Rolling and Lifting Probabilities for Sediment Entrainment

This study addresses the rolling and lifting probabilities for sediment entrainment by incorporating the probabilistic features of the turbulent fluctuation and bed grain geometry. The lognormally distributed instantaneous velocity and uniformly distributed initial grain position, along with a relation between lift coefficient and particle Reynolds number, are used to extend the theoretical formulation of the entrainment probabilities in smooth-bed flows. The two threshold conditions identified herein enable us to precisely define the probabilities of entrainment in the rolling and lifting modes. The results obtained in this study coincide well with the published data. The lifting probability increases monotonously with the dimensionless shear stress θ, which is consistent with the earlier results yet displays improved agreement with the experimental data. The maximum value of rolling probability, with a magnitude of 0.25, occurs at θ ≈ 0.15. For θ<0.05 (or θ>0.6), the rolling (or lifting) probability makes up more than 90% of the total entrainment probability and thus can be used as an approximation to the total probability of entrainment. The proposed rolling and lifting probabilities are further linked to the two separate criteria for incipient motion to explore the critical entrainment probabilities. The results reveal that a consistent probability corresponding to the critical state of sediment entrainment cannot be found.     

Near-Bed Turbulence Characteristics at the Entrainment Threshold of Sediment Beds

This experimental study is devoted to quantification of the near-bed turbulence characteristics at an entrainment threshold of noncohesive sediments. Near the bed, the departure in the distributions of the observed time-averaged streamwise velocity from the logarithmic law is more for immobile beds than for entrainment-threshold beds. In the Reynolds shear stress distributions, a damping that occurs near the bed for sediment entrainment is higher than that for immobile beds. Quadrant analysis reveals that in the near-bed flow zone, ejections and sweeps on immobile beds cancel each other, giving rise to the outward interactions, whereas sweeps are the dominant mechanism toward sediment entrainment. The bursting duration for entrainment-threshold beds is smaller than that for immobile beds. On the other hand, the bursting frequency for entrainment-threshold beds is larger than that for immobile beds. The third-order correlations indicate that during sediment entrainment, a streamwise acceleration associated with a downward flux and advection of streamwise Reynolds normal stress is prevalent. The streamwise and the downward vertical fluxes of turbulent kinetic energy (TKE) increase with sediment entrainment. The TKE budget proves that for sediment entrainment, the pressure energy diffusion changes drastically to a negative magnitude, indicating a gain in turbulence production.     

Sediment Entrainment at High Flow Velocity

In dredging practice sand is eroded at very high flow velocities using water jets. Breaching of dikes or dams is another process where sediments are eroded under the influence of high flow velocities. The existing pick-up functions were developed for relative low values of bed shear stress and hence overestimate erosion. Conventional pick-up functions can be made suitable for dealing with high-velocity erosion by taking the permeability of the sediment into account. This can be achieved by modifying the critical Shields parameter. The procedure is demonstrated using the van Rijn pick-up function. The theory is compared with experiment, and agreement is found to be good.     

Bed Sediment Entrainment Function Based on Kinetic Theory

Bed sediment entrainment function is derived based on kinetic theory. The entrainment rate is expressed as an upward flux by integrating the particle velocity over all possible upward motions. The possibility of upward motion is determined by a sediment particle velocity distribution function, which is obtained by solving the Boltzmann equation instead of using a prior assumed distribution. External forces and turbulence intensity of the flow are shown to exert significant influences on the velocity distribution function and, in turn, the entrainment rate. Comparisons between available laboratory data and the entrainment function show that the calculated entrainment rates agree well with the observations. Applications of the entrainment function to the specification of the bottom boundary condition for convection-diffusion equation of suspended load are also presented, which show that the calculated concentration profiles are in good agreement with observations. The study also suggests that kinetic theory is a promising analytical approach for the study of sediment motion near a riverbed.     

Near-Bed Sediment Concentration Distribution and Basic Probability of Sediment Movement

Sediment concentration distribution and the basic probability of sediment movement near the channel bed are two of the most important and fundamental issues in the study of sediments. Based on statistical analysis and considering the transport mechanisms, the rules of sediment concentration distribution near a channel bed are studied. Analytical expressions for the near-bed sediment concentration distribution and mean sediment concentration are derived, and the expression for the mean sediment concentration near the bed is verified by measured data, which were obtained from previous experiments. With the help of statistical theory, the expressions of basic probabilities, i.e., rolling, saltating, and suspending probabilities, for sediment movement near the bed are also derived. The expression for starting probability is verified by the measured data. The verification shows that the results from the proposed expression agree well with the measured data. This research has both theoretical and practical significance for further investigation concerning rules of bed load and suspended sediment transport.     

Influence of Coherent Flow Structures on the Dynamics of Suspended Sediment Transport in Open-Channel Flow

The influence of suspended sediments on coherent flow structures has been studied by simultaneously measuring the longitudinal and vertical components of the instantaneous velocity vector and the instantaneous suspended particle concentration with an acoustic particle flux profiler. The measurements were carried out in clear water and in particle-laden open-channel flows. In both cases, they clearly show the predominance of ejection and sweep phases that are part of a burst cycle. The analysis further demonstrates the importance of the ejection and sweep phases in sediment resuspension and transport. Ejections pick up the sediment at the bed and carry it up through the water column close to the surface. It is shown that ejections and sweeps are in near equality in the near-bottom layer, whereas ejections clearly dominate in the remaining water column. The implications of these results for sediment transport dynamics are discussed.     

Fluctuations of Suspended Sediment Concentration and Turbulent Sediment Fluxes in an Open-Channel Flow

A complex problem of turbulent-sediment interactions in an open-channel flow is approached experimentally, using specially designed field experiments in an irrigation canal. The experimental design included synchronous measurements of instantaneous three-dimensional (3D) velocities and suspended sediment concentration using acoustic Doppler velocimeters (ADV) and a water sampling system. Various statistical measures of sediment concentration fluctuations, turbulent sediment fluxes, and diffusion coefficients for fluid momentum and sediment are considered. Statistics, fractal behavior, and contributions of bursting events to vertical fluxes of fluid momentum and sediment are evaluated using quadrant analysis. It has been found that both turbulence and sediment events are organized in fractal clusters which introduce additional characteristic time and spatial scales into the problem and should be further explored. It is also shown that Barenblatt’s theory of sediment-laden flows appears to be a good approximation of experimental data.     

Hydrodynamic Forces Generated on a Spherical Sediment Particle during Entrainment

The objective of this research is to study the relationship between the coherent flow structures and the hydrodynamic forces leading to entrainment of a spherical bed sediment particle for a rough bed uniform turbulent flow. Two types of experiments, namely, movable and fixed balls, were conducted using spherical roughness-element beds with particle image velocimetry to measure the instantaneous flow-velocity field. Miniature piezoelectric pressure sensors were used to capture the instantaneous pressure on the surface of the sphere. Movable ball experiments reveal the predominance of large sweep structures at the instant of entrainment. Fixed ball experiments carried out at entrainment conditions show the importance of both vertical and horizontal pressure gradients on the ball leading to entrainment. Probability distribution function plots of pressures based on quadrant analysis of velocities also reveal the higher probability of occurrence of high magnitude force induced by sweep (Q4) events.     

Numerical Investigation of the Role of Turbulent Bursting in Sediment Entrainment

In this work we incorporate a Gram–Charlier-type joint probability distribution of near-bed two-dimensional instantaneous velocities into a simple mechanistic model to investigate the role of turbulent bursting in sediment entrainment. The results reveal that under typical values of bed-shear stress (>3?Pa), the time fractions of Quadrants 1–4 (Q1–Q4) remain constantly as 16, 34, 19, and 31%, respectively. Entrainment of the fine sediment mixtures is dominated by the lifting mode, whereas entrainment of the coarse ones is dominated by rolling. Sweeps (Q4) are consistently the most significant contributor to entrainment under various types of sediment mixtures. As the standard deviation of grain-size distribution increases, the hiding effect exerted on the finer grains of the mixture is reduced, leading to the elevated correction factors for effective hydrodynamic forces, and thus the reduced threshold velocities for entrainment. The reduced thresholds would, in turn, enhance the fractional contributions of ejections and inward interactions (Q2 and Q3), which are associated with negative longitudinal velocity fluctuations, such that the fractional contribution of outward interactions (Q1) would become less significant.     

Numerical Simulation of Flow over a Rough Bed

This paper presents results of a direct numerical simulation (DNS) of turbulent flow over the rough bed of an open channel. We consider a hexagonal arrangement of spheres on the channel bed. The depth of flow has been taken as four times the diameter of the spheres and the Reynolds number has been chosen so that the roughness Reynolds number is greater than 70, thus ensuring a fully rough flow. A parallel code based on finite difference, domain decomposition, and multigrid methods has been used for the DNS. Computed results are compared with available experimental data. We report the first- and second-order statistics, variation of lift/drag and exchange coefficients. Good agreement with experimental results is seen for the mean velocity, turbulence intensities, and Reynolds stress. Further, the DNS results provide accurate quantitative statistics for rough bed flow. Detailed analysis of the DNS data confirms the streaky nature of the flow near the effective bed and the existence of a hierarchy of vortices aligned with the streamwise direction, and supports the wall similarity hypothesis. The computed exchange coefficients indicate a large degree of mixing between the fluid trapped below the midplane of the roughness elements and that above it.     

Density Functions for Entrainment and Deposition Rates of Uniform Sediment

A model has been developed for the prediction of the density functions of bed-elevation and entrainment and deposition rates of sediment in sand bed streams within the lower regime flow condition. The model incorporates both statistical and deterministic parameters in its form. A total of 46 experimental runs have been carried out in a recirculating tilting flume under the equilibrium flow condition using three grain sizes of uniform gradation to validate the model and estimate its parameters. The model parameters are related to the hydraulic conditions of flow and fluid and sediment properties through dimensional and regression analyses. The study has shown that the density functions of bed elevation and entrainment and deposition rates can be approximated quite satisfactorily with the normal distribution curve. Transformation of the density functions into the standardized normal distribution curve provides a unique pattern for all the experimental runs regardless of the sediment grain size, flow condition, and shapes and dimensions of the bed forms. The developed density functions have been utilized to provide a closure for the probabilistic Exner equation for uniform sediment.     

Influence of Turbulence on Bed Load Sediment Transport

This paper summarizes the results of an experimental study on the influence of an external turbulence field on the bed load sediment transport in an open channel. The external turbulence was generated by (1) a horizontal pipe placed halfway through the depth h; (2) a series of grids with a clearance of about one-third of the depth from the bed, and extending over a finite length of the flume; and (3) a series of grids with a clearance in the range (0.1–1.0)h from the bed, but extending over the entire length of the flume. Two kinds of experiments were conducted: plane-bed experiments and ripple-covered-bed experiments. In the former case, the flow in the presence of the turbulence generator was adjusted so that the mean bed shear stress was the same as in the case without the turbulence generator in order to single out the effect of the external turbulence on the sediment transport. In the ripple-covered-bed case, the mean and turbulence quantities of the streamwise component of the velocity were measured, and the Shields parameter, due to skin friction, was determined. The Shields parameter, together with the RMS value of the streamwise velocity fluctuations, was correlated with the sediment transport rate. The sediment transport increases markedly with increasing turbulence level.     

Stochastic Prediction of Sediment Transport in Sand-Gravel Bed Rivers

Classical deterministic bedload transport predictors are applied to sand-gravel bed rivers. The turbulent bed shear stress is modeled according to a probability distribution to obtain realistic bedload transport rates at incipient motion. In extending the predictors to stochastic predictors for nonuniform sediment, many parameters that represent near-bed turbulence and the particle size distribution must be chosen. The parameters that give realistic results are chosen by analyzing the results of a new experimental flume dataset with relatively large water depths. Choosing other combinations of parameters may give equal total bedload transport rates, but at the cost of large errors in fractional transport rates. Attention is given to the hiding-exposure phenomenon and a hindrance effect related to nonuniform sediment. Validation based on two independent field datasets shows that successful predictions of particle sizes near the threshold for motion are feasible using the stochastic approach, while the deterministic approach gives successful predictions well above incipient motion.     

Bayesian Updating of Parameters for a Sediment Entrainment Model via Markov Chain Monte Carlo

A Bayesian framework incorporating Markov chain Monte Carlo (MCMC) for updating the parameters of a sediment entrainment model is presented. Three subjects were pursued in this study. First, sensitivity analyses were performed via univariate MCMC. The results reveal that the posteriors resulting from two- and three-chain MCMC were not significantly different; two-chain MCMC converged faster than three chains. The proposal scale factor significantly affects the rate of convergence, but not the posteriors. The sampler outputs resulting from informed priors converged faster than those resulting from uninformed priors. The correlation coefficient of the Gram–Charlier (GC) probability density function (PDF) is a physical constraint imposed on MCMC in which a higher correlation would slow the rate of convergence. The results also indicate that the parameter uncertainty is reduced with increasing number of input data. Second, multivariate MCMC were carried out to simultaneously update the velocity coefficient C and the statistical moments of the GC PDF. For fully rough flows, the distribution of C was significantly modified via multivariate MCMC. However, for transitional regimes the posterior values of C resulting from univariate and multivariate MCMC were not significantly different. For both rough and transitional regimes, the differences between the prior and posterior distributions of the statistical moments were limited. Third, the practical effect of updated parameters on the prediction of entrainment probabilities was demonstrated. With all the parameters updated, the sediment entrainment model was able to compute more accurately and realistically the entrainment probabilities. The present work offers an alternative approach to estimating the hydraulic parameters not easily observed.     

Response of Velocity and Turbulence to Sudden Change of Bed Roughness in Open-Channel Flow

The experimental study shows how an open-channel flow would respond to a sudden change (from smooth to rough) in bed roughness. Using a two-dimensional acoustic Doppler velocimeter and a laser Doppler velocimeter, the velocity, turbulent intensities, and Reynolds stress profiles at different locations along a laboratory flume were measured. Additionally, the water surface profile was also measured using a capacitance-type wave height meter. The experimental data show the formation of an internal boundary layer as a result of the step change in bed roughness. The data show that this boundary layer grows much more rapidly than that formed in close-conduit flows. The results also show that the equivalent bed roughness, bed-shear stress, turbulent intensities, and Reynolds stress change gradually over a transitional region, although the bed roughness changes abruptly. The behavior is different from that observed in close-conduit flows, where an overshooting property—which describes the ability of the bed-shear stress to attain a high-peak value over the section with the larger roughness, was reported. A possible reason for the difference is the variation of the water surface profile when an open-channel flow is subjected to a sudden change in bed roughness.     

Unified View of Sediment Transport by Currents and Waves. I: Initiation of Motion, Bed Roughness, and Bed-Load Transport

Attention is given to the properties of sediment beds over the full range of conditions (silts to gravel), in particular the effect of fine silt on the bed composition and on initiation of motion (critical conditions) is discussed. High-quality bed-load transport data sets are identified and analyzed, showing that the bed-load transport in the sand range is related to velocity to power 2.5. The bed-load transport is not much affected by particle size. The prediction of bed roughness is addressed and the prediction of bed-load transport in steady river flow is extended to coastal flow applying an intrawave approach. Simplified bed-load transport formulas are presented, which can be used to obtain a quick estimate of bed-load transport in river and coastal flows. It is shown that the sediment transport of fine silts to coarse sand can be described in a unified model framework using fairly simple expressions. The proposed model is fully predictive in the sense that only the basic hydrodynamic parameters (depth, current velocity, wave height, wave period, etc.) and the basic sediment characteristics (d10, d50, d90, water temperature, and salinity) need to be known. The prediction of the effective bed roughness is an integral part of the model.     

Coherent Structures in Flat-Bed Abutment Flow: Computational Fluid Dynamics Simulations and Experiments

Numerical computations and laboratory experiments are carried out to investigate the three-dimensional structure of large-scale (coherent) vortices induced by bridge abutments on a flat bed. A finite-volume numerical method is developed for solving the unsteady, three-dimensional Reynolds-averaged Navier–Stokes equations, closed with the k–ω turbulence model, in generalized curvilinear coordinates and applied to study the flow in the vicinity of a typical abutment geometry with a fixed, flat bed. The computed flowfields reveal the presence of multiple, large-scale, unsteady vortices both in the upstream, “quiescent,” region of recirculating fluid and the shear-layer emanating from the edge of the foundation. These computational findings motivated the development of a novel experimental technique for visualizing the footprints of large-scale coherent structures at the free surface. The technique relies on digital photography and employs averaging of instantaneous images over finite-size windows to extract coherent eddies from the chaotic turbulent flow. Application of this technique to several abutment configurations yielded results that support the numerical findings.     

One-Dimensional Model for Transient Flows Involving Bed-Load Sediment Transport and Changes in Flow Regimes

This study presents a novel, simple, but rather accurate approximation of the eigenvalues of the system formed by the Saint-Venant–Exner equations, based on the comparison between eigenvalues for the complete system and eigenvalues for the water phase only. Moreover, a strategy is proposed to compute efficiently the intercell fluxes by properly adapting a Harten, Lax, and van Leer scheme for each equation. Two examples of transient transcritical flows are developed: the erosive migration of a knickpoint induced by an increase in the bed slope, and the evolution of a hydraulic jump over a mobile bed.