The limits to growth: how large can subaqueous,flow-transverse bedforms ultimately become?

Based on field and experimental evidence, the average initial spacing (seed wavelength) of flow-transverse bedforms (ripples and dunes) appears to lie between 80 and 130 grain diameters (L = 80–130D_mm). Starting with an average initial spacing of L = 100D_mm, subsequent bedform growth proceeds by amalgamation of two successive bedforms, which results in a doubling of the spacing in each step. Geometric principles dictate that the combined volume of two smaller bedforms lacks about 40% of the volume required for a fully developed amalgamated bedform. The missing volume is gained by excavation of the troughs, i.e., by lowering the base level. Where base level lowering is prevented by the presence of a coarse-grained armor layer or hard ground pavement, the larger amalgamated bedform remains sediment starved. In its simplest form, bedform growth proceeds by continuous doubling of the spacing in response to increases in flow velocity, the process being reversible in response to flow decelerations. Bedform growth terminates when the shear velocity (u_*) at the crest reaches the mean settling velocity (w_s) of the sediment. At this point, 40% of the bed material is in suspension, at which point the missing volume can no longer be compensated by trough excavation. In shallow water, maximum bedform size is dictated by the water depth, whereas in deep water, bedforms can potentially grow to their ultimate size. Evaluation of bedform data from deep water settings suggests that the largest two-dimensional, flow-transverse bedforms in terms of grain size (phi) can be approximated by the equations: lnL_max = 13.72–4.03D_phi and lnH_max = 9.95–3.47D_phi for grain sizes <  ~ 0.2 mm (> ~ 2.32 phi), with L and H representing bedform spacing and height in meters and D the grain size in phi. For grain sizes >  ~ 0.2 mm (< ~ 3.23 phi), the corresponding relationships are lnL_max = 6.215–0.69 D_phi and lnH_max = 3.18–0.56D_phi, with notations as before, or in terms of grain diameters in mm: L_max = 5 × 10⁵D_mm.

     

The causes of bedload pulses in a gravel channel: the implications of bedload grain‐size distributions

Unsteady bedload transport was measured in two c. 5 m wide anabranches of a gravel‐bed braided stream draining the Haut Glacier d'Arolla, Switzerland, during the 1998 and 1999 melt seasons. Bedload was directly sampled using 152 mm square Helley–Smith type samplers deployed from a portable measuring bridge, and independent transport rate estimates for the coarser size fractions were obtained from the dispersion of magnetically tagged tracer pebbles. Bedload transport time series show pulsing behaviour under both marginal (1998) and partial (1999) transport regimes. There are generally weak correlations between transport rates and shear stresses determined from velocity data recorded at the measuring bridge. Characteristic parameters of the bedload grain‐size distributions (D₅₀, D₈₄) are weakly correlated with transport rates. Analysis of full bedload grain‐size distributions reveals greater structure, with a tendency for transport to become less size selective at higher transport rates. The bedload time series show autoregressive behaviour but are dif?cult to distinguish by this method. State–space plots, and associated measures of time‐series separation, reveal the structure of the time series more clearly. The measured pulses have distinctly different time‐series characteristics from those modelled using a one‐dimensional sediment routing model in which bed shear stress and grain size are varied randomly. These results suggest a mechanism of pulse generation based on irregular low‐amplitude bedforms, that may be generated in‐channel or may represent the advection of material supplied by bank erosion events. Copyright © 2003 John Wiley & Sons, Ltd.     

Flow resistance in steep mountain streams

Resistance to flow at low to moderate stream discharge was examined in five small (12–77 km² drainage area) tributaries of Chilliwack River, British Columbia, more than half of which exhibit planar bed morphology. The resulting data set is composed of eight to 12 individual estimates of the total resistance to flow at 61 cross sections located in 13 separate reaches of five tributaries to the main river. This new data set includes 625 individual estimates of resistance to flow at low to moderate river stage. Resistance to flow in these conditions is high, highly variable and strongly dependent on stage. The Darcy–Weisbach resistance factor (ff) varies over six orders of magnitude (0·29–12 700) and Manning's n varies over three orders of magnitude (0·047–7·95). Despite this extreme range, both power equations at the individual cross sections and Keulegan equations for reach‐averaged values describe the hydraulic relations well. Roughness is divided into grain and form (considered as all non‐grain sources) components. Form roughness is the dominant component, accounting for about 90% of the total roughness of the system (i.e., form roughness is on average 8.6 times as great as grain roughness). Of the various quantitative and qualitative form‐roughness indicators observed, only the sorting coefficient (σ = D₈₄/D₅₀) correlates well with form roughness. Copyright © 2008 John Wiley & Sons, Ltd.     

Channel flow competence and sediment transport in upland streams in southeast Australia

Bedload transport data from planebed and step‐pool reach types are used to determine grain size transport thresholds for selected upland streams in southeast Australia. Morphological differences between the reach types allow the effects of frictional losses from bedforms, microtopography and bed packing to be incorporated into the dimensionless critical shear stress value. Local sediment transport data are also included in a regime model and applied to mountain streams, to investigate whether empirical data improve the delineation of reach types on the basis of dimensionless discharge per unit width (q*) and dimensionless bedload transport (q_b*). Instrumented planebed and step‐pool sites are not competent to transport surface median grains (D_50s) at bankfull discharge (Q_bf). Application of a locally parametrized entrainment equation to the full range of reach types in the study area indicates that the majority of cascades, cascade‐pools, step‐pools and planebeds are also not competent at Q_bf and require a 10 year recurrence interval flood to mobilize their D_50s. Consequently, the hydraulic parameters of the regime diagram, which assume equilibrium conditions at bankfull, are ill suited to these streams and provide a poor basis of channel delineation. Modifying the diagram to better reflect the dominant transported bedload size (equivalent to the D₁₆ of surface sediment) made only slight improvements to reach delineation and had greatest effect on the morphologies with smaller surface grain sizes such as forced pool‐riffles and planebeds. Likewise, the Corey shape factor was incorporated into the regime diagram as an objective method for adjusting a base dimensionless critical shear stress (τ*_c50b) to account for lithologically controlled grain shape on bed packing and entrainment. However, it too provided only minor adjustments to reach type delineation. Copyright © 2007 John Wiley & Sons, Ltd.     

Bedform effect on the reorganization of surface and subsurface grain size distribution in gravel bedded channels

Quantification of river bedform variability and complexity is important for sediment transport modeling as well as for characterization of river morphology. Alluvial bedforms are shown to exhibit highly nonlinear dynamics across a range of scales, affect local bed roughness, and vary with local hydraulic, hydrologic, and geomorphic properties. This paper examines sediment sorting on the crest and trough of gravel bedforms and relates it to bed elevation statistics. The data analysed here are the spatial and temporal series of bed elevation, grain size distribution of surface and subsurface bed materials, and sediment transport rates from flume experiments. We describe surface topography through bedform variability in height and wavelength and multiscale analysis of bed elevations as a function of discharge. We further relate bedform migration to preferential distribution of coarse and fine sediments on the troughs and crests, respectively, measuring directly surface and subsurface grain size distributions, and indirectly the small scale roughness variations as estimated from high resolution topographic scans.     

Dimensionless critical shear stress evaluation from flume experiments using different gravel beds

Flume experiments were conducted using four different gravel beds (D₅₀ + 12–39 mm) and a range of marked particles (10–65 mm). The shear stresses were evaluated from friction velocities, when initial movement of marked particles occurred. Two kinds of equations were produced: first for the threshold of initial movement, and second for generalized movement. Equations of the type 0_c + a(D_i/D₅₀)^b, as proposed by Andrews (1983) are applicable even if the material is relatively well sorted. However, the values of a and b are lower (respectively 0·050 and -0·70) for initial movement. Generalized movement requires a higher shear stress (a + 0·068 and b + -0·80). D₉₀ of the bed material and y₀ (the bed roughness parameter) were also used as reference values in place of D₅₀. They produced lower values than in natural streams, mainly owing to the fact that the material used in the flume is better sorted: clusters are less well developed and the bed roughness is lower.     

Flow modelling in gravel‐bed rivers: rethinking the bottom boundary condition

A key problem in computational fluid dynamics (CFD) modelling of gravel‐bed rivers is the representation of multi‐scale roughness, which spans the range from grain size, through bedforms, to channel topography. These different elements of roughness do not clearly map onto a model mesh and use of simple grain‐scale roughness parameters may create numerical problems. This paper presents CFD simulations for three cases: a plane bed of fine gravel, a plane bed of fine gravel including large, widely‐spaced pebble clusters, and a plane gravel bed with smaller, more frequent, protruding elements. The plane bed of fine gravel is modelled using the conventional wall function approach. The plane bed of fine gravel including large, widely‐spaced pebble clusters is modelled using the wall function coupled with an explicit high‐resolution topographic representation of the pebble clusters. In these cases, the three‐dimensional Reynolds‐averaged continuity and Navier–Stokes equations are solved using the standard k ? ε turbulence model, and model performance is assessed by comparing predicted results with experimental data. For gravel‐bed rivers in the field, it is generally impractical to map the bed topography in sufficient detail to enable the use of an explicit high‐resolution topography. Accordingly, an alternative model based on double‐averaging is developed. Here, the flow calculations are performed by solving the three‐dimensional double‐averaged continuity and Navier‐Stokes equations with the spatially‐averaged 〈k ? ε〉 turbulence model. For the plane bed of fine gravel including large, widely‐spaced pebble clusters, the model performance is assessed by comparing the spatially‐averaged velocity with the experimental data. The case of a plane gravel bed with smaller, more frequent, protruding elements is represented by a series of idealized hypothetical cases. Here, the spatially‐averaged velocity and eddy viscosity are used to investigate the applicability of the model, compared with using the explicit high‐resolution topography. The results show the ability of the model to capture the spatially‐averaged flow field and, thus, illustrate its potential for representing flow processes in natural gravel‐bed rivers. Finally, practical data requirements for implementing such a model for a field example are given. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Controls on at‐a‐station hydraulic geometry in steep headwater streams,Colorado, USA

Detailed hydraulic measurements were made in nine step‐pool, five cascade and one plane‐bed reach in Fraser Experimental Forest, Colorado to better understand at‐a‐station hydraulic geometry (AHG) relations in these channel types. Average values for AHG exponents, m (0·49), f (0·39), and b (0·16), were well within the range found by other researchers working in steep gradient channels. A principal component analysis (PCA) was used to compare the combined variations in all three exponents against five potential control variables: wood, D₈₄, grain‐size distribution (σ), coefficient of variation of pool volume, average roughness‐area (projected wetted area) and bed gradient. The gradient and average roughness‐area were found to be significantly related to the PCA axis scores, indicating that both driving and resisting forces influence the rates of change of velocity, depth and width with discharge. Further analysis of the exponents showed that reaches with m > b + f are most likely dominated by grain resistance and reaches below this value (m < b + f) are dominated by form resistance. Copyright © 2010 John Wiley & Sons, Ltd.     

Relation between flow,surface‐layer armoring and sediment transport in gravel‐bed rivers

This study investigates trends in bed surface and substrate grain sizes in relation to reach‐scale hydraulics using data from more than 100 gravel‐bed stream reaches in Colorado and Utah. Collocated measurements of surface and substrate sediment, bankfull channel geometry and channel slope are used to examine relations between reach‐average shear stress and bed sediment grain size. Slopes at the study sites range from 0·0003 to 0·07; bankfull depths range from 0·2 to 5 m and bankfull widths range from 2 to 200 m. The data show that there is much less variation in the median grain size of the substrate, D_50s, than there is in the median grain size of the surface, D₅₀; the ratio of D₅₀ to D_50s thus decreases from about four in headwater reaches with high shear stress to less than two in downstream reaches with low shear stress. Similar trends are observed in an independent data set obtained from measurements in gravel‐bed streams in Idaho. A conceptual quantitative model is developed on the basis of these observations to track differences in bed load transport through an idealized stream system. The results of the transport model suggest that downstream trends in total bed load flux may vary appreciably, depending on the assumed relation between surface and substrate grain sizes. Copyright © 2007 John Wiley & Sons, Ltd.     

Experimental study on transient and steady‐state dynamics of bedforms in supply limited configuration

The purpose of the present study is to investigate experimentally the development of bedforms in a configuration where the sediment supply is limited. The experimental setup is a rectangular closed duct combining an innovative system to control the rate of sediment supply Q_in , and a digitizing system to measure in real time the 3D bedform topography. We carried out different sets of experiments with two sediment sizes (100 µm and 500 µm) varying both the sediment supply and the water flow rate to obtain a total of 46 different configurations. After a transient phase, steady sub‐centimeter bedforms of various shapes have been observed: barchans dunes, straight transverse dune, linguoid transverse dunes and bedload sheets. Height, spacing, migration speed, and mean bed elevation of the equilibrium bedforms were measured. For a given flow rate, two regimes were identified with fine sediment: (i) a monotonic increasing regime where the equilibrium bedform height and velocity increase with the sediment supply rate Q_in and (ii) an invariant regime for which both parameters are almost independent of Q_in. For coarse sediment, only the first regime is observed. We interpret the saturation of height and velocity for fine sediment bedforms as the transition from a supply‐limited regime to a transport‐limited regime in which the bedload flux has reached its maximum value under the prevailing flow conditions. We also demonstrate that all experiments can be rescaled if the migration speed and height of the bedforms are, respectively, divided and multiplied by the cube of the shear velocity. This normalization is independent of grain size and of bedform morphology. These experimental results provide a new quantification of the factors controlling equilibrium height and migration speed of bedforms in supply‐limited conditions against which theoretical and numerical models can be tested.     

The impact of stress history on bed structure

Recent research has started to focus on how prolonged periods of sub‐threshold flows may be capable of imparting structural changes that contribute to increased bed stability. To date, this effect (termed ‘stress history’) has been found to be significant in acting to increase a bed's critical shear stress at entrainment threshold. However, it is supported by only limited, qualitative and often speculative information on the mechanisms of this stabilization process in grade‐specific studies. As such, this paper uses high resolution laser scanning to quantitatively ascertain the granular mechanics underpinning the relationship between stress history and entrainment threshold for beds of a range of grain size distributions. Employing a bed slope of 1/200, three grain size distributions with median grain sizes (D₅₀) of 4·8 mm [uniform (σ_g = (D₈₄/D₁₆)^0.5 = 1·13; bimodal (σ_g = 2·08); and, unimodal (σ_g = 1·63)] were exposed to antecedent stress histories of 60 and 960 minutes duration. Antecedent shear stress magnitude was set at 50% of the critical shear stress for the D₅₀ when no stress history period was employed. Two laser displacement scans of the bed surface (approximate area 100 mm × 117 mm) were taken, one prior to the antecedent period and one after this period, so that changes to surface topography could be quantified (resolution of x = 0·10 mm, y = 0·13 mm and z = 0·24 mm). Rearrangement of bed surface structure is described using statistical analysis and two‐dimensional (2D) semi‐variograms to analyse scaling behaviour. Results reveal vertical settlement, changes to bed roughness and particle repositioning. However, the bed grain size distribution influences the relative importance of each mechanism in determining stress history induced bed stability; this is the focus of discussion in this paper. Copyright © 2012 John Wiley & Sons, Ltd.     

Effects of rock fragment size and cover on overland flow hydraulics,local turbulence and sediment yield on an erodible soil surface

The interactions between overland flow hydraulics and sediment yield were studied in flume experiments on erodible soil surfaces covered by rock fragments. The high erodibility of a non-cohesive fine sediment (D₅₀ + 0·09mm) permitted the effects of local turbulence and scour on sediment yield to be examined. Overland flow hydraulics and sediment yield were compared for experiments with pebble (D₅₀ + 1·5cm) and cobble (D₅₀ + 8·6cm) rock fragment covers. Cover percentages range from 0 to 99 per cent. Rock fragment size strongly affects the relations between flow hydraulics and rock fragment cover. For pebbles spatially-averaged hydraulic parameters (flow velocity, flow depth, effective flow width, unit discharge, total shear stress, Darcy-Weisbach friction factor, percentage grain friction and grain shear stress) vary most rapidly within cover percentages at low covers (power functions). In contrast, for cobbles these parameters vary most rapidly within cover percentages at high covers (exponential functions). As the type of the function that describes the relation between flow hydraulics and cover percentage can be deduced from the ratio of rock fragment height to flow depth, the continuity equation can be employed to determine the actual coefficients of the functions, provided the regression of one hydraulic parameter (e.g. flow velocity) with cover percentage is known and a good estimate exists for two values of another hydraulic variable for a low and a high cover percentage. The variation of sediment yield with cover percentage is also strongly dependent on rock fragment size, but neither the convex-upward relation for pebbles, nor the positive relation for cobbles can be solely attributed to the spatially averaged hydraulics of sheet-flow. Rock fragments induce local turbulence that leads to scour hole development on the stoss side of the rock fragments while deposition commonly occurs in the wake. This local scour and deposition substantially affects sediment yield. However, scour dimensions cannot be predicted by spatially averaged flow hydraulics. An adjustment of existing scour formulas that predict scour around bridge piers is suggested. Sediment yield from non-cohesive soils might then be estimated by a combination of sediment transport and scour formulas.     

Evolution of grain size distributions and bed mobility during hydrographs in gravel-bed braided rivers

Evolution of bed material mobility and bedload grain size distributions under a range of discharges is rarely observed in braiding gravel-bed rivers. Yet, the changing of bedload grain size distributions with discharge is expected to be different from laterally-stable, threshold, channels on which most gravel bedload theory and observation are based. Here, simultaneous observations of flow, bedload transport rate, and morphological change were made in a physical model of a gravel-bed braided river to document the evolution of grain size distributions and bed mobility over three experimental event hydrographs. Bedload transport rate and grain size distributions were measured from bedload samples collected in sediment baskets. Morphological change was mapped with high-resolution (~1 mm precision) digital elevation models generated from close-range digital photogrammetry. Bedload transport rates were extremely low below a discharge equivalent to ~50% of the channel-forming discharge (dimensionless stream power ~70). Fractional transport rates and plots of grain size distributions indicate that the bed experienced partial mobility at low discharge when the coarsest grains on the bed were immobile, weak selective mobility at higher discharge, and occasionally near-equal mobility at peak channel-forming discharge. The transition to selective mobility and increased bedload transport rates coincided with the lower threshold for morphological change measured by the morphological active depth and active width. Below this threshold discharge, active depths were of the order of D₉₀ and active widths were narrow (< 3% of wetted width). Above this discharge, both increased so that at channel-forming discharge, the active depth had a local maximum of 9D₉₀ while active width was up to 20% of wetted width. The modelled rivers approached equal mobility when rates of morphological change were greatest. Therefore, changes in the morphological active layer with discharge are directly connected to the conditions of bed mobility, and strongly correlated with bedload transport rate. © 2018 John Wiley & Sons, Ltd.     

Microtopographic evolution of mineral surfaces as a tool to identify and date young fault scarps in bedrock

Faulting that results in surface ruptures through bedrock can be particularly difficult to date. For example, stratigraphic control on the age of faulting, based on the age of the bedrock, often leaves unacceptably large uncertainty on the age of the faulting. From a paleoseismological perspective, there is a clear need to determine if a bedrock fault scarp is actually a young feature. For young fault ruptures that create fresh mineral surfaces, analysis of microtopography developed by weathering of the mineral surface may provide a quantifiable method for determining the fault age. The direct quantitative measurement of mineral surface microtopography using Atomic Force Microscopy affords a novel method to study the rupture ages of active faults. The method for using microtopographic evolution of mineral surfaces depends on three conditions. The first condition is that freshly exposed mineral cleavage surfaces, which can be described geometrically as planes, are formed during a rupture event. The formation of these fresh surfaces is analogous to the initiation of a weathering ‘clock’ that defines time t=0. Following cleavage formation dissolution of the planar mineral surface occurs. The rate of dissolution for a mineral species under given climatic conditions, governs the rate of mineral surface alteration. Thus as dissolution proceeds, the roughness of the mineral surface increases. We suggest that the progression of microtopographic roughness over time, which can be estimated by computing quantitative statistics derived from digital mineral surface topography, will systematically vary until a steady state surface topography is reached. The fractal dimension, D_f, is one such measure of surface roughness where, D_f at time t=0 is 2. The dissolution of the mineral surface increases the fractal dimension as the removal of material proceeds. We posit that somewhere between D_f=2 and D_f=3, the microtopography reaches a steady state. Therefore, in the pre-steady state stage of surface roughness, the quantitative measure of roughness of the mineral may serve as a measure of time elapsed since faulting. The period of time this initial stage of surface roughening represents is dependent on the mineral and as a consequence, its dissolution rate, in a specific set of environmental conditions. The time elapsed since fault rupture and grain cleavage can also be estimated from the measurement of the volume of material removed through dissolution. If part of the original cleavage surface remains and can be identified then AFM measurements of the surface microtopography can be used to calculate the dissolved volume per unit area.     

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.     

Threshold of coarse sediment transport in broad and narrow natural streams

The threshold of coarse sediment transport has been examined in natural streambeds in an upland Pennine (U.K.) area. Threshold values of the total boundary shear stress (T₀) (for a given grain size), in a narrow natural stream (W/D < 11) are considerably higher than values of T₀ in a broad stream (W/D > 11). Efficiency in the entrainment process is related not only to the overall channel geometry, but also varies as a function of discharge in channels characterized by compound roughness. Empirical curves relating T₀ and a mean grain size (d ₅) are presented, but are limited in application to streams of similar physical and hydraulic characteristics as the ones examined in this investigation. Considerable divergence is noted between these empirical functions and a summary empirical function for general application obtained from a published source. The reasons for this divergence are discussed. The influence of grain shape was found not to be important in the initiation of motion criterion. This conclusion may reflect the limited range of natural grain shapes in the study streams, but might reasonably apply to other field investigations of similar streams. Modifications of the Shields' and Yalin diagrams are suggested for practical applications in shallow streams with poorly-graded bed material. The Shields' parameter may be regarded as an inverse function of the relative protrusion of individual grains in the shallow flow depth (d ₅/D). The increased importance of augmented drag forces, in the entrainment process in shallow flows, is suggested as the physical explanation for the reduced values of the Shields' parameter. However, the relationships presented should not be applied to laboratory experiments concerned with well-graded sediments (therefore beds with little deviation in level), in which the Shields' parameter may be regarded as constant at high Reynolds' grain numbers. Consistent estimated field values of ?, a threshold sediment transport parameter, might be used to compare field data to threshold values derived from statistical arguments and laboratory experiments reported in the literature.     

Effects of grain-size distribution and shape on sediment bed stability,near-bed flow and bed microstructure

Different studies investigating the stability of mixed sediment have found that the fine fraction can either stabilize or mobilize the bed. This study aims to find where the transition between these two modes occurs for sandy sediment and to identify the underlying (grain-scale) processes. Flume experiments with bimodal sediment were used to investigate near-bed processes of a non-cohesive sediment bed, and in particular how the grain shape and the ratio of different grain sizes influence bed mobility. Medium sand (D_50,c ≈ 400 μm) was mixed with 40 % fine material of different diameters (D_50,f = 53; 111; 193 μm) and subjected to increasing flow velocities (U = 1.3–22.2 cm s^-1). The bed mobility (i.e. the change of the bed level over time), turbidity and near-bed hydrodynamics were analysed. Selected results were compared with similar previous experiments with spherical glass beads. The findings indicate that, due to the complex grain shapes of natural sediment, a sand bed is more stable than a bed composed of glass beads. The grain-size ratio RD = D_c /D_f between the coarse and fine grain diameters controls whether the mixed bed is stabilized or mobilized by the presence of fines, with the transition between the modes occurring at RD = 4–5.5. Mixed beds with a very low RD < 2 behave like a unimodal bed. The results suggest that RD and grain shape influence bed roughness, near-bed flow, bed microstructure and the flow into and through the upper bed layers, which subsequently governs bed mobility. The interplay between all these processes can explain the transition between the stabilizing effect (high RD, small pore space) and the mobilizing effect (low RD, large pore space) of a fine fraction in a grain-size mixture. © 2018 John Wiley & Sons, Ltd.     

Grain size and topographical differences between static and mobile armour layers

A series of laboratory flume experiments under conditions of sediment starvation (zero sediment feeding) and recirculation were conducted in order to identify the temporal evolution and surface properties of static and mobile armour layers. The experiments were carried out in an 8 m long flume using a bimodal grain‐size mixture (D₅₀ = 6·2 mm) and a range of shear stresses ranging from 4·0 to 8·6 N m^–2. The results confirm that a static armour layer is coarser than a mobile one, and that the grain size of a mobile armour layer is rather insensitive to changes in the imposed flow strength. An analysis of laser scan bed surveys revealed the highly structured and imbricated nature of the static armour layer. Under these conditions the vertical roughness length scale of the bed diminished and it became topographically less complex at higher forming discharges. The topography of mobile armour layers created by rising discharges differed. They exhibited a greater roughness length scale and were less organized, despite the fact that the grain size of the surface material maintained an approximately constant value during recirculation. Also, the mobile armour tended to create larger cluster structures than static armour layers when formed by higher discharges. These differences were mainly due to the transport of the coarser fraction of bed sediments, which diminished to zero over the static armour because of being hidden within the bed, whereas in the mobile armour the coarser particles protruded into the flow and were actively transported, increasing the vertical roughness length scale. Overall, the results show that an examination of the grain size characteristics of armour layers cannot be used to infer sediment mobility and bed roughness. Detailed elevation models of exposed surfaces of gravel‐bed rivers are required to provide critical insight on the sediment availability and sedimentation processes. Copyright © 2011 John Wiley & Sons, Ltd.     

Sediment transport in high‐speed flows over a fixed bed: 2. Particle impacts and abrasion prediction

Single bed load particle impacts were experimentally investigated in supercritical open channel flow over a fixed planar bed of low relative roughness height simulating high‐gradient non‐alluvial mountain streams as well as hydraulic structures. Particle impact characteristics (impact velocity, impact angle, Stokes number, restitution and dynamic friction coefficients) were determined for a wide range of hydraulic parameters and particle properties. Particle impact velocity scaled with the particle velocity, and the vertical particle impact velocity increased with excess transport stage. Particle impact and rebound angles were low and decreased with transport stage. Analysis of the particle impacts with the bed revealed almost no viscous damping effects with high normal restitution coefficients exceeding unity. The normal and resultant Stokes numbers were high and above critical thresholds for viscous damping. These results are attributed to the coherent turbulent structures near the wall region, i.e. bursting motion with ejection and sweep events responsible for turbulence generation and particle transport. The tangential restitution coefficients were slightly below unity and the dynamic friction coefficients were lower than for alluvial bed data, revealing that only a small amount of horizontal energy was transferred to the bed. The abrasion prediction model formed by Sklar and Dietrich in 2004 was revised based on the new equations on vertical impact velocity and hop length covering various bed configurations. The abrasion coefficient k_v was found to be vary around k_v ~ 10⁵ for hard materials (tensile strength f_t > 1 MPa), one order of magnitude lower than the value assumed so far for Sklar and Dietrich's model. Copyright © 2017 John Wiley & Sons, Ltd.