Particle dislodgement from a flat sand bed by wind

The rate, with respect to area and time, at which grains are dislodged from a sand bed for given wind conditions is an important factor in determining the grain transport rate and the intensity of grain activity in each of the transport modes. The literature of the subject contains little direct information about particle dislodgement. The paper describes a series of experiments in which dyed sand grains, spread on the surface of quartz dune sand in a wind-tunnel, were photographed at five second intervals while the sand was exposed to wind. The data on rate of loss of coloured grains was used, for two of three chosen size fractions, to deduce the dislodgement rate for each size fraction. The variation of this dislodgement rate with shear velocity is shown graphically for values of u_* between 24 cm s^?1 and 50 cm s^?1. Because of the artificial method of distribution of the coloured sand grains, the results should be applied with caution to natural conditions. The interpretation of the observations of dyed grain loss involved the numerical simulation of the process which comprises removal of coloured grains, slightly offset by replenishment as upwind coloured grains settle briefly in the observed zone. An estimation of grain excursion length has to be incorporated in the simulation. This estimation was made by trial, but general corroboration was found from earlier work. Comparisons are made between dislodgement rates obtained thus and rates estimated by Anderson (1986) and by Jensen and Sorensen (1986). Reasonable agreement with the latter is found in the u_* range 30 cm s^?1.     

Sand transport measurements in Chioggia inlet,Venice lagoon: Theory versus observations

This paper presents results of recent measurements of sand transport made in Chioggia inlet as part of an extensive monitoring programme in the Venetian inlets. Measurements were made in order: (1) to define a relationship between sand transport magnitude and tidal flow; (2) to derive the thresholds for sand transport; (3) to identify the dominant modes of transport; (4) to evaluate the concentration profiles of sand within the benthic boundary layer; (5) to compare bedload transport observations with model predictions using existent bedload formulae; and (6) to produce yearly estimates of bedload transport across the inlet. The vertical distribution of sand in the water column was sampled using modified Helley–Smith bedload samplers at three sites. Transport was found to vary according to the flow and bed grain size, with considerable temporal and spatial variability. A difference of up to three orders of magnitude in transport was observed through the inlet, with higher transport rates measured on the seaward part. The dominant mode of transport in the central inlet was suspension, while bedload was dominant in the mouths. The measured profiles of sand concentration varied with the tidal stage and seabed grain size according to the Rouse parameter (R). R was high at the inlet mouths (1<R<2), indicative of a well-developed bedload layer. The inverse movability number (W_s/U_*) was also higher at these sites and appeared to be grain size dependant. Formulae for bedload transport were tested against field data; stochastic methods such as Einstein–Brown, Engelund–Hansen and Van Rijn produce the best fits. The coupled model SHYFEM-Sedtrans05 appears to simulate well observed transport for most conditions of flow. Long-term bedload predictions indicate a dominant export of sand, with a yearly average of 4500 m³.     

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.     

A wind tunnel investigation of the influences of fetch length on the flux profile of a sand cloud blowing over a gravel surface

Wind tunnel tests were conducted to examine the fetch effect of a gravel surface on the ?ux pro?le of the sand cloud blowing over it using typical dune sand. The results suggest that the ?ux pro?le of blown sand over a gravel surface differs from that over a sandy surface and is characterized by a peak ?ux at a height above the surface while that over a sandy surface decreases exponentially with height. The ?ux pro?le of a sand cloud over a gravel surface can be expressed by a Gaussian peak function: q = a + b exp (?0·5((h ? c)/d)²), where q is the sand transport rate at height h, and a, b, c and d are regression coef?cients. The signi?cance of the coef?cients in the function could be de?ned in accordance with the fetch length of the gravel surface and wind velocity. Coef?cient c represents the peak ?ux height and increases with both wind velocity and fetch length, implying that the peak ?ux height is related to the bounce height of the particles in the blowing sand cloud. Coef?cient d shows a tendency to increase with both wind velocity and fetch length. The sum of a and b, representing the peak ?ux, increases with wind velocity but decreases with fetch length. The average saltation height derived from the cumulative percentage curve shows a tendency to increase with both the fetch length and wind velocity. For any fetch length of a gravel surface the sand transport equation is expressed as Q = C(1 ? U_t/U)(ρ/g)U³, where Q is the sand transport rate, U is the wind velocity, U_t is the threshold velocity measured at the same height as U, g is the gravitational acceleration, ρ is the air density, C is a proportionality coef?cient that decreases with the fetch length of the gravel surface. At a given wind velocity, the sand transport rate over a gravel surface is only 52–68 per cent of that over a sandy surface. The ?ux rate in true creep over a gravel surface increases with wind velocity but decreases with the fetch length, whereas the creep proportion (the ratio of creep ?ux to the sand transport rate) decreases with both the wind velocity and fetch length. Two‐variable (including fetch length and wind velocity) equations were developed to predict the peak ?ux height, average saltation height and transport rate. Copyright © 2004 John Wiley & Sons, Ltd.     

Field observations of the vertical distribution of sand transport characteristics over fine,medium and coarse sand surfaces

The vertical distribution of sand transport characteristics is an important issue in aeolian research. Surface characteristics affect sand transport processes, but their effects are not yet fully understood. To provide more data on this subject, we observed sand transport in 16 field experiments above surfaces covered by fine, medium and coarse sand. The sand transport rate over relatively coarser‐grained medium and coarse surfaces could be expressed as a Gaussian peak function: q _z = a + b exp (?0.5[(|z – C _h|)/d ]^e), where q _z is the measured sediment transport at height z above the bed and a , b , C _h, d , and e are regression coefficients. The measured sand transport flux peak values (H _h) were linearly related to C _h, and both values were significantly related to the mean surface grain size. However, for the relatively finer‐grained medium and fine sand surfaces, the sediment transport could be expressed as an exponential function. The cumulative sand transport below 0.1 m was directly related to the mean surface grain size, and the relationship could be expressed as the following exponential function: C _z = f + g exp –M _z/i , where C _z is the cumulative sand transport at height z above the bed, M _z is the mean grain size and f , g , and i are regression coefficients. Above 0.1 m, there were no significant relationships between the cumulative sand transport and the mean surface grain size. The mean grain size decreased with increasing height below the peak height and then increased with increasing height. The surface grain size distribution and proportions of the particles in different grain size categories controlled the mean grain size as a function of height. The observed changes in the sand transport rate and grain size with height will provide support for sand disaster mitigation, numerical modelling and studies of dune formation. Copyright © 2016 John Wiley & Sons, Ltd.     

Splash detachment of sand particles under varying contact stress field of wind-driven raindrop impact

The effects of wind-driven rain (WDR) on sand detachment were studied under various raindrop obliquities. Results suggested a significant reduction in compressive stress on sand surfaces for a two-dimensional experimental set-up in a wind tunnel. During experiments, sand particles in splash cups were exposed to both wind-free rain (WFR) and WDR driven by horizontal winds of 6.4, 8.9 and 12.8 m s⁻¹ and rainfall intensities of 50, 60, 75 and 90-mm h⁻¹ to assess the sand detachment rate (D, in g m⁻² s⁻¹). The effects of sand moisture state (dry and wet) on the detachment of different-sized particles (0.20–0.50 and 0.50–2.00 mm, respectively) were also tested. Factorial analysis of variance showed that shear and compressive stress components evaluated by horizontal and vertical kinetic energy flux terms (KE_x and KE_y, respectively, in J m⁻² s⁻¹) along with their vector sum (KE_r, in J m⁻² s⁻¹) explained the variation in D. Neither sand size nor sand moisture was statistically significant alone although binary interactions of KE_r, KE_x and KE_y with the sand size and three-way interaction of KE_x, sand size and moisture were statistically significant. These results can be explained by size-dependent variation in sand compressibility and surface friction related to the total stress field developed by a given partition of shear and compressive stresses of wind-driven oblique raindrops (KE_x/KE_y). Further analysis of the variation of the unit sand detachment rate (D_u = D/KE_r = g J⁻¹) with rain inclination (α, in degrees) better revealed the effect of WDR obliquity on D_u that further changed with sand size class and moisture state. Finally, the difference in the resulting stress field differentiable by the oblique raindrop trajectories of the experiment over sand surface significantly affected the non-cohesive particle detachment rates, to some extent interacted with size-dependent compressibility and interface shear strength of sand grains.     

A simple parameterization of bulk canopy resistance from climatic variables for estimating hourly evapotranspiration

This paper examines a model for estimating canopy resistance r_c and reference evapotranspiration ET_o on an hourly basis. The experimental data refer to grass at two sites in Spain with semiarid and windy conditions in a typical Mediterranean climate. Measured hourly ET_o values were obtained over grass during a 4 year period between 1997 and 2000 using a weighing lysimeter (Zaragoza, northeastern Spain) and an eddy covariance system (Córdoba, southern Spain). The present model is based on the Penman–Monteith (PM) approach, but incorporates a variable canopy resistance r_c as an empirical function of the square root of a climatic resistance r* that depends on climatic variables. Values for the variable r_c were also computed according to two other approaches: with the r_c variable as a straight‐line function of r* (Katerji and Perrier, 1983, Agronomie 3 (6): 513–521) and as a mechanistic function of weather variables as proposed by Todorovic (1999, Journal of Irrigation and Drainage Engineering, ASCE 125 (5): 235–245). In the proposed model, the results show that r_c/r_a (where r_a is the aerodynamic resistance) presents a dependence on the square root of r*/r_a, as the best approach with empirically derived global parameters. When estimating hourly ET_o values, we compared the performance of the PM equation using those estimated variable r_c values with the PM equation as proposed by the Food and Agriculture Organization, with a constant r_c = 70 s m^?1. The results confirmed the relative robustness of the PM method with constant r_c, but also revealed a tendency to underestimate the measured values when ET_o is high. Under the semiarid conditions of the two experimental sites, slightly better estimates of ET_o were obtained when an estimated variable r_c was used. Although the improvement was limited, the best estimates were provided by the Todorovic and the proposed methods. The proposed approach for r_c as a function of the square root of r* may be considered as an alternative for modelling r_c, since the results suggest that the global coefficients of this locally calibrated relationship might be generalized to other climatic regions. It may also be useful to incorporate the effects of variable canopy resistances into other climatic and hydrological models. Copyright © 2005 John Wiley & Sons, Ltd.     

A numerical study of the heat transfer through a fluid layer with recirculating flow between concentric and eccentric spheres

A numerical study has been made of the heat transfer through a fluid layer with recirculating flow. The outer fluid surface was assumed to be spherical, while the inner surface consisted of a sphere concentrically or eccentrically located with respect to the outer spherical surface. The recirculating flow was assumed to be driven by a gas flow creating stress on the fluid's outer surface so that creeping (low Reynolds number) flow developed in its interior. The present study solves the Stokes equation of motion and the convective diffusion equation in bispherical coordinates and presents the streamline and isotherm patterns.Nomenclature a _i inner sphere radius - a _d outer sphere radius - A ₁ defined by equation (5) - A ₂ defined by equation (6) - B ₁ defined by equation (7) - B ₂ defined by equation (8) - c dimensional factor for bispherical coordinates - C constant in equation (4) - d narrowest distance between the two eccentric spheres - E ² operator defined by equation (1) in spherical coordinates and by equation (21) in bispherical coordinates - G modified vorticity, defined in equation (22) - G ^* non-dimensional modified vorticity, defined in equation (28) - h metric coefficient of bispherical coordinate system, defined in equation (18) - k _w thermal conductivity of water - K ₁ defined by equation (9) - K ₂ defined by equation (10) - N _Re Reynolds number=2a _dU/gn - N _Pe,h Peclet number=2a _dU/ - n integer counter - q heat flux - r radius - r ^* non-dimensional radius=r/a _d - S surface area - t time - t ^* non-dimensional time=t/a _d ² - T temperature - T _o temperature at inner sphere surface - T _a temperature at outer sphere surface - T ^* non-dimensional temperature;=(T–T _o)/(T_a–T_o) - u velocity - u _r radial velocity in spherical coordinates - u angular velocity in spherical coordinates - u radial velocity in bispherical coordinates - u angular velocity in bispherical coordinates - U free stream velocity - u _r ^* =u _r/U - u ^* =u /U - u ^* =u /U - u ^* =u /U Greek symbols a ₁ small displacement - vorticity, defined in equation (17) - ^* non-dimensional vorticity, defined in equation (27) - radial bispherical coordinates - _o bispherical coordinate of inner sphere - _a bispherical coordinate of outer sphere - angular coordinate in spherical coordinates - thermal diffusivity - _w thermal diffusivity of water - kinematic viscosity - angular bispherical coordinate - spherical coordinate - streamfunction - non-dimensional streamfunction for spherical coordinates, = /(U a _d ² ) - ^* non-dimensional streamfunction for bispherical coordinates, defined in equation (26)     

Factors controlling the formation of coppice dunes (nebkhas) in the Negev Desert

Due to their role in increasing fertility, coppice dunes (nebkhas) are regarded by many researchers as important contributors to aridland ecosystems. Yet, despite their frequent occurrence, little information exists regarding the rate and factors that control their formation. The goal of the current study is to examine the formation rate and factors that determine the establishment of coppice dunes in the Hallamish dune field in the western Negev Desert. The rate in which sand and fines, hereafter aeolian input (AI) was trapped and its particle size distribution (PSD) were examined by means of the solidification of 2 m × 2 m plots using surface stabilizers, and by the installation of three pairs of artificial shrubs (SH), three pairs of artificial trees (TR), and a pair of control (CT) plots. Measurements were annually conducted during June 2004 and June 2008, with monthly collection during June 2004 and May 2006. The PSD was compared to coppice dunes located on the fine‐grained playa surface. AI was trapped at SH, while it was not trapped at TR and CT. The annual rate of AI accretion under the canopy was highly variable ranging between 1405 and 13 260 g m^?2, with a four‐year average of 5676 g m^?2, i.e. 3.8 mm a^?1. It depended upon the wind power, with drift potential having a threshold velocity of U_t > 10 m s^?1 yielding the higher correlations with the monthly AI (r² = 0.59–0.84). No significant relations were obtained between the monthly AI and shrub height. Sand saltation, suspension and creep are seen responsible for mound formation, which based on the current rates of sand accretion are relatively fast with a 60 cm‐high coppice dune forming within ~150–160 years. The current data highlight the problematic design of some previous research using conventional traps and confining the measurements only to certain seasons. Copyright © 2015 John Wiley & Sons, Ltd.     

Energy balance and evaporation loss of an agricultural reservoir in a semi‐arid climate (south‐eastern Spain)

A typical agricultural water reservoir (AWR) of 2400 m² area and 5 m depth, located in a semi‐arid area (southern Spain), was surveyed on a daily basis for 1 year. The annual evaporation flux was 102·7 W m^?2, equivalent to an evaporated water depth of 1310 mm year^?1. The heat storage rate G exhibited a clear annual cycle with a peak gain in April (G ～ 45 W m^?2) and a peak loss in November (G ～ 40 W m^?2), leading to a marked annual hysteretic trend when evaporation (λE) was related to net radiation (R_n). λE was strongly correlated with the available energy A, representing 91% of the annual AWR energy loss. The sensible heat flux H accounted for the remaining 9%, leading to an annual Bowen ratio in the order of 0·10. The equilibrium and advective evaporation terms of the Penman formula represented 76 and 24%, respectively, of the total evaporation, corresponding to a annual value of the Priestley–Taylor (P–T) coefficient (α) of 1·32. The P–T coefficient presented a clear seasonal pattern, with a minimum of 1·23 (July) and a maximum of 1·65 (December), indicating that, during periods of limited available energy, AWR evaporation increased above the potential evaporation as a result of the advection process. Overall, the results stressed that accurate prediction of monthly evaporation by means of the P–T formula requires accounting for both the annual cycle of storage and the advective component. Some alternative approaches to estimating R_n, G and α are proposed and discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Temporal variation of suspended sediment transport in the Koga catchment,North Western Ethiopia and environmental implications

Event sediment transport and yield were studied for 45 events in the upstream part of the 260 km² agricultural Koga catchment that drains to an irrigation reservoir. Discharge and turbidity data were collected over a period of more than a year, accompanied by grab sampling. Turbidity was very well correlated with the sediment concentrations from the samples (r = 0.99), which allowed us to estimate the temporal patterns of sediment concentrations within events. The hysteresis patterns between discharge and sediment concentrations were analysed to provide insight into the different sediment sources. Anticlockwise patterns are the dominant hysteresis patterns in the area, suggesting smaller contributions of suspended sediment from the river channels than from the hillslopes and agricultural areas. Complicated types of hysteresis patterns were mostly observed for long events with multiple peaks. For a given discharge, sediment yields in August and September, when the catchment was almost completely covered with vegetation, were much smaller than during the rest of the rainy season. The hysteresis patterns and timing suggest that the sediment availability from the agricultural areas and hillslopes affects sediment yields more strongly than does peak discharge. Two distinct types of sediment rating curves were observed for the season when the agricultural land was covered with vegetation and when it was not, indicating the dominating contribution of land use/cover to sediment yields in the catchment. The rate of suspended sediment transport in the area was estimated as 25.6 t year^?1 ha^?1. Copyright © 2013 John Wiley & Sons, Ltd.     

EXPERIMENTAL INVESTIGATION AND ANALYSIS OF HEC-6 RIVER MORPHOLOGICAL MODEL

Only comparatively few experimental studies have been carried out to investigate the performance of the HEC-6 river morphological model. The model was developed by the Hydrologic Engineering Center of the US Army Corps of Engineers. In this study, experiments were carried out in a 20 m long concrete flume 0.6 m wide with varying rectangular cross-sections. The channel bed is paved with uniform sand of D₅₀ = 0.9 mm and D₉₀ = 1.2 mm within the test reach of 12 m. Two types of experiments were carried out with sediment transport, one under steady uniform flow and another under steady non-uniform flow conditions. Nine steady uniform flow experiments were carried out to compare the measured equilibrium relationship of flow and sediment transport rate with two bedload formulae, namely, Du Boys and Meyer–Peter and Muller, and with three total load formulae, namely, Toffaleti, Laursen and Yang. It was found that even though the sediment transport consists of a certain portion of bedload, the total load formulae give satisfactory results and better agreement than the two bedload formulae. Five steady non-uniform flow experiments were carried out under various conditions of varying bed profile and channel width and also with sediment addition and withdrawal. The measured transient water surface and bed profiles are compared with the computed results from the HEC-6 model. It was found that the Toffaleti and Yang total load formulae used in the HEC-6 model give the most satisfactory prediction of actual bed profiles under various conditions of non-uniform flow and sediment transport. The effects of Manning's n, variations of sediment inflow, various sediment transport formulae, sediment grain size and the model numerical parameters, i.e. distance interval Δx and numerical weighting factor, on the computed water surface and bed profiles were determined. It was found that the selection of the sediment transport formulae has the most significant effect on the computed results. It can be concluded that the HEC-6 model can predict satisfactorily a long-term average pattern of local scour and deposition along a channel with either a small abrupt change in geometry or gradually varying cross-sections. However, the accuracy of the model prediction is reduced in the regions where highly non-uniform flow occurs.     

The application of uranium series disequilibrium concepts to sediment yield determination

The determination of uranium series disequilibria in fluvial environments is proposed as a method of calculating catchment mass balances. The technique is based on two main principles. Firstly, ²³⁴U is more mobile than ²³⁸U, especially during the early stages of weathering. Secondly, uranium is far more mobile than either thorium or protactinium. Consequently, teaching during weathering results in the loss of the uranium found in the fresh rock, leaving the two immobile daughters behind. The ratio of uranium carried by sediment to that dissolved, U_S/U_W can, therefore, be determined from river water and sediment isotopic activity ratios. Fluxes of uranium can then be calculated from average concentrations in the water and the associated sediment, from which a sediment yield can be inferred. The Witham catchment in Lincolnshire has been used to test the proposed method. A U_S/U_W ratio of between 5 and 7 is determined and a sediment yield of 2.51 ± 2.12 tonnes yr^?1 km^?2 is proposed. Although some problems concerning environmental chemistry have arisen, the validity of the approach is confirmed by the close correspondence between the results obtained and those inferred by earlier workers using more conventional methods.     

Parameterized expressions for an improved Rouse equation

The equilibrium profile of suspended sediment concentration （SSC） in steady, uniform turbulent flow has been extensively studied since the proposition of Rouse equation （Rouse, 1937）. Many researchers keep studying and attempting to improve the Rouse equation by modifying the mixing length concept. Bose and Dey （2009） improved Rouse equation based on the modified sediment diffusivity, however, their proposed sediment diffusivity has two parameters, the depth modification factor α and the reciprocal of the sediment Schmidt number β = 1/S, and the corresponding expressions were not given properly in their paper. This paper aims to parameterize the relevant coefficients, the results shows： （1） α is parameterized from a reasonable approximation by the analysis of surface boundary condition of SSC; （2） considering some effect factors on the settling velocity, β can be expressed by an extended and modified Montes-Ippen formula, and its related parameters are calibrated by substantial data about the relationship between the primary Rouse parameter Z. = ω/ku and its counterpart Z＇ = ω/βku.. Through verification with some experimental and field datasets, and comparison with related formula, the results show that the sediment diffusivity and SSC profiles have a good agreement with measured data used the present parameterized expressions of a and,8, so the present improved Rouse equation is reasonable, and can be applied in practical applications. Finally, an approximation and simplified expression of the improved Rouse equation is deduced by using the approach of perturbation, which can be applied easily for the estimation of suspended sediment transport rate.     

Clearance rates of Cerastoderma edule under increasing current velocity

Estimates of clearance rates (CR) of Cerastoderma edule (300 ind. m⁻²) as a function of free-stream current velocity (U) (from 5 to 40 cm s⁻¹) were compared between a small annular (60 l) and a large racetrack (8850 l) flume with different hydrodynamic conditions. Results showed that the flumes differ considerably in their hydrodynamic characteristics. The relationship between CR and U is different in the two flume tanks, however there appears to be a straightforward unimodal trend between CR and shear velocity (U_*). It was found that the cockles themselves influence the benthic boundary layer (BBL) characteristics, by causing steeper velocity gradients and increasing the mixing over the cockle bed compared to bare sediment. This provides new evidence on how endobenthic organisms can affect the BBL. However, the influence of CR on U_* could not be quantified because these parameters have interactive effects that cannot be dissociated.     

Threshold relations for the transport of sediment by overland flow on desert hillslopes

Although the Shields relation was developed for rivers, it has been applied to sediment transport by overland flow. According to the Shields relation, where the critical boundary Reynolds number Re_*c exceeds 40, the critical Shields number F_*c is independent of both Re_*c and the ratio of the critical flow depth to particle diameter d_c/D. Analyses of data collected from runoff plots in southern Arizona reveal that F_*c is positively correlated with both Re_*c and d_c/D. Thus the Shields relation does not apply to overland flow on debris-covered desert hillslopes. Multiple regression analysis is employed to develop alternative threshold relations in which critical boundary shear stress τ_c is related to D and d_c/D (R² = 0.782) and to D and S_c (critical gradient) (R² = 0.625). The computed R² values derive in large part from the spurious correlations of d_c/D and S_c with τ_c. Nevertheless, the relations may be utilized to predict τ_c. In this regard, the latter relation is likely to prove more useful than the former because S_c is generally known, whereas d_c is not. An investigation of the functional relation between τ_c and D reveals that τ_c varies approximately with D² for overland flow on the desert hillslopes under study, whereas the Shields relation predicts a linear relation (i.e. a D exponent of 1). This result is consistent with Cheng's data which show that F_*c varies with (d_c/D)^?1 where 0.4 < d_c/D < 2 and may be explained in terms of increased energy dissipation both in separation zones downslope of particles and in distortion of the water surface as d_c/D decreases. Consequently, larger values of τ_c, and hence F_*c, are required to initiate the transport of particles of a given size D as d_c decreases.     

Bed-flow instability of the longshore current

An initially uniform longshore current on a plane erodible beach is considered and a linear stability analysis of the bed-flow system is performed in order to investigate the growth of alongshore periodic topographic features such as transverse or oblique bars. γ, numerical model based on the shallow water equations and a simple sediment transport formula is used. For a wide range of parameters instability is found, leading to the growth of large-scale topographic features (lengthscale of the order of the current width) downflow progressing. The growth rates and the dominant unstable mode depend mainly on R = c_d/β parameter, where c_d is the bottom friction coefficient and β is the beach slope. For a small R, say less than 0.1, instability is very weak, probably negligible. For R between 0.1 and 0.7 instability increases with R, leading typically to a quite simple transverse bars pattern. A further increase in R produces a far more complicated behaviour where complex patterns with downcurrent oriented oblique bars, bumps and holes can be dominant. In this region growth rates may either decrease or increase with R depending on the beach slope and the maximum Froude number of the basic flow, F. Usually, the most complex behaviour is found for gently sloping beaches. The physical mechanism of the instability is found to lie on the disturbances of potential vorticity caused by topographically induced differences in bottom friction. In this sense it is similar to the alternate bars growth in a river rather than the dunes or antidunes occurrence for 1D channel flow. The predictions of the model compare well with the available experimental data. The alongshore wavelength, γ, typically of the order of one to four times the width of the current, is close to four times for the most common values of R. The typical growth time is proportional to γ² and for a wavelength of 100 m can be of the order of one day, depending on the sediment transport rate. The migrational speed is inversely proportional to γ, in accordance to earlier field data reported by Sonu (1969) Collective movement of sediment in littoral environment.     

What controls the disequilibrium state of gravel-bed rivers?

A river at equilibrium is described by a statistically-stationary mean bed elevation profile that arises in response to steady supplies of relief, water and sediment. Outside of the profile shape, how is the equilibrium state of a river most reliably identified and rigorously defined? Motivated by a proposed link between equilibrium and physical processes, we use scaling theory to develop the dimensionless channel response number ξ=KU_b/U_p. ξ is a metric for the local disequilibrium state of gravel-bed mountain streams, which reflects a balance between the rate of topographic adjustment U_b, and the rate of bed sediment texture adjustment U_p. The coefficient K can take one of two forms depending on choice of length scale for topographic adjustment. We hypothesize that equilibrium occurs where and when ξ≈O(1), and consequently, disequilibrium is the more general state captured by conditions of ξ≉O(1). The rates U_b and U_p are controlled by the mechanics of sediment deposition and entrainment at the local scale of the channel width. The extent to which either process regulates disequilibrium depends on the bed strength, which is set by the time-varying grain size distribution and packing. We use flume experiments to understand ξ and find that in the limit ξ>>1, the time-varying response of an experimental channel depends sensitively on the spatially-averaged bed shear stress ratio τ/τ_ref. When τ/τ_ref≈1.5, U_b was the dominant control on disequilibrium. However, when τ/τ_ref≈2.0, U_p contributed more significantly to disequilibrium. These results suggest that after an upstream supply perturbation, the equilibrium timescale is governed by U_p, which we show is consistent with expectations from linear damping theory. Our experimental test of ξ is promising, but inconclusive with respect to our hypothesis. This uncertainty can be readily addressed with numerical or additional physical experiments. © 2019 John Wiley & Sons, Ltd.     

Coarse sediment transport in mountain streams in Colorado and Wyoming,USA

Since the early 1990s, US Forest Service researchers have made thousands of bedload measurements in steep, coarse‐grained channels in Colorado and Wyoming, USA. In this paper we use data from 19 of those sites to characterize patterns and rates of coarse sediment transport for a range of channel types and sizes, including step–pool, plane‐bed, pool–riffle, and near‐braided channels. This effort builds upon previous work where we applied a piecewise regression model to (1) relate flow to rates of bedload transport and (2) define phases of transport in coarse‐grained channels. Earlier, the model was tested using bedload data from eight sites on the Fraser Experimental Forest near Fraser, Colorado. The analysis showed good application to those data and to data from four supplementary channels to which the procedure was applied. The earlier results were, however, derived from data collected at sites that, for the most part, have quite similar geology and runoff regimes. In this paper we evaluate further the application of piecewise regression to data from channels with a wider range of geomorphic conditions. The results corroborate with those from the earlier work in that there is a relatively narrow range of discharges at which a substantial change in the nature of bedload transport occurs. The transition from primarily low rates of sand transport (phase I) to higher rates of sand and coarse gravel transport (phase II) occurs, on average, at about 80 per cent of the bankfull (1·5‐year return interval) discharge. A comparison of grain sizes moved during the two phases showed that coarse gravel is rarely trapped in the samplers during phase I transport. Moreover, the movement and capture of the D₁₆ to D₂₅ grain size of the bed surface seems to correspond with the onset of phase II transport, particularly in systems with largely static channel surfaces. However, while there were many similarities in observed patterns of bedload transport at the 19 studied sites, each had its own ‘bedload signal’ in that the rate and size of materials transported largely reflected the nature of flow and sediment particular to that system. Published in 2005 by John Wiley & Sons, Ltd.