Rates of aerodynamic entrainment in a developing boundary layer

Despite its significance for inception of grain transport by wind, the initial dislodgement of grains from a static surface by aerodynamic forces of drag and lift in the absence of grain collision has received little attention. This paper describes a series of wind-tunnel experiments in which the erosion of narrow strips of loose grains from the roughened surface of a flat plate exposed to a range of wind speeds was examined. The progressive downwind development of the boundary layer over the plate provided a range of airflow conditions which permitted systematic evaluation of grain entrainment rates arising from purely aerodynamic forces. Use of closely graded size fractions in flat, single grain layers resting on identical, fixed grain support eliminated the effects of surface irregularities and impacts from saltation. Results show that erosion of strips of loose grains develops with time according to an inverse exponential function in which the entrainment rate time constant relates to Shields dimensionless shear stress function. An empirical expression defining aerodynamic entrainment rate in terms of rate of strip erosion is derived and comparisons are made between present and published data. The need for additional data to resolve several questions raised by the present investigation is stressed. In addition, a simple, objective technique for accurate determination of the aerodynamic entrainment threshold of any loose, granular sediment is proposed.     

Measurements of sand transport by wind on a natural beach

Bagnold's (1954) and Kawamura's (1951) formulae may be used for the calculation of the sand movement on a natural beach, provided the shear stress velocity U_* > 0·D4 m/s. Great discrepancies have been found between calculated and measured sand transport rates for U_* < 0·D4 m/s, mainly because of the capillary forces acting on a wet beach. The measured critical shear velocity U_*c at the beginning of sand movement on a clean dry beach agrees very well with that predicted by Bagnold's formula. On a dry beach where the sand grains are stuck together, U_*c was found to be about 10% higher. On a wet beach U_*c appeared to depend on the moisture content of the surface layer. Grain size is a determining parameter in the U_*c-moisture content relation. When the angle a between the wind direction at sea and the dune face is between 15° and 85° the streamlines of the wind will bend in the vicinity of the dune face. In consequence this may influence the direction of sediment movement.     

Aerodynamic grain‐size distribution of blown sand

Aeolian sand entrainment, saltation and deposition are important and closely related near surface processes. Determining how grains are sorted by wind requires a detailed understanding of how aerodynamic sand transport processes vary within the saltating layer with height above the bed. Grain‐size distribution of sand throughout the saltation layer and, in particular, how the associated flux of different grain size changes with variation in wind velocity, remain unclear. In the present study, a blowdown wind tunnel with a 50 cm thick boundary layer was used to investigate saltating sand grains by analyzing the weight percentage and transport flux of different grain‐size fractions and the mean grain size at different wind velocities. It was found that mean grain size decreases with height above the sand bed before undergoing a reversal. The height of the reversal point ranges from 4 to 40 cm, and increases with wind velocity following a non‐linear relationship. The content of the finer fractions (very fine and fine sand) initially increases above the sand bed and then decreases slightly with height, whereas that of the coarser fractions (medium and coarse sand) exhibits the opposite trend. The content of coarser grains and the mean grain size of sand in the saltation layer increase with wind velocity, indicating erosional selectivity with respect to grains in multi‐sized sand beds; but this size selectivity decreases with increasing wind velocity. The vertical mass flux structure of fine sand and very fine sand does not obey a general exponential decay pattern under strong wind conditions; and the coarser the sand grain, the greater the decrease rate of their transport mass with height. The results of these experiments suggest that the grain‐size distribution of a saltating sand cloud is governed by both wind velocity and height within the near‐surface boundary layer.     

Steady state saltation in air

Coupled equations of motion for steady state saltation over an infinite plane are derived and solved for a simplified model of the grain-surface impact process. Experimentally observed features of the wind velocity profile in saltation are qualitatively reproduced, including a diminution of the sub-saltation layer mean wind speed, as the friction speed increases. In this model the surface impact velocity of the saltating grains remains relatively constant over a wide range of free-stream shear stresses, and the grain mass flux increases with friction speed u_f* less rapidly than u_f³.     

Experimental study of sand streaks formed in turbulent boundary layers

Fine- to medium-grained sand transported as bedload moves in lanes parallel to the flow that are thought to be preserved as parting lineation. A series of six flume experiments was designed to discover the morphology and spacing of these lanes, here called sand streaks, as functions of local shear velocity, U* (9 × 10^-3 to 4.8 × 10^-2 m s^-1), depth (5 × 10^-2 and 9.5 × 10^-2 m), mean grain diameter (150, 200, 290, 1380 μm), and sediment bedload concentration (0.0–0.39). Low U* flows produce predominantly straight, non-intersecting sand streaks, moderate U* flows produce sub-parallel and en échelon sand streaks, and moderate to high U* flows produce wavy sand streaks and secondary streaks with a spacing an order of magnitude larger. The wavy sand streaks are thought to be composed of sand grains in suspension close to the bed. An upper grain-size limit for the sand streak structure occurs at a grain size between 290 and 1380μm. The spacings of the fine-and medium-grained sand streaks, at low to moderate U* (0.9 × 10^-2 to 3 × 10^-2m s^-1), are similar to those predicted for low-speed fluid streaks, although the fine-grained sand forms more closely-spaced streaks than the medium-grained sand. The spacings of sand streaks formed at moderate to high U* and at bedload concentrations greater than 0.15, are wider than those predicted for the low-speed fluid streaks. The wider spacing is thought to reflect a new type of flow immediately above the moving bed layer in which the formation of low-speed streaks is inhibited. This results from an increase in either grain concentration or grain size. The spacing of parting lineation, also wider than that predicted for low-speed streaks, may reflect this.     

Influence of the saffman force,lift force,and electric force on sand grain transport in a wind–sand flow

Quasi-horizontal trajectories of salting sand grains were found using high-speed video-recording in the desertified territory of the Astrakhan region. The sizes and displacement velocities of the saltating sand grains were determined. A piecewise logarithmic approximation of the wind profile in a quasi-stationary wind–sand flow is suggested, which is consistent with the data of observations and modeling. It was established that, in the regime of stationary saltation, the wind profile in the lower saltation layer of the wind–sand flow depends only slightly on the wind profile variations in the upper saltation layer. The vertical profiles of the horizontal wind component gradient in a quasi-stationary wind–sand flow were calculated and plotted. It was shown using high-speed video recording of the trajectory of a sand grain with an approximate diameter of 95 μm that the weightlessness condition in the desertified territory of the Astrakhan region in a stationary wind–sand flow is satisfied at a height of approximately 0.15 mm. The electric parameters of a wind–sand flow, which can provide for compensation of the force of gravity by the electric force, were estimated. In particular, if the specific charge of a sand grain is 100 μC/kg, the force of gravity applied to the sand grain can be compensated by the electric force if the vertical component of the electric field in a wind–sand flow reaches approximately 100 kV/m. It was shown that the quasi-horizontal transport of sand grains in the lower millimeter saltation layer observed in the desertified territory can be explained by the joint action of the aerodynamic drag, the force of gravity, the Saffman force, the lift force, and the electric force.     

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.     

Characteristics of particle size for creeping and saltating sand grains in aeolian transport

Creep and saltation are the primary modes of surface transport involved in the fluid‐like movement of aeolian sands. Although numerous studies have focused on saltation, few studies have focused on creep, primarily because of the experimental difficulty and the limited amount of theoretical information available on this process. Grain size and its distribution characteristics are key controls on the modes of sand movement and their transport masses. Based on a series of wind tunnel experiments, this paper presents new data regarding the saltation flux, obtained using a flat sampler, and on the creeping mass, obtained using a specifically designed bed trap, associated with four friction velocities (0·41, 0·47, 0·55 and 0·61 m sec^?1). These data yielded information regarding creeping and saltating sand grains and their particle size characteristics at various heights, which led to the following conclusions: (i) the creeping masses increased as a power function (q = ?1·02 + 14·19u_*³) of friction wind velocities, with a correlation (R²) of 0·95; (ii) the flux of aeolian sand flow decreases exponentially with increasing height (q = a exp(–z/b)) and increases as a power function (q = ?26·30 + 428·40 u_*³) of the friction wind velocity; (iii) the particle size of creeping sand grains is ca 1·15 times of the mean diameter of salting sand grains at a height of 0 to 2 cm, which is 1·14 times of the mean diameter of sand grains in a bed; and (iv) the mean diameter of saltating sand grains decreases rapidly with increasing height whereas, while at a given height, the mean diameter of saltating sand grains is positively correlated with the friction wind velocity. Although these results require additional experimental validation, they provide new information for modelling of aeolian sand transport processes.     

Pivoting analyses of the selective entrainment of sediments by shape and size with application to gravel threshold

Measured variations of pivoting angles with grain size, shape (‘reliability’ and angularity) and imbrication are employed in analyses of grain threshold to examine how these factors influence selective grain entrainment and sorting. With a bed of uniform grain sizes, as employed experimentally to establish the standard threshold curves such as that of Shields, the threshold condition depends on grain shape and fabric. The analysis demonstrates quantitatively that there should be a series of nearly-parallel threshold curves depending on grain pivoting angles. For a given grain size, the order of increasing flow strength required for entrainment is spheres, smooth ellipsoids (depending on their ‘reliability’), angular grains, and imbricated ellipsoids (depending on their imbrication angles). The relative threshold values for these different grain shapes and fabric are predicted according to their respective pivoting angles, but remain to be directly tested by actual threshold measurements. The pivoting angle of a grain also depends on the ratio of its size to those it rests upon. This dependence permits an evaluation of selective entrainment by size of grains from a bed of mixed sizes, the condition generally found in natural sediments. The pivoting model predicts systematic departures from the standard threshold curves for uniform grain sizes. Such departures have been found in recent studies of gravel threshold in rivers and offshore tidal currents. The pivoting model is compared with those threshold data with reasonable agreement. However, more controlled measurements are required for a satisfactory test of the model. It is concluded that variations in pivoting angles for grain entrainment are significant to the processes of selective sorting by grain size and shape.     

The stability of a remediated bed in Hamilton Harbour,Lake Ontario,Canada

ABSTRACT In situ measurements of lakebed sediment erodibility were made on three sites in Hamilton Harbour, Lake Ontario, using the benthic flume Sea Carousel. Three methods of estimating the surface erosion threshold (τ_c(0)) from a Carousel time series were evaluated: the first method fits measures of bed strength to eroded depth (the failure envelope) and evaluates threshold as the surface intercept; the second method regresses mean erosion rate (E_m) with bed shear stress and solves for the floc erosion rate (E_f) to derive the threshold for E_m = E_f = 1 × 10^?5 kg m^?2 s^?1; the third method extrapolates a regression of suspended sediment concentration (S) and fluid transmitted bed shear stress (τ₀) to ambient concentrations. The first field site was undisturbed (C) and acted as a control; the second (W) was disturbed through ploughing and water injection as part of lakebed treatment, whereas the third site (OIP) was disturbed and injected with an oxidant used for remediation of contaminated sediment. The main objectives of this study were: (1) to evaluate the three different methods of deriving erosion threshold; (2) to compare the physical behaviour of lacustrine sediments with their marine estuarine counterparts; and (3) to examine the effects of ploughing and chemical treatment of contaminated sediment on bed stability. Five deployments of Sea Carousel were carried out at the control site. Mean erosion thresholds for the three methods were: τ_c(0) = 0·5 (±0·06), 0·27 (±0·01) and 0·34 (±0·03) Pa respectively. Method 1 overpredicted bed strength as it was insensitive to effects in the surface 1–2 mm, and the fit of the failure envelope was also highly subjective. Method 2 exhibited a wide scatter in the data (low correlation coefficients), and definition of the baseline erosion rate (E_f) is largely arbitrary in the literature. Method 3 yielded stable (high correlation coefficients), reproducible and objective results and is thus recommended for evaluation of the erosion threshold. The results of this method correlated well with sediment bulk density and followed the same trend as marine counterparts from widely varying sites. Mass settling rates, expressed as a decay constant, k, of S(t), were strongly related to the maximum turbidity at the onset of settling (S_max) and were also in continuity with marine counterparts. Thus, it appears that differences in salinity had little effect on mass settling rates in the examples presented, and that biological activity dominated any effects normally attributable to changes in salinity. Bedload transport of eroded aggregates (2–4 mm in diameter) took place by rolling below a mean tangential flow velocity (U_y) of 0·32 ms^?1 and by saltation at higher velocities. Mass transport as bedload was a maximum at U_y = 0·4 ms^?1, although bedload never exceeded 1% of the suspended load. The proportion of material moving as bedload was greatest at the onset of erosion but decreased as flow competence increased. Given the low bulk density and strength of the lakebed sediment, the presence of a bedload component is notable. Bedload transport over eroding cohesive substrates should be greater in estuaries, where both sediment density and strength are usually higher. Significant differences between the ploughed and control sites were apparent in both the erosion rate and the friction coefficient (φ), and suggest that bed recovery after disruption is rapid (< 24 h). τ_c(0) increased linearly with time after ploughing and recovered to the control mean value within 3 days. The friction coefficient was reduced to zero by ploughing (diagnostic of fluidization), but increased linearly with time, regaining control values within 6 days. No long‐term reduction in bed strength due to remediation was apparent.     

Threshold of sediment motion under unidirectional currents

Carefully selected data for the threshold of sediment movement under unidirectional flow conditions have been utilized to re-examine the various empirical curves that are commonly employed to predict this threshold. After a review of the existing data, we employed only that data obtained from open channel flumes with parallel sidewalls where flows were uniform and steady over flattened beds of unigranular, rounded sediments. Without these restrictions, an unmanageable amount of scatter is introduced. This selected data is used to develop a modified Shields-type threshold diagram that extends the limits of the original diagram by three orders of magnitude in the grain-Reynolds number. The equally general but more easily employed Yalin diagram for sediment threshold is also examined. Although the Shields and Yalin diagrams are general in that they apply to a wide range of different liquids, in both cases somewhat different curves are obtained for threshold under air than for the liquids. The often used empirical curves of the friction velocity u_*, the velocity 100 cm above the bed u₁₀₀, the bottom stress θ_t, and Shields’ relative stress θ_t, all versus the grain diameter D, are limited in their ranges of application to certain combinations of grain density, fluid density, fluid viscosity and gravity. These conditions must be selected before the curves are generated from either the more general Shields or Yalin curves. For example, on the basis of the data selected for use in this paper, empirical threshold relationships for quartz density material in water are where the velocity u₁₀₀ measured 100 cm above the sediment bed is given in cm/sec and the grain diameter D is in cm. The limitations on any of the threshold relationships are severe. These limitations should be properly understood so that the empirical curves and relationships are not improperly employed.     

Continual erosion of bare rocks after the Wenchuan earthquake and control strategies

The newly bared rocks created by the Wenchuan earthquake are undergoing continual intensive erosion in the form of detachment and movement of individual grains. Grain erosion is defined as the phenomenon of breaking down bare rocks under the action of insolation and temperature change, detachment of grains from the rockwalls by wind, flow down of grains on the slope under the action of gravity, and accumulation of grains at the toe of the mountain, forming a deposit fan. The Wenchuan earthquake, which occurred in Sichuan on May 12, 2008, caused thousands of avalanches and landslides and left scars on slopes and a huge area of bare rocks. Grain erosion causes flying stones, injured humans and resulted in numerous slope debris flows. The process of grain erosion and strategies to limit the erosion were studied by field investigations and field experiments. According to these field investigations and field studies, the most serious grain erosion occurs in spring and early summer when it is very dry. Rocks are broken down to grains under the action of insolation and temperature change. Then, wind blows the grains from the bare rock down slope. Experimental results showed that the amount of grains blown down by wind per area of rock surface per unit time is proportional to the fourth power of the wind speed. However, the size of the grains blown down by wind increases linearly with the wind speed. An experiment proved that grain erosion can be controlled with two moss species. Moss spores were mixed with clay suspension and splashed on bare rocks. The moss species germinated on the rock surface in one month and greened the bare rocks in two months. The moss layer protected the rocks from insolation and mitigated the effects of temperature change, thus effectively mitigated grain erosion.     

The initiation of particle movement by wind

When air blows across the surface of dry, loose sand, a critical shear velocity (fluid threshold, ut), must be achieved to initiate motion. However, since most natural sediments consist of a range of grain sizes, fluid threshold for any sediment cannot be defined by a finite value but should be viewed as a threshold range which is a function of the size, shape, sorting and packing of the surface sediment. In order to investigate the initiation of particle movement by wind a series of wind-tunnel tests was carried out on a range of pre-screened fluvial sands and commercially available glass beads with differing mean sizes and sorting characteristics. A sensitive laser-monitoring system was used in conjunction with a high speed counter to detect initial grain motion and to count individual grain movements. Test results indicate that when velocity is slowly increased over the sediment surface the smaller or more exposed grains are first entrained by the fluid drag and lift forces either in surface creep (rolling) or in saltation (bouncing or hopping downwind). As velocity continues to rise, larger or less exposed grains may also be moved by fluid drag. On striking the surface saltating grains impart momentum to stationary grains. This impact may result in the rebound of the original grain as well as the ejection of one or more stationary grains into the air stream at shear velocities lower than that required to entrain a stationary particle by direct fluid pressure. As a result, there is a cascade effect with a few grains of varying size initially moving over a range of shear velocities (the fluid threshold range) and setting in motion a rapidly increasing number of grains. Results of the tests showed that the progression from fluid to dynamic threshold, based on grain movement, can be characterized by a power function, the coefficients of which are directly related to the mean size and sorting characteristics of the sediment.     

Fine particle deposition to initially starved,stationary, planar beds

Reported here are results from new flume experiments examining deposition and entrainment of inert, silt‐sized particles (with spherical diameters in the range from 20 to 60 μm) to and from planar, impermeable and initially starved beds underlying channel flows. Bed surfaces comprised smooth or fixed sand‐size granular roughness and provided hydraulically smooth to transitionally rough boundaries. Results of these experiments were analysed with a simple model that describes the evolution of vertically averaged concentration of suspended sediment and accommodates the simultaneous delivery to and entrainment of grains from the bed. The rate of particle arrival to a bed diminishes linearly, and the rate of particle entrainment increases by the 5/2 power, as the value of the dimensionless Saffman parameter S = u_*³/g’ν approaches a threshold value of order unity, where u is the conventional friction velocity of the turbulent channel flow, g’ is the acceleration due to gravity adjusted for the submerged buoyancy of individual particles and ν is the kinematic viscosity of the transporting fluid. This transport behaviour is consistent with the notion that non‐cohesive, silt‐sized particles can neither reach nor remain on an impermeable bed under flow conditions where mean lift imposed on stationary particles in the viscous sublayer equals or exceeds the submerged weight of individual particles. Within the size range of particles used in these experiments, particle size and the characteristic size of granular roughness, up to that of medium sand, did not affect rates of dimensionless arrival or entrainment to a significant degree. Instead, a new but consistent picture of fine‐particle transport is emerging. Silt‐sized material, at least, is subject to potentially significant interaction with the bed during intermittent suspension transport at intermediate flow speeds greater than the value required for initiation of transport (ca 20 cm sec^?1) but less than the value (ca 50 cm sec^?1) required by the Saffman criterion ensuring transport in fully passive suspension or, equivalently, ‘wash‐load’.     

Particle trapping in stratified estuaries: Application to observations

Estuarine turbidity maxima (ETM) retain suspended particulate matter (SPM) through advection, settling, aggregation, and nonlinearities in bed processes, but the relative importance of these processes varies strongly between systems. Observations from two strongly advective systems (the Columbia and Fraser Rivers) are used to investigate seasonal cycles of SPM retention and the effects of very high flows. Results for the Fraser and Columbia plus literature values for 13 other estuaries illustrate the applicability of scaling parameters and the response of ETM phenomena to a range of river flow (U _r ) levels and tidal forcing. The most efficient trapping (represented by Trapping EfficiencyE, the ratio of maximum ETM concentration to the source SPM concentration) occurs for low ratios of river flow to tidal current amplitude (U_T), represented by low values of the Supply number S_r.E in the Columbia is found to be maximal in a null zone where advection or tidal asymmetry (represented by Advection numberA) is weak(A ∼ 0). The ratio of aggregation to disaggregation (the Floc number Θ) is maximal on neap tides, while the ratio of erosion to deposition (the Erosion number P) is maximal on spring tides. The ratio of settling velocity to vertical mixing (Rouse numberP) is relatively constant in the Columbia ETM(P ∼ 0.7), because particle settling velocity and turbulence levels adjust together. Assuming that this result applies broadly, scaling variables and data are combined to express ETM properties in terms of the friction velocity (U_*),U _r , andU _T , allowing a considerable simplification of the parameters used to describe ETM.     

Air density effects on aeolian sand movement: Implications for sediment transport and sand control in regions with extreme altitudes or temperatures

Aeolian sand transport results from interactions between the ground surface and airflow. Previous research has focused on the effects on sand entrainment and mass transport of surface features and wind velocity, but the influence of air density, which strongly constrains airflow characteristics and the resulting sand flow, has not been widely considered. In the present study, entrainment, saltation characteristics and transport rates were examined at nine experimental sites ranging in elevation from ?154 m below sea‐level (Aiding Lake) to 5076 m above sea‐level (Tanggula Mountain pass on the Qinghai–Tibetan plateau). At each site, a portable wind tunnel and high‐speed camera system were set up, and the friction wind velocity, threshold friction velocity and sand flow structure were observed systematically. For a given volumetric airflow, lower air density increases the wind velocity. Low air density also creates a high threshold friction velocity. The Bagnold wind erosion threshold model remains valid, but the value of empirical parameter A decreased with decreasing air density and ranged from 0·10 to 0·07, the smallest values reported in the literature. For a given wind velocity, increased altitude reduced total sand transport and creeping, but the saltation rate and saltation height increased. The present results provide insights into the fundamental mechanisms of the initiation and transport of sand by wind in regions with an extreme temperature or altitude (for example, alpine deserts and low‐lying lake basins) or on other planets, including Mars. These results also provide theoretical support for improved sand‐control engineering measures. The data and empirical equations provided in this paper improve the ability to estimate threshold and transport conditions for wind‐blown sand.     

Applications of grain-pivoting and sliding analyses to selective entrapment of gravel and to flow-competence evaluations

Models of sediment threshold by grain pivoting or sliding over underlying particles are examined in order to explore their application to evaluations of selective entrainment of gravel by flowing water. Of special interest is whether such process-based models provide satisfactory evaluations of flow competence and the movement of large clasts by floods. A detailed derivation is undertaken, focusing first on the fluid flow and forces at the particle level. The resulting threshold equation for the particle-level velocity is then modified to yield the mean entrainment stress for the flow as a whole. This approach is appropriate for considerations of selective entrainment of grains of varying sizes within a deposit, the sorting being due to their relative projection distances above the bed and the dependence of their pivoting angles on grain size and shape. The resulting threshold equations contain a number of coefficients (e.g. drag and lift) whose values are poorly known, but can be constrained by requiring agreement with the Shields curve for the threshold of grains in uniform deposits. If pivoting coefficients based on laboratory measurements with tetrahedral arrangements of particles are used in the models, smaller degrees of selective sorting are predicted than found in the field measurements of gravel entrainment. However, if reasonable modifications of those coefficients are made for expected field conditions, then the models yield good agreement with the data. Sliding models, where sorting is due entirely to projection distances of the grains above the bed, yield somewhat poorer agreement with the field data; however, the sliding models may have support from laboratory experiments on gravel entrainment in that the data and theoretical curves have similar concave trends. The existing measurements lack documentation of the mechanisms of grain movement, so it is not possible to conclusively determine the relative importance of grain pivoting versus sliding. In spite of such uncertainties, the results are encouraging and it is concluded that pivoting and sliding models for grain entrainment do have potential for field computations of selective entrainment and flow competence.     

A comparison between Shields' threshold criterion and the movement of loosely packed gravel in a tidal channel

Observations of the threshold of movement of loosely packed gravel in a tidal current are described. For gravel with equivalent ‘spherical’ diameters D in the range 0.2 ?D? 5.0cm the critical friction velocity u*_c, corresponding to the initiation of sediment transport, is given by u*_c=7.0 D^0.2. At large values of D within the quoted range, the value u*_c is significantly lower than would be obtained by a Shields experiment (u*_c∞D^0.5). By comparing our values of u*_c with those obtained under well-controlled laboratory conditions, the discrepancy with Shields is shown to be due to the open spacing between, and exposure of, individual pebbles on the seabed. By comparing our results with those from upland gravel streams and flume experiments, it is suggested that Shields assumed an excessively large water depth to particle size ratio as a constraint within which the critical sediment entrainment number 0_c is valid.