Laboratory investigations into the threshold of movement of natural sand-sized sediments under unidirectional, oscillatory and combined flows

The threshold of movement of sediment obtained from sandbanks within the Bristol Channel (UK) is investigated under unidirectional, oscillatory and combined flows. The experiments were undertaken in a recirculating, unidirectional laboratory flume containing an oscillating plate to simulate wave action, with movement along the same axis as the unidirectional flows. The sand samples consisted of cohesionless quartz grains with median grain sizes between 0·315 and 0·513 mm. The experiments were performed under flow velocities (measured at 2 cm above the bed) ranging between 0 and 24 cm s^–1 and oscillatory currents (wave periods of 5, 12 and 15 s) ranging from 0 to 28 cm s^–1. The critical conditions for the initiation of sediment movement were assessed, by visual observation, using the Yalin criterion. The results show that, under unidirectional flow, there is a slight overestimation of the threshold of naturally graded sediments derived on the basis of empirically derived threshold curves for artificially prepared sediments under similar flow conditions. In the case of oscillatory flows, the threshold for the natural sands is found to be higher than that predicted by previously derived empirical curves. Under combined flows, wave period is shown to control threshold conditions, with the unidirectional and oscillatory flow components combining in a linear fashion for long-period (12 s and 15 s) waves. In contrast, in the presence of short-period (5 s) waves, the unidirectional and oscillatory components of the flow appear to 'decouple'. For high orbital velocities, in both cases, the effect of the wave period on threshold diminishes.     

A unified model for bedform development and equilibrium under unidirectional,oscillatory and combined‐flows

The development of bedforms under unidirectional, oscillatory and combined‐flows results from temporal changes in sediment transport, flow and morphological response. In such flows, the bedform characteristics (for example, height, wavelength and shape) change over time, from their initiation to equilibrium with the imposed conditions, even if the flow conditions remain unchanged. These variations in bedform morphology during development are reflected in the sedimentary structures preserved in the rock record. Hence, understanding the time and morphological development in which bedforms evolve to an equilibrium stage is critical for informed reconstruction of the ancient sedimentary record. This article presents results from a laboratory flume study on bedform development and equilibrium development time conducted under purely unidirectional, purely oscillatory and combined‐flow conditions, which aimed to test and extend an empirical model developed in past work solely for unidirectional ripples. The present results yield a unified model for bedform development and equilibrium under unidirectional, oscillatory and combined‐flows. The experimental results show that the processes of bedform genesis and growth are common to all types of flows, and can be characterized into four stages: (i) incipient bedforms; (ii) growing bedforms; (iii) stabilizing bedforms; and (iv) fully developed bedforms. Furthermore, the development path of bedform; growth exhibits the same general trend for different flow types (for example, unidirectional, oscillatory and combined‐flows), bedform size (for example, small versus large ripples), bedform shape (for example, symmetrical or rounded), bedform planform geometry (for example, two‐dimensional versus three‐dimensional), flow velocities and sediment grain sizes. The equilibrium time for a wide range of bed configurations was determined and found to be inversely proportional to the sediment transport flux occurring for that flow condition.     

感潮河段丁坝局部冲刷三维数值模拟

针对局部冲刷和一般冲刷的不同,建立了考虑垂向水流作用的局部冲刷三维紊流泥沙数学模型,并对往复流和单向流作用下的丁坝局部冲刷进行了验证计算和数值模拟。结果表明,往复流作用下丁坝局部冲刷在冲刷过程和冲淤形态上与单向流有明显不同,若采用单向流作用下的局部冲刷模型试验结果来指导往复流作用下丁坝头防护工程的设计和施工是不利的。     

Sand waves: A model of origin and internal structure

Sand waves are large flow-transverse bedforms coupled to oscillatory boundary-layer currents of tidal origin. Like the much smaller ripple-marks generated by short-period wind waves, sand waves are observed to grow more asymmetrical with increase in the time—velocity asymmetry of the governing currents, that is, with increase in the steady component of flow (mass-transport strictly related to wave-motion) relative to the periodic component. Wind-wave ripple-marks owe their origin directly to a mass-transport component dependent on bed-curvature, which arises naturally wherever a sufficiently powerful oscillatory flow is imposed on a deformable grain boundary. This curvature-related current, flowing from troughts to crests on the bed, drifts grains mobilized by the periodic component into transverse bands. Sand waves may also owe their origin and growth to an unstable interaction within tide-generated oscillatory boundary layers between the mobile bed and a curvature-related mass-transport.Sand-wave internal structure apparently depends on the strength and degree of asymmetry of the governing currents. Relatively symmetrical forms associated with currents of low asymmetry are expected to contain comparatively small, intricately related herring-bone or climbing cross-bedding sets. Relatively asymmetrical currents shape sand waves with one side so steep that large-scale flow separation is inevitable. The predominant structure is then expected to be long avalanche bedding broken into sets by mud drapes and bioturbated zones representing periods of gentle flow, and/or by erosional discontinuities recording tidal reversals. The expected structures have parallels in the stratigraphic record and amongst modern sand waves.     

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 studies of gravel size particles under the co-linear combined action of waves and currents

Gravel size sediment beds are tested under the combined influence of simulated wave action and co-linear currents in a laboratory flume. Critical current speed, at threshold, increases with increasing size. Superimposed wave energy causes a small reduction in the unidirectional current energy. For low values of wave-induced near bed current velocities, the resistance to erosion increases when the wave period decreases from 10 to 6 s. Finally, combined critical shear stresses are found to be lower than those predicted using the Shields curve, as modified for oscillatory flow. Grain protrusion is suggested as a mechanism to explain this divergence.     

Threshold of motion and settling velocities of mollusc shell debris: Influence of faunal composition

Bioclastic particles derived from mollusc shell debris can represent a significant fraction of sandy to gravelly sediments in temperate and cool‐water regions with high carbonate productivity. Their reworking and subsequent transport and deposition by waves and currents is highly dependent on the shape and density of the particles. In this study, the hydrodynamic behaviour of shell debris produced by eight mollusc species is investigated for several grain sizes in terms of settling velocity (measurements in a settling tube) and threshold of motion under unidirectional current (flume experiments using an acoustic profiler). Consistent interspecific differences in settling velocity and critical bed shear stress are found, related to differences in shell density, shell structure imaged by scanning electron microscopy and grain shape. Drag coefficients are proposed for each mollusc species, based on an interpolation of settling velocity data. Depending on the shell species, the critical bed shear stress values obtained for bioclastic particles fall within or slightly below empirical envelopes established for siliciclastic particles, despite very low settling velocity values. The results suggest that settling velocity, often used to describe the entrainment of sediment particles through the equivalent diameter, is not a suitable parameter to predict the initiation of motion of shell debris. The influence of the flat shape of bioclastic particles on the initiation of motion under oscillatory flows and during bedload and saltation transport is yet to be elucidated.     

单向明渠流与波浪作用下植被对水沙运动影响研究综述

作为河、湖以及滨海湿地生态系统中必不可少的组成部分,水生植被具有重要的生态服务价值,且许多生态服务价值是通过改变水体动力条件实现的。含植被水流研究不仅可用于科学阐明水生植被的生态环境效应,还能指导河湖生态系统修复及污染治理的工程实践。本文考虑单向明渠流与波浪2种水动力环境,对国内外有关水生植被对水流结构以及泥沙运动影响研究的主要成果进行梳理。单向明渠流条件下,植被对水动力的影响研究主要集中于植被对水流阻力的影响以及冠层内水体的紊动结构与紊动尺度特征;波浪条件下,植被对波高与波浪流速的减弱作用以及冠层内水体的时均与紊动结构特征是研究重点。受水动力条件控制,植被影响下的泥沙运动特征也受到广泛关注,且研究焦点为单向明渠流条件下水生植被对泥沙起动与输移的影响以及波浪条件下植被对床底泥沙再悬浮的影响。     

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.     

On the threshold of transport of sand-sized sediment under the combined influence of unidirectional and oscillatory flow

While the transport of sediment by unidirectional currents or by oscillatory (wave-induced) currents has been investigated, very little attention has been paid to the problem of the threshold of transport under the two mechanisms combined. Studies were carried out using cohesionless sand-sized (mean diameters: 142, 363, 771 and 1134 μm) quartz grains in a unidirectional flume, within which an oscillatory carriage had been installed. The experiments were carried out under unidirectional velocities ranging between 0 and 27 cm s^-1, combined with simulated wave-induced currents (at periods of 5 and 15 s) ranging from 0 to 35 cm s^-1. The threshold of transport was assessed, by visual observation, using the Yalin Criterion for unidirectional flow. This criterion permitted critical conditions to be estimated subjectively by observation of incipient transport from the flat beds. The results indicated the dependence of the critical threshold velocity combination on grain size and wave period. Thresholds tend to increase with increasing grain size or decreasing period. The grain-size dependence is predictable from existing empirical relationships for the separate mechanisms; statistical fluctuations in near-bed stress (bursting) however, are invoked to explain the wave period dependence. The latter effect acts in a reverse manner for wave and current combinations than for waves alone. Graphs are presented, relating grain size to critical threshold velocity combinations, to aid in the sedimentological interpretation of field data.     

感潮河网区水沙运动的数值模拟

根据感潮河网区水沙运动特征,建立了一维感潮河网区非恒定水沙数学模型,对河网区水沙运动和河床变形进行了数值模拟,并在水沙模拟的范围内着重对河网区内动边界的处理、挟沙力公式的选用、内边界含沙量的确定等问题进行了讨论,提出了解决问题的途径和技术处理方法。采用东江下游感潮河网区的水文和河道地形资料对所建模型进行了检验,模拟结果较好地反映了感潮河网区水沙运动的往复输运特征和河道冲淤的宏观效应。     

Direct numerical simulation of bedload transport using a local, dynamic boundary condition

ABSTRACT Temporally and spatially averaged models of bedload transport are inadequate to describe the highly variable nature of particle motion at low transport stages. The primary sources of this variability are the resisting forces to downstream motion resulting from the geometrical relation (pocket friction angle) of a bed grain to the grains that it rests upon, variability of the near‐bed turbulent velocity field and the local modification of this velocity field by upstream, protruding grains. A model of bedload transport is presented that captures these sources of variability by directly integrating the equations of motion of each particle of a simulated mixed grain‐size sediment bed. Experimental data from the velocity field downstream and below the tops of upstream, protruding grains are presented. From these data, an empirical relation for the velocity modification resulting from upstream grains is provided to the bedload model. The temporal variability of near‐bed turbulence is provided by a measured near‐bed time series of velocity over a gravel bed. The distribution of pocket friction angles results as a consequence of directly calculating the initiation and cessation of motion of each particle as a result of the combination of fluid forcing and interaction with other particles. Calculations of bedload flux in a uniform boundary and simulated pocket friction angles agree favourably with previous studies.     

Bedform migration and bed-load transport in some rivers and tidal environments

Reliable field data obtained by directly measuring bed-load transport of fine- to coarse-grained bed material are extremely scarce, mainly because of the difficulty of sampling accurately. Therefore, the verification of bed-load transport formulae is largely based on flume experiments, which refer to unrealistic shallow-water conditions. In this study, some bed-load transport formulae were tested against data from natural environments. As an alternative to ascertaining the bed-load transport rate by sampling the bed-load, the transport rate was deduced from data on bedform height and bedform celerity. For this purpose, 43 sets of data from rivers, representing a wide range of bed material, bedform dimensions and hydraulic conditions were collected as were some sets of data from tidal settings. Two formulae were used for the prediction of the bed-load transport: the formula of Van Rijn (1981) and the Kalinske (1947) formula as approximated by Elzerman & Frijlink (1951) (and, in the present study, slightly modified for application to tidal waters). Both the bed-load function of Van Rijn and the modified formula of Kalinske-Frijlink require data which are easily obtained and that can be measured accurately. At those stages of the flow when bed-load transport was high the Van Rijn function tended to overestimate that transport. For flow stages when bed-load transport was low the opposite was true. The modified Kalinske-Frijlink function gave consistently good results: 86% of the transport rates predicted using the river data were within 0·5–2·0 times the values actually measured.     

Wave and tidal current sorting of shelf sediments southwest of England

The relative roles of waves and tidal currents in transporting bottom sediment on the continental shelf off Lands End, southwest England, are evaluated by study of (a) sediment grain size in relation to boundary layer measurements in tidal currents, (b) regional variation in sediment parameters in relation to peak tidal and wave-induced currents, and (c) visual observation of bedforms. (a) The sediments are mainly zoogenic sands. The average hydraulic equivalent median diameter is Mdφ=1.40φ (medium grade sand), and two-thirds of the median grain sizes fall between 0.97φ and 1.83φ. The linear bottom current which will just move this range of sizes is exceeded only slightly by the highest tidal drag velocities ū* measured in the area. Thus, sediment movement by tidal currents alone is restricted to areas of high bed roughness and strong peak tidal flows. In contrast, wave-induced oscillatory currents at 100 m depth (typical of the area) attain sufficient speed to disturb the same particle sizes over 3% of the time. This includes storm periods when much greater velocities occur. (b) The average Mdφ of the sediment decreases southwest and northeast from south of the Lizard. This correlates well with the pattern of maximum tidal current speeds, suggesting that tidal currents control the areal distribution of sediment median grain size. Most sediments are well sorted (mean σ_i=0.48φ). Sorting improves at shallower depths but does not improve in areas of faster tidal currents, suggesting that wave-induced currents exert the major control on sorting. Silt and clay proportions increase west of the Scilly Isles and are influenced by both wave and tidal currents. (c) Photographs and television pictures show that symmetrical bedforms due to wave action are dominant north and west of the western Channel. Asymmetric bedforms are more common in the western Channel itself, where tidal currents and bed roughness are both high. Results are used to construct a sediment transport model for the study area. Since medium grade well sorted sands occur in depths of over 100 m, many ancient, extensive, well sorted sand sheets may have been deposited at depths greater than previously suspected.     

Initiation of ripple marks under oscillating water

It was observed that a monolayer of glass beads which were scattered sparsely on a rigid plane floor grew into regular waves of particles under oscillatory water flow. The relative displacement of two nearby particles due to viscous fluid forces seems to be responsible for the initiation of these particle waves. It was also observed that the similar particle waves were formed on the initially flat surface of a thick sand bed and subsequently developed into oscillatory sand ripples of a common type. On the basis of these observations, it is suggested that the particle waves may be the basic cause of the initiation of general ripple marks under oscillatory flow.     

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.     

卵砾石沙波临界水流条件的水槽试验

以往对沙波的研究多针对河流中下游、河口海岸段的细沙(粒径D<1 mm),而长江上游等卵砾石输移河段(D>2 mm)是否会出现沙波以及卵砾石沙波的临界条件,尚需开展进一步研究。通过长江上游九堆子、筲箕背等卵石滩的现场踏勘,观察到明显的天然沙波形态。采用中值粒径D₅₀=1.8 mm和5.3 mm的天然沙和D₅₀=4.8 mm的轻质沙进行水槽试验,成功模拟出砾石沙波。根据恒定均匀流条件下,产生沙波的比降、水位、流量等水流条件及试验沙的粒径、比重,提出卵砾石沙波的临界条件公式。结果表明,卵砾石沙波的临界条件可以用量纲起动功率w_* 、R／D及比降S表达,并据此提出判别系数G_Dcr。当研究河段的卵砾石输移带上的水流条件满足判别系数G_Dcr,则可以判断能够产生沙波现象。     

Large-scale rhomboid bed forms and sedimentary structures associated with hurricane washover*

Hurricane washover fans from the Texas Gulf Coast exhibit large-scale rhomboid bed forms developed on washover deposits of fine sand with varying shell content. Washover processes inferred from aerial photographs, storm characteristics, and physical settings suggest that these bed forms are the product of (1) storm surge flooding or (2) high wind shear stress. Multiple bed forms, including large-scale rhombs, are responsible for sedimentary structures preserved in washover deposits. Proximal channels exhibit scour and fill sequences capped by mud drapes. Mid-channel fan deposits also have scour bases marked by shell lags which are overlain by horizontal laminations and foreset and backset laminae. Distal fan sediments are relatively shell free and are interbedded with tidal flat deposits characterized by bioturbated, alternating sand and mud laminae. Rhomboidal patterns can form on the free surface of water in response to five processes: (1) wave interference from two externally independent sources, (2) wave interference from refraction of a single set of wave fronts, (3) standing oblique waves caused by bed roughness elements, (4) standing oblique waves formed at channel boundaries and channel transitions, and (5) wind stress. Geologically, standing oblique waves from unidirectional nearly supercritical flow is probably the most important process in rhomboid bed form development.     

极浅水边界层的沉积环境效应

极浅水环境是水深远小于正常边界层厚度的环境,潮滩滩面和潮水沟就经常处于这种环境之中。来自江苏潮滩的观察资料表明,落潮后期滩面和潮水沟在薄层低速水流作用下可形成浅水波痕、平床和次级潮水沟形态,而边界层内的流速结构仍然得以维持,物质输运强度也与Von Kármán-Prandtl模型所定义的u100数值相一致。涨急时段中潮位附近形成的滩面涌潮是极浅水边界层的另一种动力学行为,它代表薄层高速水流作用下发生的底部边界层系统的崩溃,此时Von Kármán-Prandtl模型所刻画的流速结构不复存在。滩面涌潮高度是系统崩溃的临界水深,它可以定量地表示为Hb=4z0。极浅水边界层过程对潮滩沉积和地貌形成具有独特的作用。     

Hummocky cross-stratification, tropical hurricanes, and intense winter storms

Duke (1985b) argues that ‘most examples (of hummocky cross-stratification) were formed by tropical hurricanes.’ His statement is based on the assumption that ‘hurricane-generated surface gravity waves form powerful oscillating or multidirectional flows at the water-sediment interface which do not possess a significant unidirectional component.’ It is true, as one of us has previously stated, that hurricanes are rapidly-moving, short-lived, localized, and infrequent systems as compared with mid-latitude storms; midlatitude storms are consequently more efficient in coupling with the shelf water-column than are hurricanes. However, Duke's argument that hummocky cross-stratification may be the result of purely oscillatory flow is untenable. His reasoning contradicts established theory about oscillatory bedforms, and his numerous examples of hummocky cross-stratification come largely from continental shelf settings where the storms (tropical or otherwise) would have created concurrent alongshelf undirectional flow as well as wave oscillatory motion. There is no theoretical or observational basis for the belief that water movement on the sea-floor during hurricanes is qualitatively different from water movement during mid-latitude storms. Consequently, hummocks are no more liable to form beneath hurricanes than they are beneath mid-latitude storms.