Principle of equivalency of bed structures and bed load motion

Step-pool systems and cobble clusters are structures composed of boulders and cobbles on mountain streambeds rearranged by flood flow to reach high resistance and high bed stability.Both bed structures and bed load motion can protect the riverbed from incision.At each step-pool,the flow energy is transformed into turbulence,and finally into heat.Bed load motion also consumes flow energy and plays a role to protect the bed from erosion.The collision of bed load particles with the bed results in a force,known as dispersive force,which balances the lift force and controls the erosion of bed sediment.Field investigations and field experiments were conducted in the Xiaojiang River basin on the Yunnan-Guizhou plateau of China,where there were incised streams and stable streams with bed load motion or with step-pool systems.This study reveals that for a given stream power, strong bed structures are associated with low or zero bed load transportation;and weak or no bed structures are associated with intensive bed load motion.Experiments showed that for incised streams, the final bed profiles were the same if there was bed load motion or there were bed structures.When key stones that made up the bed structures,for instance the large boulders in steps,were removed,the flow immediately scoured the sediment bed.The bed load transportation sharply increased by 100 times and the median diameter of bed load increased by 2-20 times.Bed structures and bed load motion are mutually replaceable for their effects on flow energy consumption and streambed incision control.This is the principle of equivalency of bed load motion and bed structures.It is due to the principle that there was no bed load motion in the Yalutsangpo Grand Canyon,where a very strong step-pool system had developed,although the bed gradient and shear stress of flow were extremely high.A possible application of this principle for incision control of the downstream reaches of the Three Gorges Dam is also discussed in this paper.     

A new mixing equation for bed material composition in bed form dominant conditions

Vertical mixing beneath the bed surface and its effect on sediment composition has long been underestimated. This paper proposes a mixing equation to illustrate the temporal and spatial variations of bed material composition for bed form dominant rivers. A continuous mass conservation equation for elevation-specific nonuniform bed material composition is initially presented. A vertical mixing equation is finally derived as a diffusion-type partial differential equation with a source term charact...     

Particle size distribution of bed materials in the sandy river bed of alluvial rivers

The particle size distribution of bed materials in the sandy river bed of alluvial rivers is important in the study of topics such as friction, river bed evolution, erosion, and siltation. It also can reflect the dependency relation between river bed sediment and flow intensity. In this paper, the critical pattern of sediment movement in the near-wall region of a sandy river bed was analyzed. According to the principle of momentum balance, the critical settling-rising condition of bed material in a sandy river bed was found to be instantaneous turbulent velocity equal to 2.7 times the sediment settling velocity in quiescent water. Based on a vertical instantaneous turbulent velocity with a Gaussian distribution, a theoretical relation for calculating the particle size distribution of bed materials in a sandy river bed without pre-known characteristic grain sizes was developed by solving a stochastic equation. The for-mula is verified using measured data, and the results show that the proposed formula was in accordance with the measured data. This study has theoretical significance and practical value for determining the bed material particle size distribution of the sandy bed of alluvial rivers.     

Velocity profiles and bed shear stress over various bed configurations in a river bend

Vertical velocity profiles measured over various bed configurations (plane beds, ripples, and dunes) in. the meandering River South Esk, Glen Clova, Scotland are presented on semilogarithmic paper. Local bed shear stress and roughness height are calculated from the lowermost parts of the profiles using the Karman-Prandtl law of the wall; these parameters, and the geometrical properties of the profiles, are related to the various bed configurations. A graphical model is used to identify profiles developed on specific regions of dune geometry, in order to discriminate those profiles that define bed shear effective in transporting sediment over dunes. An assessment is made of the errors involved in estimating local mean velocity from extrapolating the law of the wall to the water surface. A Darcy-Weisbach friction coefficient is related to bed configuration and local stream power.     

Comparison of bed shear stress in plane and curvilinear bed channel using multiple criteria

Experimental investigation on fluvial hydraulics needs a correct and accurate estimation of bed shear stress, which governs the hydrodynamics of the sediment transport. Present work compares bed shear stress estimated from the reach-averaged bed shear stress, Log profile, Quadratic stress law, Prandtl’s seventh power law, Reynolds shear stress, turbulent kinetic energy and graphical method approaches by doing experimentation on plane bed and curvilinear bed channel. On plane bed condition, the bed shear estimated from Reynolds stresses and Graphical methods are comparable to the reach-averaged bed shear stress (the difference is within 10%). However, all approaches estimate approximately less than 10% from reach-averaged bed shear stress in curvilinear bed channel.     

Total load transport in gravel bed and sand bed rivers case study:Chelichay watershed

Field experiments were conducted on total load transport in the Chelichay River Basin,a mountainous catchment (1,400 km~2) located in north eastern of Iran,to evaluate total load formulas including four gravel bed rivers and a sand bed river(Qaresoo River).Gravel bed rivers in Chelichay River Basin can be grouped into two types;steep slope rivers with high shear values(Chehelchay River and Khormaloo River) and mild slope rivers with low shear values(Narmab River and Soosara River).Two depth integrating suspended load samplers(DH-48 and D-49),and two bed load samplers(Helley-Smith and BLSH) were used to measure total load.The performance is tested of 8 total load transport formulae including 4 macroscopic and 4 microscopic methods.A systematic and thorough analysis of 59 sets of data collected from sand bed river indicate that Yang and Engelund and Hansen reach to the better results, and from four gravel bed rivers confirmed that the methods of Karim and Kennedy and Engelund and Hansen yields the best results for steep slope rivers,and the methods of Einstein and Bijker are ranked highest in gradual slope rivers.     

Evaluation of the saltation process of bed materials by video imaging under altered bed roughness

The purpose of this paper is to examine the nature of particle saltation and movement over the beds of fixed roughness from flume experiments. A series of experiments are carried out to study the saltation of individual sand particles of different sizes over rough beds under different flow conditions. A 3‐D acoustic Doppler velocimeter is used to record the fluid velocity components; subsequently, under different flow conditions, the images of released sand particles are recorded using high‐speed video imaging technique. Systematic analysis is made with regard to the forces acting on the grains and the variation of their magnitudes along the saltation trajectories of the grains. Relations between the saltation parameters, flow intensity and bed roughness are developed. The distributions of the angle of orientations during a single saltation follows almost a Gaussian distribution. The shape of the Gaussian distribution depends on the particle size and bed roughness. Particle collisions with rough beds and the resulting coefficients of restitution are also discussed. A theoretical framework is developed to compute the mean particle velocity considering the spin in the energy balance equation. Results of the detailed analysis using the imaging technique are much better than in previously reported studies. Copyright © 2013 John Wiley & Sons, Ltd.     

Coarse bed load transport in an alluvial gravel bed stream,Dupuyer Creek,Montana

Coarse bed load was sampled in a gravel/cobble bed stream during two major floods in the snowmelt runoff season. The channel is characterized by high rates of bank erosion and, therefore, high rates of sediment supply and bed load flux. Peak discharge reached four times bank‐full, and bed load was sampled at flows 0·7–1·7 times bank‐full. A large aperture bed load sampler (1 m by 0·45 m) captured the largest particles in motion, and specifically targeted the coarse bed load size distribution by using a relatively large mesh (32 mm or D₂₅ of streambed surface size distribution). Bed load flux was highly variable, with a peak value of 0·85 kg/s/m for the coarse fraction above 38 mm. Bed load size distribution and maximum particle size was related to flow strength. Entrainment was size selective for particles D₇₀ and larger (88–155 mm), while particles in the range D₃₀–D₇₀ (35–88 mm) ceased to move at essentially the same flow. Bed load flux was size selective in that coarse fractions of the streambed surface were under‐represented in or absent from the bed load. Painted tracer particles revealed that the streambed surface in the riffles could remain stable even during high rates of bed load transport. These observations suggest that a large proportion of bed load sediments was sourced from outside the riffles. Repeat surveys confirmed major scour and fill in pools (up to 0·75 m), and bank erosion (>2 m), which together contributed large volumes of sediment to the bed load. Copyright © 2007 John Wiley & Sons, Ltd.     

The influence of microform bed roughness elements on flow and sediment transport in gravel bed rivers

Pebble clusters are reported widely as characteristic of gravel river beds and are known to influence the initial entrainment of bedload. A field assessment suggests that their distribution is not ubiquitous, favouring channel bars, but also reveals a tendency towards a preferred stream wise spacing. A series of laboratory flume experiments shows that flow resistance rises to, and falls from, a peak value as the longitudinal spacing of pebble clusters decreases, in a manner similar to that shown by others for strip roughness, isolated blocks, and simulated ripples and dunes. The experiments also reveal a strong inverse relationship between bedload flux rates and the flow resistance induced by the concentration of pebble clusters. It is concluded that pebble cluster spacing tends towards an equilibrium that is regulated by a feedback process involving sediment transport rates and that the spatial concentration of these microforms will adjust to the point where they induce maximum flow resistance.     

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.     

Heterotrophic denitrification using fluidized bed reactor

Groundwater denitrification was carried out in a fluidized bed reactor. This type of reactor is suited well to conditions of low substrate concentrations and high flow rates which are typical in groundwater denitrification processes. The reactor is characterized by the efficient contact between biomass and substrate, a high biomass concentration, and the absence of clogging or channeling. These characteristics provide for high treatment capacities (10.8 g/(L·d) NO₃^?N) and short retention times (less than 3 minutes) resulting in small reactor volume. Start-up procedure, biomass and nitrate profiles, and biofilm characteristics are presented in this article.     

Flow resistance of gravel bed channels

Existing resistance formulas produce a wide range of friction-factor estimates for gravel bed streams. The purpose of this paper is to develop a reliable resistance formula in terms of the Darcy-Weisbach friction factor f Published data were screened and used to establish the formula. The existing formulas have considered thatfis a function of relative roughness D84/R only, where R is the hydraulic radius and 1984 is the particle size referred to the intermediate diameter that equals or exceeds that of 84 percent of bed sediments. In this paper, f is considered as a ftmction of Froude number in addition to the relative roughness, ffor D84/R〉l displays a different trend than that for Dsn/R〈l perhaps due to the invalid assumption of a logarithmic velocity distribution for D84/R〉l. Anfformula for Dsa/R〈l has been established.     

Estimators of alluvial bed load transport

The equilibrium stream represents a compromise between three tendencies: (i) to maximize grain size, (ii) to maximize quantity of bed load transported, and (iii) to minimize bed shear stress (which represents, among other things, water discharge).     

Experimental study on the effects of artificial bed roughness on turbidity currents over abrupt bed slope change

A series of experimental observations are presented in the current study to discuss the effects of artificial bed roughness on the turbidity current flowing in a rectangular channel with an abrupt change in bed slope.For this purpose,two different types of elements,sinusoidal and trapezoidal,with various heights and arrangements are considered as artificial bed roughness.A Vectrino velocity meter was used to measure the velocity and sediment concentration profiles.The effects of inlet sediment concentration on front velocity,body velocity,unit discharge,sediment concentration,and suspended load transport rate also were investigated.Accurate equations were developed for estimation of the velocity of a turbidity current over smooth and rough beds.The unexpected experimental results showed that unlike the effect of roughness height,a change in the roughness arrangement has no significant influence on the velocity of a turbidity current.Also,the effect of bed roughness on the front velocity of a denser current is more significant.     

Interference processes on scouring at bed sills

The local scouring downstream of bed sills forming a sequence for bed stabilization in steep channels has been investigated in a laboratory flume. The initial bed slopes ranged from 0·078 to 0·148. The bed alluvium was characterised by a non‐uniform grain size distribution. The results show that when the ratio between the critical water depth h_c and the sill spacing L rises above a characteristic value the scouring dynamics become heavily affected by the presence of the downstream sill, associated with the onset of a form of “interference” which renders the scouring process less effective. The difference with an “undisturbed” case is demonstrated. Self‐affinity of scour holes is confirmed and the scour length appears to be the reference parameter from which the scour depth might be evaluated. Copyright © 2003 John Wiley & Sons, Ltd.     

Suspended load in flows on erodible bed

Steady state suspended-load of sediment transported in flow over erodible beds usually is treated by the advection-diffusion approach, though in recent years, it is being treated as a two-phase flow phenomenon incorporating kinetics of sediment particles. Among the advection-diffusion approaches, Rouse＇s equation is the well-known, although a number of researchers in later periods have attempted to improve it by modifying the mixing length concept taking into account other aspects. In this paper, the advection-diffusion approach and associated logarithmic law of flow velocity are revisited. It is concluded from the logarithmic law that the Reynolds shear stress is a linear function of height above the bed, which reduces to bed shear stress in the case of a long horizontal channel. As a consequence, it is shown that the volumetric concentration of sediment is best approximated by the sum of two power laws of height above the bed. An equation is derived for the suspended-load transport rate in terms of elementary functions.