particle dynamics method, in which the equations of motion of each of many particles are solved directly, is applied to model the movement of sediment particles. The particle-fluid interaction is expressed by a velocity-squared fluid drag force exerted on each sediment particle. Both computer simulation results and theoretical analysis have shown that the velocities of both sediment and fluid during intense sediment transport decrease exponentially with depth in the top layers of a fast-moving sediment—water mixture. The thickness of the moving sediment layers, obtained from the computer simulation results, is proportional to the shear stress, which agrees with previous experimental observations.     

Threshold for particle entrainment into suspension

ABSTRACT Laboratory observations regarding the limit conditions for particle entrainment into suspension are presented. A high‐speed video system was used to investigate conditions for the entrainment of sediment particles and glass beads lying over a smooth boundary as well as over a rough bed. The results extend experimental conditions of previous studies towards finer particle sizes. A criterion for the limit of entrainment into suspension is proposed which is a function of the ratio between the flow shear velocity and particle settling velocity. Observations indicate that particles totally immersed within the viscous sublayer can be entrained into suspension by the flow, which contradicts the conclusions of previous researchers. A theoretical analysis of the entrainment process within the viscous sublayer, based on force–balance considerations, is used to show that this phenomenon is related to turbulent flow events of high instantaneous values of the Reynolds stress, in agreement with previous observations. In the case of experiments with a rough bed, a hiding effect was observed, which tends to preclude the entrainment of particles finer than the roughness elements. This implies that, as the ratio between particle and roughness element sizes becomes smaller, progressively higher bed shear stresses are required to entrain particles into suspension. On the other hand, an overexposure effect was also observed, which indicates that a particle moving on a smooth bed is more prone to be entrained than the same particle moving on a bed formed by identical particles.     

An experimental study of flow, bedload transport and bed topography under conditions of erosion and deposition and comparison with theoretical models

The nature of flow, sediment transport and bed texture and topography was studied in a laboratory flume using a mixed size-density sediment under equilibrium and non-equilibrium (aggradational, degradational) conditions and compared with theoretical models. During each experiment, water depth, bed and water surface elevation, flow velocity, bed shear stress, bedload transport and bed state were continuously monitored. Equilibrium, uniform flow was established with a discharge of about 0.05 m³ s^?1, a flow depth of about 0.01 m, a flow velocity of about 0.81–0.88 m s^?1, a spatially averaged bed shear stress of about 1.7–2.2 Pa and a sediment transport rate of about 0.005–0.013 kg m^?1 s^?1 (i.e. close to the threshold of sediment transport). Such equilibrium flow conditions were established prior to and at the end of each aggradation or degradation experiment. Pebble clusters, bedload sheets and low-lying bars were ubiquitous in the experiments. Heavy minerals were relatively immobile and occurred locally in high concentrations on the bed surface as lag deposits. Aggradation was induced by (1) increasing the downstream flow depth (flume tilting) and (2) sediment overloading. Tilt-induced aggradation resulted in rapid deposition in the downstream half of the flume of a cross-stratified deposit with downstream dipping pebbles (pseudo-imbricated). and caused a slight decrease in the equilibrium mean water surface slope and total bedload transport rate. These differences between pre- and post-aggradation equilibrium flow conditions are due to a decrease in the local grain roughness of the bed. Sediment overloading produced a downstream fining and thinning wedge of sediment with upstream dipping pebbles (imbricated), whereas the equilibrium flow and sediment transport conditions remained relatively unchanged. Degradation was induced by (1) decreasing the downstream flow depth (flume tilting) and (2) cutting off the sediment feed. Tilt-induced degradation produced rapid downstream erosion and upstream deposition due to flow convergence with little change to the equilibrium flow and sediment transport conditions. The cessation of sediment feed produced degradation and armour development, a reduction in the mean water surface slope and flow velocity, an increase in flow depth, and an exponential decrease in bedload transport rate as erosion proceeded. A bedload transport model predicted total and fractional transport rates extremely well when the coarse-grained (or bedform trough) areas of the bed are used to define the sediment available to be transported. A sediment routing model, MIDAS, also reproduced the equilibrium and non-equilibrium flow conditions, total and fractional bedload transport rates and changes in bed topography and texture very well.     

Fine particle deposition to initially starved,stationary, planar beds

Reported here are results from new flume experiments examining deposition and entrainment of inert, silt‐sized particles (with spherical diameters in the range from 20 to 60 μm) to and from planar, impermeable and initially starved beds underlying channel flows. Bed surfaces comprised smooth or fixed sand‐size granular roughness and provided hydraulically smooth to transitionally rough boundaries. Results of these experiments were analysed with a simple model that describes the evolution of vertically averaged concentration of suspended sediment and accommodates the simultaneous delivery to and entrainment of grains from the bed. The rate of particle arrival to a bed diminishes linearly, and the rate of particle entrainment increases by the 5/2 power, as the value of the dimensionless Saffman parameter S = u_*³/g’ν approaches a threshold value of order unity, where u is the conventional friction velocity of the turbulent channel flow, g’ is the acceleration due to gravity adjusted for the submerged buoyancy of individual particles and ν is the kinematic viscosity of the transporting fluid. This transport behaviour is consistent with the notion that non‐cohesive, silt‐sized particles can neither reach nor remain on an impermeable bed under flow conditions where mean lift imposed on stationary particles in the viscous sublayer equals or exceeds the submerged weight of individual particles. Within the size range of particles used in these experiments, particle size and the characteristic size of granular roughness, up to that of medium sand, did not affect rates of dimensionless arrival or entrainment to a significant degree. Instead, a new but consistent picture of fine‐particle transport is emerging. Silt‐sized material, at least, is subject to potentially significant interaction with the bed during intermittent suspension transport at intermediate flow speeds greater than the value required for initiation of transport (ca 20 cm sec^?1) but less than the value (ca 50 cm sec^?1) required by the Saffman criterion ensuring transport in fully passive suspension or, equivalently, ‘wash‐load’.     

输沙能力模式在坡面非恒定输沙过程中的应用

在坡面土壤侵蚀输沙计算中,可选用的输沙能力模式较多,但这些模式多运用于恒定输沙,在非恒定输沙中运用不多。建立了坡面土壤侵蚀非恒定输沙数学模型,模型中的输沙能力运用水流切应力、水流功率、单位水流功率3种模式,对模型过程采用有限差分格式离散求解。根据实测水沙资料进行模型参数率定,运用3种输沙能力模式于不同降雨强度、不同坡度的非恒定坡面输沙过程中。结果表明:在坡面非恒定输沙计算中,不同输沙能力模式对计算结果有明显影响,在降雨强度较小时,单位水流功率模式结果较其他两个模式为好,而在雨强较大时,切应力模式计算结果较好。     

Sensitivity of incipient particle motion to fluid flow penetration depth within a packed bed

A discrete element method is applied to a three‐dimensional analysis related to sediment entrainment on a micro‐scale. Sediment entrainment is the process by which a fluid medium accelerates particles from rest and advects them upward until they are either transported as bedload or suspended by the flow. Modelling of the entrainment process is a critically important aspect for studies of erosion, pollutant resuspension and transport, and formation of bedforms in environmental flows. Previous discrete element method studies of sediment entrainment have assumed the flow within the particle bed to be negligible and have only allowed for the motion of the topmost particles. At the same time, micro‐scale experimental studies indicate that there is a small slip of the fluid flow at the top of the bed, indicating the presence of non‐vanishing fluid velocity within the topmost bed layers. The current study demonstrates that the onset of particle incipient motion, which immediately precedes particle entrainment, is highly sensitive to this small fluid flow within the topmost bed layers. Using an exponential decay profile for the inner‐bed fluid flow, the discrete element method calculations are repeated with different fluid penetration depths within the bed for several small particle Reynolds numbers. For cases with slip velocity corresponding to that observed in previous experiments with natural sediment, the predicted particle velocity is found to be a few percent of the fluid velocity at the top of the viscous wall layer, which is a reasonable range of velocities for observation of incipient particle motion. This method for prescribing the fluid flow within the particle bed allows for the current discrete element method to be extended in future studies to the analysis of sediment entrainment under the influence of events such as turbulent bursting. Additionally, predictions for the slip velocities and fluid flow profile within the bed suggest the need for further experimental studies to provide the data necessary for additional improvement of the discrete element method models.     

细颗粒对粗颗粒床沙质输沙率影响的初步研究

考虑高含沙紊流涡团中细颗粒絮凝形成网络结构对粗颗粒运动影响后,建立了粗颗粒悬移质泥沙的输沙率计算方法.该方法中包含的细颗粒影响项反映了流域因素对粗颗粒泥沙输沙的影响,证明细颗粒的影响是引起多沙河流中“多来多排”现象的一个重要因素.与黄河实测资料的对比表明,该计算方法能够反映高含沙紊流输沙时随流域细颗粒增多粗颗粒悬移质输沙率相对增大的现象,并具有较好的计算精度     

Flow and sediment dynamics in a low sinuosity, braided river: Calamus River, Nebraska Sandhills

The interaction between channel geometry, flow, sediment transport and deposition associated with a midstream island was studied in a braided to meandering reach of the Calamus River, Nebraska Sandhills. Hydraulic and sediment transport measurements were made over a large discharge range using equipment operated from catwalk bridges. The relatively low sinuosity channel on the right-hand side of the island carries over 70% of the water discharge at high flow stages and 50–60% at low flow stages. As a result, mean velocity, depth, bed shear stress and sediment transport rate tend to be greater here than in the more strongly curved left-hand channel. The loci of maximum flow velocity, depth and bed shear stress are near the centre of the channel upstream of the island, but then split and move towards the outer banks of both channels downstream. Variations in these loci depend on the flow stage. Topographically induced across-stream flows are generally stronger than the weak, curvature-induced secondary circulations. Water surface topography is controlled mainly by centrifugal accelerations and local changes in downstream flow velocity. The averaged water surface slope of the study reach varies very little with discharge, having values between 0·00075 and 0·00090. As bed shear stress generally varies in a similar way to mean velocity, friction coefficients vary little, normally being in the range 0·07–0·13. These values are similar to those in straight channels with sandy dune-covered beds. Bedload is moved mainly as dunes at all flow stages. Grain size is mainly medium sand with coarse sand moved in thalwegs adjacent to the cut banks, and with fine sand at the downstream end of the island. These patterns of flow velocity, depth, water surface topography, bed shear stress, bedload transport rate and mean grain size can be accurately predicted using theoretical models of flow, bed topography and sediment transport rate in single river bends, applied separately to the left and right channels. During high flow stages deposition occurs persistently near the downstream end of the island, and cut banks are eroded. Otherwise, erosion and deposition occurs only locally within the channel as discharge varies. Abandonment and filling of a strongly curved channel segment may occur by migration of an upstream bar into the channel entrance at a high flow stage.     

波流边界层水沙运动数值模拟——II.泥沙运动模拟

为解析波流边界层内泥沙运动,建立了基于水动力-泥沙-床面互馈过程的波流边界层1DV泥沙数学模型,可用于模拟不同床面形态下粉沙-沙的含沙量过程。床面形态模块提供床面形态类型和相应参数;给出了平底和沙波床面粗糙高度和泥沙扩散系数的确定方法;采用了适宜粉沙及沙的制约沉速、底部参考浓度和起动剪切应力等公式;引入含沙量层化效应和制约沉降反映水动力与泥沙之间的相互影响。水槽试验资料验证表明,建立的模型较好地模拟了不同床面不同波流组合条件下的含沙量剖面。在此基础上,讨论了不同床面含沙量剖面模拟方法的差异,指出床面形态是决定含沙量变化的重要因素之一,仅通过改变床面粗糙高度不足以反映漩涡沙波床面的含沙量剖面特征。该模型可为研究波流边界层内泥沙运动和物质输运提供工具。     

Rates of aerodynamic entrainment in a developing boundary layer

Despite its significance for inception of grain transport by wind, the initial dislodgement of grains from a static surface by aerodynamic forces of drag and lift in the absence of grain collision has received little attention. This paper describes a series of wind-tunnel experiments in which the erosion of narrow strips of loose grains from the roughened surface of a flat plate exposed to a range of wind speeds was examined. The progressive downwind development of the boundary layer over the plate provided a range of airflow conditions which permitted systematic evaluation of grain entrainment rates arising from purely aerodynamic forces. Use of closely graded size fractions in flat, single grain layers resting on identical, fixed grain support eliminated the effects of surface irregularities and impacts from saltation. Results show that erosion of strips of loose grains develops with time according to an inverse exponential function in which the entrainment rate time constant relates to Shields dimensionless shear stress function. An empirical expression defining aerodynamic entrainment rate in terms of rate of strip erosion is derived and comparisons are made between present and published data. The need for additional data to resolve several questions raised by the present investigation is stressed. In addition, a simple, objective technique for accurate determination of the aerodynamic entrainment threshold of any loose, granular sediment is proposed.     

Initial motion and pivoting characteristics of sand particles in uniform and heterogeneous beds: experiments and modelling

Experiments are described in which the threshold conditions for sediment entrainment are measured for uniform and mixed sand beds beneath both steady and combined steady/oscillatory flows. Derived critical shear stresses are compared with the mixed bed entrainment model of Wiberg & Smith (1987). As predicted by the model, coarser grains within a sand mixture are entrained at lower bed shear stresses than progressively finer grains. Entrainment occurs generally at lower shear stresses than predicted by the model, especially under unidirectional flows. This may be the result of grains resting in unusually unstable positions during the experiments because the beds are ‘unworked’ at the start of the experiments. The model of Wiberg and Smith predicts threshold conditions more accurately for the mixed beds if the bed pivoting angle is correctly defined. The pivoting angles of the beds used here are measured using a new technique designed specifically for comparison with the threshold data. The measured angles repeat the finding that the coarse grains are more mobile than the finer fractions of a mixture. The results are poorly described by the pivoting angle model presented by Wiberg & Smith (1987) and are better represented by a model of the form Φ = αD^γ(D_i/D₅₀)^β (after 21 ), where α, γ and β are empirical constants. The threshold model is found to be more effective using the improved pivoting relationship. The entrainment of grains is found to be easier beneath unidirectional flows than combined flows, in accordance with previous authors’ findings. A suggestion that this result is caused by a change in the erosion mechanism beneath wave flows is made. Wave boundary layers may act as an extended laminar sublayer over bed grains and reduce the erosive efficiency of the overlying current flow. The results of the experiment have implications for the natural sorting mechanisms of sediment beds being deposited in near-threshold flows.     

Kaolinite deposition from moving suspensions: The roles of flocculation,salinity, suspended sediment concentration and flow velocity/bed shear

Understanding how mud moves and deposits is essential for conceptualizing the dynamic nature of surface environments and their ancient counterparts. Experimental study has largely been pursued by civil engineers, using kaolinite as an active ingredient. Yet, applying their data to the physical comprehension of mudstone sedimentology is hampered by multiple flume configurations between labs, and data sets tailored to specific engineering needs. The need for a better grasp of underlying processes is acute, given recent flume studies that show that moving suspensions form large bedload floccules, migrating floccule ripples and bed accretion under currents capable of moving sand grains. To advance mudstone sedimentology, integrated study of suspended sediment concentration, salinity and bed shear stress on the deposition of floccules is crucial. Described here is a set of tightly controlled experiments that explored suspended sediment concentrations from 70 to 900 mg/l, freshwater, brackish and marine salinities, flow velocities in the 5 to 50 cm/s range (equivalent to 0.01 to 0.58 Pa bed shear), measured the size of in-flow and bedload floccules, and the critical velocity of sedimentation that marks the onset of sustained bedload accumulation. The critical velocity of sedimentation of kaolinite clays is in the 26 to 28 cm/s flow velocity range (0.22 to 0.25 Pa), appears insensitive to a wide range of suspended sediment concentrations and salinities, and coincides with the formation of sand-size bedload floccules. Further decrease of flow velocity/bed shear stress is accompanied by a steady increase in the size of bedload floccules. Large bedload floccules appear to form in the high-shear basal part of the flow, a phenomenon requiring further investigation. Better understanding of the mechanisms that facilitate mud deposition from moving suspensions is critical for more realistic assessments of the depositional conditions of mud and mudstones, as well as for refining predictive models for the flux of fine-grained sediments across the Earth's surface.     

Bed forms in bimodal sand–gravel sediments: laboratory and field analysis

Bed forms were studied in Goodwin Creek and a laboratory flume channel. The bed sediment of the field site and flume had median diameters of 8·3 (modes of 0·4, 22·6 mm) and 1·82 mm (modes of 0·5, 5·6 mm), respectively. The laboratory and field channels had similar values of bimodal parameters, ratios of flow depth to median bed material diameter, and ratios of shear stress to critical shear stress and were judged to be comparable in the transport of bed load sediment and the resulting bed forms. Three groupings of bed forms from the laboratory flume experiments (ripple-like bed forms, bed load sheets, low-relief bed waves) were identified using the height and period of the bed forms. For the range of flow depths and discharges investigated in the flume, bed forms became higher and longer with increasing bed shear stress. Bed forms from Goodwin Creek were similar to those from the flume with comparable ratios between bed form length, height, and flow depth. The bed forms in the flume provide a positive link between rate and size fluctuations measured in the field and the bed forms. The smaller bed forms identified were sediment starved and are not considered to be dunes, while the largest bed forms in which all of the bed material sizes were mobilized in the field and laboratory were judged to be dunes.     

Migration and growth of aeolian bedforms

A two-dimensional analytical model is developed for the morphodynamics of aeolian dunes. The basis of the model is the sediment continuity equation, which is solved using a linearized sediment transport formula. The air flow over the topography is calculated with a steady-state boundary-layer model. This results in a series of analytical expressions for the shear stress, sediment transport, topography through time, and growth and migration of a sine-shaped dune. These expressions give quantitative relationships between bedform behavior (i.e., growth and migration) and factors such as wind velocity and surface roughness. In this way it can be seen that growth and migration rates increase for higher wind velocity, higher surface roughness and higher wave numbers (i.e., shorter wave lengths).     

Boundary skin friction and sediment transport about an animal-tube mimic

ABSTRACT
A flume study was made of fluid flow, boundary skin friction, and sediment transport about an animal-tube mimic. The effect of a tube on momentum transfer depends most strongly on its height. A tube increases the net boundary skin friction locally and tends to promote sediment entrainment near its base. Flow in this region appears to be governed by the same similarity laws that apply to cylinders with much larger body Reynolds number. Particles travelling as suspended load may be deposited immediately downstream of the tube. The net sedimentological effect of any tube (i.e. deposition or scour) will depend both on its height and on the boundary shear stress imposed by the external flow. The near-wake region of a tube is dominated by a strong cross-stream exchange of momentum. Wake perturbations decay downstream seemingly in accordance with similarity laws which also govern mounted, two-dimensional structures.     

The decrease in shear stress and increase in transport rates subsequent to an increase in sand supply to a gravel-bed channel

It is generally accepted that a gravel-bed river will aggrade if the supply of sediment to the river is increased. In a series of flume experiments using constant discharge and gravel feed rate, sand feed rates were increased to 6.1 times that of gravel. The slope of the bed decreased with increasing sand supply, indicating that the increased sediment load could be transported at the same rate due to a decrease in shear stresses. These results extend previous experiments to a wider range of boundary conditions. A recent surface transport model is used to predict the changes in bed composition and transport using the same sediment supply composition and feed rates as in the laboratory experiments. This model reasonably predicts a decrease in the reference shear stresses of the sand and gravel fractions as the sand supply is increased. An increase in sand supply can increase the mobility of gravel fractions in the stream bed, which can lead to bed degradation and preferential evacuation of these sediments from the river.     

Development of deflation lag surfaces

A series of wind tunnel tests were carried out to investigate the development of deflation lags in relation to the non-erodible roughness element concentration. Glass spheres (18 mm in diameter) were placed along the complete length of the wind tunnel working section in regular staggered arrays using three different spacings (d=18, 30 and 60 mm) and completely covered with a 0.27-mm erodible sand. A pre-selected free stream velocity above threshold (8m s^?1) was established above the surface and the sediment transport measured at 2-s intervals using a wedge-shaped trap in which an electronic balance is incorporated. Throughout each test, the emerging lag surface was periodically photographed from above at two locations upwind of the trap. The photographs were electronically scanned and analysed to calculate the lag element coverage and location, as well as mean height and frontal area for each time period. Test results indicate that lag development has a profound effect on both the sediment flux and wind profile characteristics. Initially, there is an increase in sediment flux above that for a rippled sand bed because of increased erosion around and reduced kinetic energy loss in highly elastic collisions with the emerging roughness elements. With further emergence, a dynamic threshold is reached whereupon the sediment flux decreases rapidly, tending towards zero. At this point, the supply of grains to the air stream through fluid drag follows a reduction in aerodynamic roughness and, therefore, surface shearing stress. At least as important is the lesser potential for grain ejection at impact because of reduced momentum imparted from the air stream during saltation. Although recent shear stress partitioning models indicate when particle movement may commence on varying surfaces, our experimental results demonstrate that this partitioning has a further direct bearing upon the saltation flux ratio.