A prediction method for the size distribution of saltating particles above a mixed-size bed

In aeolian saltation, the sand bed is a mixture of sand particle with a wide range of particle sizes. Generally, the particle size distribution (PSD) of saltating particles is ignored by previous aeolian transport models, which will result in differences between predictions and observations. To better understand the saltation process, a prediction method of the PSD of saltating particles was proposed in this article. The probability of contact between incident sand and bed sand was introduced into the particle-bed collision process. An artificial PSD of the incident saltating particles was set as the initial condition. A stochastic particle-bed collision model considering contact probability was then used in each iteration step to calculate a new PSD of saltating particles. Finally, the PSD of saltating particles can be determined when aeolian saltation reaches a steady state (saltation is in a steady state when its primary characteristics, such as horizontal mass flux and the concentration of saltating particles, remain approximately constant over time and distance). Meanwhile, according to the experimental results, a calculation formula for the contact parameter n is given, which characterizes the shielding effect of particles on each other. That is, if soil PSD and friction velocity were given, the PSD of saltating particles can be determined. Our results do not depend on the initial conditions, and the predicted results are consistent with the experimental results. It indicated that our method can be used to determine the PSD of saltating particles. © 2020 John Wiley & Sons, Ltd.     

On the mechanisms of the saltating motion of bedload

Saltation of sediment particles is an important pattern of bedload transport.Based on force analysis for sediment particles,a Lagrangian model was proposed for the saltating motion of bedload in river flows,which was then solved with numerical method.Simulation results on the saltating trajectories neglecting particle rotation and turbulence effects compare fairly well with experimental observations.The mean values of the saltation parameters (saltation height,length and velocity) also agree well with the previous experimental data.Based on the numerical results,regression equations for the dimensionless saltation height,length and velocity were presented.Using the numerically achieved characteristics of the sediment saltation,we also obtained mathematical expression for the sediment transport rate.The studies in this paper are significant for its contribution to mechanism of the bedload motion and the computation of sediment transport rate.     

Particle velocity and concentration profiles in bedload experiments on a steep slope

Depth profiles of particle streamwise velocity, concentration and bedload sediment transport rate were measured in a turbulent and supercritical water flow. One‐size 6 mm diameter spherical glass beads were transported at equilibrium in a two‐dimensional 10% steep channel with a mobile bed. Flows were filmed from the side by a high‐speed camera. Particle tracking algorithms made it possible to determine the position, velocity and trajectory of a very large number of particles. Approximately half of the sediment transport rate was composed by rolling grains, and the other half by saltation. This revealed a complex structure, with several concentration and flux peaks due to rolling, and one peak due to saltation. With an increase of the sediment transport rate, the depth structure remained the same at the water/granular interface, with peak value increases but with no shift in elevations. The saltation region expanded towards higher elevations with an increase of the particle velocity commensurate to the water velocity. The proportion of the sediment transport rate in saltation did not vary significantly. The particle streamwise velocity profiles exhibited three segments: an exponential decay in the bed, a linear increase where rolling and saltation co‐existed, and above this, a logarithmic‐like shape due to saltating particles. These results are comparable to profiles measured and modelled in dry granular free surface flows and in more intense bedload such as sheet flows. Copyright © 2014 John Wiley & Sons, Ltd.     

Modeling the effect of saltation on surface layer turbulence

Particle–turbulence interaction has been a research focus in the field of pneumatic transport, especially in aeolian environments. However, knowledge regarding the effect of saltating particles on the turbulence characteristics is very limited. In this article, a process of sand-laden flow from forming sand streamers to stability is investigated via a coupled mathematical model of wind-blown sand that includes the spatiotemporal development. The variations in the turbulence characteristics, such as the mean velocity and turbulence intensity in clean air or sand-laden flow field, are analyzed. The results show that the splash process of sand grains near the wall decrease the wind speed in the saltation layer and destroy the low-speed streaks. Moreover, the profiles of streamwise turbulence intensity exhibit a transition from ‘decreasing’ to ‘increasing’ and approximately intersect at an ‘intensity focus’, which is presented for the first time. Furthermore, it was found that saltating particles could enhance the Reynolds stress. Meanwhile, it was also noticed that the shear stress at the wall surface is greater than the impact threshold and that there is a tendency towards the impact threshold. Therefore, saltation makes the particle Reynolds number of sand-laden flow higher than that under non-saltation conditions, thus changing the particles’ effect on the turbulence intensity. Gravity-dominated saltation is probably the most essential difference between wind-blown sand and other traditional two-phase flows. © 2020 John Wiley & Sons, Ltd.     

Vertical dispersion of dust particles in a turbulent boundary layer

The flow of glass dust particles in air was investigated experimentally over a flat bed in a wind tunnel. Particle concentrations were measured by light scattering diffusion (LSD) and digital image processing. It was verified that saltation is the main mechanism for ejection of dust particles. Vertical mean dust concentrations for ‘pure dust’ and two mixtures of dust and saltating glass particles were determined and analysed. The experiments confirmed that for the ‘pure dust’ configuration the mean concentration decreases as a power function with height. For the mixture configurations and for free stream velocities close to the threshold velocity, the mean concentration also decreases in a power function. For higher velocities, mean concentration decreases respectively as a power function or exponential function for large and small ratios of the dust:saltating particles respectively. The exponent of the power law reflects the dust:particle ratio and the free stream flow velocity. Copyright © 2007 John Wiley & Sons, Ltd.     

Effect of saltating sediment on flow resistance and bed roughness in overland flow

The acceleration of saltating grains by overland flow causes momentum to be transferred from the flow to the grains, thereby increasing flow resistance and bed roughness. To assess the impact of saltating sediment on overland flow hydraulics, velocity profiles in transitional and turbulent flows on a fixed sand-covered bed were measured using hot-film anemometry. Five discharges were studied. At each discharge, three flows were measured: one free of sediment, one with a relatively low sediment load, and one with a relatively high sediment load. In these flows from 83 to 90 per cent of the sediment was travelling by saltation. As a result, in the sediment-laden flows the near-bed velocities were smaller and the velocity profiles steeper than those in the equivalent sediment-free flows. Sediment loads ranged up to 87·0 per cent of transport capacity and accounted for as much as 20·8 per cent of flow resistance (measured by the friction factor) and 89·7 per cent of bed roughness (measured by the ratio of the roughness length to median grain diameter). It is concluded that saltating sediment has a considerable impact on overland flow hydraulics, at least on fixed granular beds. Saltation is likely to have a relatively smaller effect on overland flow on natural hillslopes and agricultural fields where form and wave resistance dominate. Still, saltation is generally of greater significance in overland flow than in river flow, and for this reason its effect on overland flow hydraulics is deserving of further study. © 1998 John Wiley & Sons, Ltd.     

3D Lagrangian modelling of saltating particles diffusion in turbulent water flow

A 3D Lagrangian model of the saltation of solid spherical particles on the bed of an open channel flow, accounting for turbulence-induced mechanisms, is proposed and employed as the key tool of the study. The differences between conventional 2D models and a proposed 3D saltation model are discussed and the advantages of the 3D model are highlighted. Particularly, the 3D model includes a special procedure allowing generation of 3D flow velocity fields. This procedure is based on the assumption that the spectra of streamwise, vertical and transverse velocity components are known at any distance from the bed. The 3D model was used to identify and quantify effects of turbulence on particle entrainment and saltation. The analysis of particle trajectories focused on their diffusive nature, clarifying: (i) the effect of particle mobility parameter; (ii) the effect of bed topography; and (iii) the effect of turbulence. Specifically, the results of numerical simulations describing the abovementioned effects on the change in time of the variance are presented. In addition, the change in time of the skewness and kurtosis, which are likely to reflect the turbulence influence on the spread of particles, are also shown. Two different diffusion regimes (local and intermediate) for each of the investigated flow conditions are confidently identified.     

Bed load transport under different streambed conditions-a field experimental study in a mountain stream

Bed load transport in mountain streams is closely linked to streambed structures.Strambed structures are arrangements of boulders and cobbles deposited during extreme floods,in a stable configuration exhibiting high dissipation of flow.Field experiments were carried out in a mountain stream in Yunnan,southwestern China,studying bed load movement on three typical streambeds,i.e.,with well developed,partially developed,and no structures.An underwater observation and video-capturing system was designed to observe and measure the movement of bed load particles.The initiation mode, trajectory,velocity,and acceleration of bed load particles under the three conditions were observed and analyzed.Results showed that the bed load movement was highly associated with streambed condition.With well-developed structures,bed load particles moved intermittently through saltation and the bed load transport rate was very low.For partially-developed structures most bed load particles moved through saltation but a portion of sediment moved in sliding and rolling.In the case with no streambed structure(plane bed) contact load motion(sliding and rolling) gradually became dominant.Moreover,laminated load motion occurred and became the main component of bed load transport when the flow discharge and incoming sediment load were very high.Laminated load motion was a special form of bed load motion with an extremely high intensity.Bed load transport and streambed structure both acted to dissipate flow energy and were mutually constraining.High rates of bed load transport occurred in the streams with no or poor bed structures,and low bed load transport was associated with well developed structures.The bed load transport rate was inversely correlated to the degree of streambed development.     

‘Bedload’ dynamics: Grain impacts,momentum transfer and derivation of a grain froude number

A test is proposed for Bagnold's postulate that the normal weight stress due to moving ‘bedload’ is balanced by a solid transmitted stress due to the rate of change of momentum produced by grain impacts on unit area of the stationary bed. The test involves derivation of an expression for normal momentum transfer due to saltating grains at moderate transport stages when grain-to-grain collisions and partial suspension during saltation may be ignored. A dimensionless number, Φ, (a grain Froude Number) is derived, given by ū²/g where ū is the mean grain forward velocity, g is the gravitational acceleration and L? is the length of a single saltation ‘jump’. Equilibrium demands that Φ be unity during bedload transport involving saltating grains if Bagnold's postulate is correct. Experimental data shows Φ < 1, the discrepancy between theory and experiment being due to the existence of lift forces acting upon bedload grains. Bagnold's postulate is correct for concentrated dispersions of grains, as in grain flows, when fluid lift forces may be neglected due to high particle concentration.     

Evaluation of the saltation process of bed materials by video imaging under altered bed roughness

The purpose of this paper is to examine the nature of particle saltation and movement over the beds of fixed roughness from flume experiments. A series of experiments are carried out to study the saltation of individual sand particles of different sizes over rough beds under different flow conditions. A 3‐D acoustic Doppler velocimeter is used to record the fluid velocity components; subsequently, under different flow conditions, the images of released sand particles are recorded using high‐speed video imaging technique. Systematic analysis is made with regard to the forces acting on the grains and the variation of their magnitudes along the saltation trajectories of the grains. Relations between the saltation parameters, flow intensity and bed roughness are developed. The distributions of the angle of orientations during a single saltation follows almost a Gaussian distribution. The shape of the Gaussian distribution depends on the particle size and bed roughness. Particle collisions with rough beds and the resulting coefficients of restitution are also discussed. A theoretical framework is developed to compute the mean particle velocity considering the spin in the energy balance equation. Results of the detailed analysis using the imaging technique are much better than in previously reported studies. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

3D numerical simulation of particle-particle collisions in saltation mode near stream beds

The importance of particle-particle collisions in sediment saltation in the bed-load layer is analyzed herein by means of numerical simulation. The particle saltation theoretical/numerical model follows a Lagrangian approach, and addresses the motion of sediment particles in an open channel flow described by a logarithmic velocity profile. The model is validated with experimental data obtained from the literature. In order to evaluate the importance of the phenomenon, simulations with and without particle-particle collisions were carried out. Results for two different sediment concentrations are presented, namely 0.13% and 2.33%. For each concentration of particles, three different flow intensities were considered, and trajectories of two different particle sizes, within the sand range were computed. Changes in particle rotation, particle velocity, and angle of trajectory before and after particle-particle collisions appear to be relatively important at lower shear stresses, whereas they decrease in significance with increasing flow intensities. Analyses of the evolution in time of the second order moment of particle location suggest that inter-particle collisions introduce transverse diffusion in saltating particles in the span-wise direction.     

What is suspended sediment?

Suspended sediment is conventionally regarded as that sediment transported by a fluid that it is fine enough for turbulent eddies to outweigh settling of the particles through the fluid. Early work in the fluvial field attributed suspension to turbulence, and led to the notion of a critical threshold for maintaining sediment in suspension. However, research on both turbulence structures and the interactions between suspended sediment and bedforms in rivers has shown a more complex story and, although there appear to have been no studies of the impact of bedforms on aeolian suspended sediment concentrations, turbulent flow structures and transport rates of saltating particles have been shown to be affected. This research indicates that suspended sediment neither travels with the same velocity as the flow in which it is suspended, nor is it likely to remain in suspension in perpetuity, even under conditions of steady flow or in unsteady flow the where dimensionless critical threshold is permanently exceeded. Rather, like bedload, it travels in a series of hops, and is repeatedly deposited on the bed where it remains until it is re‐entrained. Is there, therefore, a qualitative difference between suspended and saltating sediment, or is it just a quantitative difference in the size of the jump length and the frequency of re‐entrainment? It is our contention that the distinction of suspension as a separate class of sediment transport is both arbitrary and an unhelpful anthropocentric artefact. If we recognize that sediment transport is a continuum and applies to any fluid medium rather than split into different “processes” based on arbitrary thresholds and fluids, then recognizing the continuity will enable development of an holistic approach sediment transport, and thus sediment‐transport models that are likely to be viable across a wider range of conditions than hitherto. Copyright © 2015 John Wiley & Sons, Ltd.     

Aeolian sediment flux decay: Non-linear behaviour on developing deflation lag surfaces

Wind tunnel simulations of the effect of non-erodible roughness elements on sediment transport show that the flux ratio q/q_s, shear velocity U*, and roughness density λ are co-dependent variables. Initially, the sediment flux is enhanced by kinetic energy retention in relatively elastic collisions that occur at the roughness element surfaces, but at the same time, the rising surface coverage of the immobile elements reduces the probability of grain ejection. A zone of strong shearing stress develops within 0·03 to 0·04 m of the rough bed because of a relative straightening of velocity profiles which are normally convex with saltation drag. This positive influence on fluid entrainment is opposed by declining shear stress partitioned to the sand bed. Similarly, because the free stream velocity U_f is fixed while U_* increases, velocity at height z and particle momentum gain from the airstream decline, leading eventually to lower numbers of particles ejected on average at each impact. When the ratio of the element basal area to frontal area σ is approximately equal to 3·5, secondary flow effects appear to become significant, so that the dimensionless aerodynamic roughness parameter Z₀/h and shear stress on the exposed sand bed T_s decrease. It is at this point that grain supply to the airstream and saltation drag appear to be significantly reduced, thereby intensifying the reduction in U_*. The zone of strong fluid shear near the bed dissipates.     

An analysis of the characteristics of rough bed turbulent shear stresses in an open channel

Entrainment of sediment particles from channel beds into the channel flow is influenced by the characteristics of the flow turbulence which produces stochastic shear stress fluctuations at the bed. Recent studies of the structure of turbulent flow has recognized the importance of bursting processes as important mechanisms for the transfer of momentum into the laminar boundary layer. Of these processes, the sweep event has been recognized as the most important bursting event for entrainment of sediment particles as it imposes forces in the direction of the flow resulting in movement of particles by rolling, sliding and occasionally saltating. Similarly, the ejection event has been recognized as important for sediment transport since these events maintain the sediment particles in suspension. In this study, the characteristics of bursting processes and, in particular, the sweep event were investigated in a flume with a rough bed. The instantaneous velocity fluctuations of the flow were measured in two-dimensions using a small electromagnetic velocity meter and the turbulent shear stresses were determined from these velocity fluctuations. It was found that the shear stress applied to the sediment particles on the bed resulting from sweep events depends on the magnitude of the turbulent shear stress and its probability distribution. A statistical analysis of the experimental data was undertaken and it was found necessary to apply a Box-Cox transformation to transform the data into a normally distributed sample. This enabled determination of the mean shear stress, angle of action and standard error of estimate for sweep and ejection events. These instantaneous shear stresses were found to be greater than the mean flow shear stress and for the sweep event to be approximately 40 percent greater near the channel bed. Results from this analysis suggest that the critical shear stress determined from Shield's diagram is not sufficient to predict the initiation of motion due to its use of the temporal mean shear stress. It is suggested that initiation of particle motion, but not continuous motion, can occur earlier than suggested by Shield's diagram due to the higher shear stresses imposed on the particles by the stochastic shear stresses resulting from turbulence within the flow.     

A framework for predicting abrasion rupture of crusts in wind erosion

Crusts play a crucial role in the reduction or control of wind erosion. In this regard, the resilience and durability of crusts are of prime importance. Crusts have high resilience and durability against wind flow shear stresses; however, they are prone to abrasion induced by saltating particles. Therefore, estimating crust durability in abrasion rupture has practical importance. In this study, a cyanocrust and a biocemented sand crust were subjected to a controlled flux of saltating particles for different sandblasting periods to provide a framework for predicting crust rupture. The velocity and pre- and post-collision energy of the saltating particles were measured using high-speed photography. The changes in the strength of the crusts after different periods of sandblasting were determined using a scratch test. The results suggested that the average strength of the cyanocrust and biocemented sand crust became 0.25 and 0.7 of their corresponding initial values after 30 min of sandblasting. Also, the average stiffness of the cyanocrust and biocemented sand crust decreased to 0.5 and 0.9 of their initial values, respectively. Furthermore, the amount of impact energy absorbed by the crusts increased by the deterioration of the crusts. Compiling the results of the wind tunnel experiment and scratch tests yielded an exponential equation which can be used to estimate crust durability in a given condition of saltation. Based on this equation, the cyanocrust and biocemented sand crust will break down entirely after 23 and 449 min, respectively, at a wind velocity of 6.8 m/s and a saltation flux of 1 g/s/m.     

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.     

One-dimensional morphodynamic model for retrogressive erosion based on a sediment entrainment theory at high flow velocity

Retrogressive erosion is a high-speed erosion process that usually occurs during the rapid release of stored water in reservoirs built on sandy rivers.Retrogressive erosion has been utilized in the practice of reservoir sedimentation control,but accurate prediction of the bed deformation process by numerical models has rarely been reported.The current study presents a one-dimensional morphodynamic model for simulating the evolution process of retrogressive erosion induced by high-velocity flows on steep slopes.The governing equations apply a Cartesian coordinate system with a vertically oriented z axis.The bed surface gradient and friction terms in the flow equations include correction factors to take account of the effects of high slope on flow movement.The net vertical sediment flux term in the sediment transport and bed deformation equations is calculated using an equation of erosion velocity.Particularly,this equation is based on an empirical relation between the sediment entrainment rate and the Shields parameter in contrast to the traditional sediment transport capacity,and the critical Shields parameter is modified by taking into account the permeability of the sediment layer and the stability of particles on a slope.The feedback of scoured sediment on the flow movement is considered by additional terms in the governing equations.Flume experiments of retrogressive erosion in literature were simulated to validate the model.The temporal variations of the longitudinal profiles of the free surface and channel bed and the sediment transport rate were well predicted.The algorithm calculating sediment entrainment in the proposed model also was validated for an experiment measuring entrainment rate from the literature.More importantly,it was found that the morphodynamic model using the sediment transport capacity equation predicts the trend of cumulative erosion contrary to the measurements,while results of the proposed model can follow a similar trend with the observed data in the retrogressive erosion process.     

On the numerical analysis of bed-load transport of saltating grains

The focus of this paper is on the analysis of the influence of particles’ velocity distribution and their concentration on the sediment transport rate in bed-load from the Lagrangian perspective.Such aims are addressed by use of the relevant Lagrangian model of spherical saltating particles in which turbulence plays a significant role.The Monte Carlo approach is employed in the simulations to obtain the velocity and concentration of the saltating particles.Numerical simulations using two saltating particle models:(1) with;and(2) without particle-particle collisions are carried out.Based on the numerical results,we address the hypothesis that instead of averaged characteristics,the distributions of particles’ velocity and sediment concentration should be taken into account in the calculation of sediment transport rate.Moreover,our results also show that the interaction between particles during their collisions is the key for better understanding of the physics of sediment transport.All results are compared with well-known experimental formulae i.e.Meyer-Peter and Muller and Fernandez Luque and van Beek.     

Controls on the aerodynamic roughness length and the grain‐size dependence of aeolian sediment transport

Estimates of the wind shear stress exerted on Earth's surface using the fully rough form of the law‐of‐the‐wall are a function of the aerodynamic roughness length, z₀. Accurate prediction of aeolian sediment transport rates, therefore, often requires accurate estimates of z₀. The value of z₀ is determined by the surface roughness and the saltation intensity, both of which can be highly dynamic. Here we report field measurements of z₀ values derived from velocity profiles measured over an evolving topography (i.e. sand ripples). The topography was measured by terrestrial laser scanning and the saltation intensity was measured using a disdrometer. By measuring the topographic evolution and saltation intensity simultaneously and using available formulae to estimate the topographic contribution to z₀, we isolated the contribution of saltation intensity to z₀ and document that this component dominates over the topographic component for all but the lowest shear velocities. Our measurements indicate that the increase in z₀ during periods of saltation is approximately one to two orders of magnitude greater than the increase attributed to microtopography (i.e. evolving sand ripples). Our results also reveal differences in transport as a function of grain size. Each grain‐size fraction exhibited a different dependence on shear velocity, with the saltation intensity of fine particles (diameters ranging from 0.125 to 0.25 mm) saturating and eventually decreasing at high shear velocities, which we interpret to be the result of a limitation in the supply of fine particles from the bed at high shear velocities due to bed armoring. Our findings improve knowledge of the controls on the aerodynamic roughness length and the grain‐size dependence of aeolian sediment transport. The results should contribute to the development of improved sediment transport and dust emission models. © 2018 John Wiley & Sons, Ltd.