Three-dimensional saltating processes of multiple sediment particles

The purpose of this study was to investigate the interacting mechanism between the saltating particles near a channel bed. A three-dimensional real-time flow visualization technique was developed to measure the interparticle collision behaviors during the saltating process. Based on the experimental data, the distribution of the collision points was found to be symmetric. This confirms the assumption that the projections of the collision points onto the reasonable plane are uniformly distributed. A three-dimensional saltating model was also developed. This model produced satisfactory results. The model is able to simulate the continuous saltating trajectories of several particles. The simulated dimensionless saltating height, longitudinal and vertical saltation velocity components were found to increase as the dimensionless particle diameter and the dimensionless flow transport capacity parameter increase, while the simulated lateral saltation velocity component varies inversely with the dimensionless flow transport capacity parameter. A regression equation for the bed load transport rate was also obtained.     

Small scale turbulent diffusion determined with underwater flow visualization

Dye plumes were generated at three depths in the seasonal thermocline between 7 and 11 m, 22 km south of Key West on 21 August 1980 and photographed at about 10 second intervals with an underwater camera system. Eleven pairs of consecutive pictures are analyzed to determine the mean current vertical shear and the width of the plumes by positioning reference points relative to the rod attached to the camera system. The relative distances of reference points are calibrated with the stereophotogrammetric method for one pair. The eddy diffusivity is calculated by use of a model of turbulent diffusion developed byTaylor (1921). Its values range from 5 to 25 cm²s^–1 for the plume widths ranging from 33 to 132 cm. The Richardson number is calculated for each pair of pictures with the vertical density gradient estimated from temperature profiles. Its values are higher than the critical value of 0.25 except for one case. The diffusivity was higher by orders of magnitude than the molecular one and indicates the presence of turbulence together with billow like features of the plumes in spite of high Richardson numbers. This suggests that the billow turbulence might be caused by effects of surface gravity waves and not by the Kelvin-Helmholtz instability.     

3D non-hydrostatic modelling of bottom stability under impact of the turbulent ship propeller jet

New three-dimensional numerical non-hydrostatic model with a free surface that was designed for modelling the bottom and bank stability subjected by ship propeller jets is presented. Unlike all known models, it describes three-dimensional fields of velocities generated by ship propellers, turbulence intensity and length scale in the given domain of arbitrary bottom and coastal topography. Results of simulations are compared with the laboratory experiments.     

Experimental determination of saltating glass particle dispersion in a turbulent boundary layer

A horizontal saltation layer of glass particles in air is investigated experimentally over a flat bed and also over a triangular ridge in a wind tunnel. Particle concentrations are measured by light scattering diffusion (LSD) and digital image processing, and velocities using particle image velocimetry (PIV). All the statistical moments of the particle concentration are determined such as mean concentration, root mean square concentration fluctuations, skewness and flatness coefficients. Over the flat bed, it is confirmed that the mean concentration decreases exponentially with height, the mean dispersion height being a significant length scale. It is shown that the concentration distribution follows quite well a lognormal distribution. Over the ridge, measurements were made at the top of the ridge and in the cavity region and are compared with measurements without the ridge. On the hill crest, particles are retarded, the saltation layer decreases in thickness and concentration is increased. Downwind of the ridge, particle flow behaves like a jet, in particular no particle return flow is observed. Copyright © 2006 John Wiley & Sons, Ltd.     

Historical overview of 2D and 3D hydrodynamic modelling of shallow water flows in the Netherlands

Ocean Dynamics - This paper contains a historical overview of 2D and 3D hydrodynamic modelling in the Netherlands from the 1960s till now. It started in the 1960s with two-dimensional...     

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.     

Determining drag coefficients and their application in modelling of turbulent flow with submerged vegetation

Vegetation is a key aspect of water resources and ecology in natural rivers, floodplains and irrigation channels. The hydraulic resistance of the water flow is greatly changed when submerged vegetation is present. Three kinds of drag coefficients, i.e., the drag coefficient for an isolated cylinder, the bulk drag coefficient of an array of cylinders and the vertically distributed or local drag coefficient, have been commonly used as parameters to represent the vegetation drag force. In this paper, a comprehensive experimental study of submerged stems in an open channel flow is presented. Empirical formulae for the three drag coefficients were obtained based on our experimental results and on data from previous studies. A two-layer model was developed to solve the mean momentum equation, which was used to evaluate the vertical mean velocity profile with each of the drag coefficients. By comparing the velocity distribution model predictions and the measurement results, we found that the model with the drag coefficient for an isolated cylinder and the local drag coefficient was good fit. In addition, the model with the bulk drag coefficient gave much larger velocity values than measurements, but it could be improved by adding the bed friction effect and making choice of the depth-averaged velocity within the canopy layer.     

Lagrangian dispersion in sheared flow

Two-dimensional Lagrangian trajectories are studied near an idealized ocean front with shear and convergence plus an uncorrelated random walk. Applications include fixed-depth drifters and plankton patches with perfect depth regulation.     

A conceptual model of wind erosion of soil surfaces by saltating particles

A conceptual model is described for the prediction of wind erosion rates dependent on the distribution of impact energy delivered to the surface by saltating grains, P[Ei], and the distribution of local surface strength, P[Es]. Methods are presented for the measurement of both distributions and consequent loss of material from the bed. It is concluded that saltating sand grains can rupture weak crusts under even moderate wind conditions, and that the rate of erosion will depend on the shape of the distribution tails. Copyright © 1999 John Wiley & Sons, Ltd.     

3D Numerical modelling of flow divisions at open channel junctions with or without vegetation

The flow division at an open channel junction is affected by the inflow discharge and the downstream water depths of the junction. The growth of vegetation in a channel system is environmental friendly, but its effect on the flow in an open channel junction can be significant. In this work a 3D RANS (Reynolds Averaged Navier–Stokes equation) model has been implemented to investigate the flow phenomena in channel junctions with or without vegetation. The model is first validated by two cases: flow in an open channel T-junction without vegetation, and flow in a single open channel with vegetation. The model is then applied to simulate flow in an open channel T-junction with varying width ratio and vegetation density of the branch channel. The results quantitatively predict the trend of increasing flow in the branch channel with the increase in branch channel width and/or the decrease in vegetation density. The overall energy loss coefficient of the system, however, decreases with the amount of flow in the branch channel.     

An analysis of soil crust strength in relation to potential abrasion by saltating particles

Wind erosion depends on the ease with which particles can be detached from the soil surface, but suitable tests to characterize this property are not available. Two possible methods to determine surface soil strength in the field were therefore compared on a range of artificially ‘crusted’ surfaces. These were made by spraying or tension wetting aggregates (10–2, 2–0.5 and <0.5 mm) from a structurally unstable sandy loam, followed by drying. Each test involved measuring the force exerted on a probe driven at a steady rate into the surface, using either a flat-tipped 0.6 mm diameter penetrometer or a flat-ended cylindrical punch with inner and outer diameters of 5 and 6 mm, respectively. Both probes showed that crusts could be produced reproducibly. Depending on the probe and aggregate size, penetration mainly occurred either as a result of aggregates being deflected out of the pathway of the probe or by genuine rupture of aggregates or of the crusted surface. The penetrometer, because it was comparable to the size of sand grains, gave results that can be used to characterize surface erodibility to saltating particles. The punch gave results that would be unsuitable for this purpose, as would other strength tests that are on too large a scale. Penetrometer results were analyzed to calculate the energy required for penetration. It was thus possible to demonstrate that only the spray-wetted fine aggregates had a surface that could undergo large-scale rupture by saltating sand grains. For all other surfaces, saltating particles would be unable to supply sufficient energy to rupture aggregates or the crusted surface. Erosion could only occur by a slower process of abrasion in which smaller particles or aggregates are chipped away from the surface. However, it is shown that saltating particles could rupture the interaggregate bonding in the 2–0.5 mm aggregate surfaces, thus permitting creep. An alternative and potentially simpler way of characterizing surface erodibility by using a surface modulus of elasticity is also discussed. Our results demonstrate that the small diameter penetrometer is a promising technique for characterizing erodibility of aggregated and crusted surfaces. © 1997 by John Wiley & Sons, Ltd.     

A new scheme for numerical modelling of flow and transport processes in 3D fractured porous media

The objective of this work is to develop a new numerical approach for the three-dimensional modelling of flow and transient solute transport in fractured porous media which would provide an accurate and efficient treatment of 3D complex geometries and inhomogeneities. For this reason, and in order to eliminate as much as possible the number of degrees of freedom, the fracture network, fractures and their intersections, are solved with a coupled 2D–1D model while the porous matrix is solved independently with a 3D model. The interaction between both models is accounted for by a coupling iterative technique. In this way it is possible to improve efficiency and reduce CPU usage by avoiding 3D mesh refinements of the fractures. The approach is based on the discrete-fracture model in which the exact geometry and location of each fracture in the network must be provided as an input. The formulation is based on a multidimensional coupling of the boundary element method-multidomain (BEM-MD) scheme for the flow and boundary element dual reciprocity method-multidomain (BE-DRM-MD) scheme for the transport. Accurate results and high efficiency have been obtained and are reported in this paper.     

三维孔洞储层建模及其地震波场正演模拟

本文研究的内容有二,一是针对塔河油田六区东中、下奥陶统碳酸盐岩孔洞储层发育的特征,通过精细的层位标定、构造解释与时深转换,搭建深度域等时地层框架模型,然后采用协克里金算法,将波阻抗反演体作为协变量,对孔洞储集体的三维孔隙度分布进行确定性建模;二是应用二维横向各向同性介质中的弹性波波动方程,基于交错网格差分格式,考虑初始...     

3D magnetotelluric modelling including surface topography

An edge finite‐element method has been applied to compute magnetotelluric (MT) responses to three‐dimensional (3D) earth topography. The finite‐element algorithm uses a single edge shape function at each edge of hexahedral elements, guaranteeing the continuity of the tangential electric field while conserving the continuity of magnetic flux at boundaries. We solve the resulting system of equations using the biconjugate gradient method with a Jacobian preconditioner. The solution gives electric fields parallel to the slope of a surface relief that is often encountered in MT surveys. The algorithm is successfully verified by comparison with other numerical solutions for a 3D‐2 model for comparison of modelling methods for EM induction and a ridge model. We use a 3D trapezoidal‐hill model to investigate 3D topographic effects, which are caused mainly by galvanic effects, not only in the Zxy mode but also in the Zyx mode. If a 3D topography were approximated by a two‐dimensional topography therefore errors occurring in the transverse electric mode would be more serious than those in the transverse magnetic mode.     

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.     

Motion of particles in turbulent flow: Hyperbolicity,strange attractors and dynamic stochasticity of a system

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Lagrangian singularities of steady two-dimensional flow

The Lagrangian complex-space singularities of the steady Eulerian flow with stream function sin x ₁ cos x ₂ are studied by numerical and analytical methods. The Lagrangian singular manifold is analytic. Its minimum distance from the real domain decreases logarithmically at short times and exponentially at large times.     

Approaches to modelling coupled flow and reaction in a 2D cementation experiment

Porosity evolution at reactive interfaces is a key process that governs the evolution and performances of many engineered systems that have important applications in earth and environmental sciences. This is the case, for example, at the interface between cement structures and clays in deep geological nuclear waste disposals. Although in a different transport regime, similar questions arise for permeable reactive barriers used for biogeochemical remediation in surface environments.The COMEDIE project aims at investigating the coupling between transport, hydrodynamics and chemistry when significant variations of porosity occur. The present work focuses on a numerical benchmark used as a design exercise for the future COMEDIE-2D experiment. The use of reactive transport simulation tools like Hytec and Crunch provides predictions of the physico-chemical evolutions that are expected during the future experiments in laboratory. Focus is given in this paper on the evolution during the simulated experiment of precipitate, permeability and porosity fields.A first case is considered in which the porosity is constant. Results obtained with Crunch and Hytec are in relatively good agreement. Differences are attributable to the models of reactive surface area taken into account for dissolution/precipitation processes. Crunch and Hytec simulations taking into account porosity variations are then presented and compared. Results given by the two codes are in qualitative agreement, with differences attributable in part to the models of reactive surface area for dissolution/precipitation processes. As a consequence, the localization of secondary precipitates predicted by Crunch leads to lower local porosities than for predictions obtained by Hytec and thus to a stronger coupling between flow and chemistry. This benchmark highlights the importance of the surface area model employed to describe systems in which strong porosity variations occur as a result of dissolution/precipitation. The simulation of highly non-linear reactive transport systems is also shown to be partly dependent on specific numerical approaches.     

A multigrid solver for 3D electromagnetic diffusion

The performance of a multigrid solver for the time‐harmonic electromagnetic problem in geophysical settings is investigated. The frequencies are sufficiently small for waves travelling at the speed of light to be negligible, so that a diffusive problem remains. The discretization of the governing equations is obtained by the finite‐integration technique, which can be viewed as a finite‐volume generalization of Yee's staggered grid scheme. The resulting set of discrete equations is solved by a multigrid method. The convergence rate of the multigrid method decreased when the grid was stretched. The slower convergence rate of the multigrid method can be compensated by using bicgstab2 , a conjugate‐gradient‐type method for non‐symmetric problems. In that case, the multigrid solver acts as a preconditioner. However, whereas the multigrid method provides excellent convergence with constant grid spacings, it performs less than satisfactorily when substantial grid stretching is used.