A stability criterion inherent in laws governing alluvial channel flow

The stability criterion of maximum flow efficiency (MFE) has previously been found inherent in typical alluvial channel flow relationships, and this study investigates the general nature of this criterion using a wider range of flow resistance and bedload transport formulae. For straight alluvial channels, in which the effect of sediment sorting is insignificant, our detailed mathematical analysis demonstrates that a flow efficiency factor ε occurs generally as the ratio of sediment (bedload) discharge Q_s to stream power Ω (γQS) in the form of . When ε is maximized (i.e. Q_s is maximized or Ω is minimized), maximally efficient straight channel geometries derived from most flow resistance and bedload transport formulae are found compatible with observed bankfull hydraulic geometry relations. This study provides support for the use of the criteria of MFE, maximum sediment transporting capacity and minimum stream power for understanding the operation of alluvial rivers, and also addresses limitations to the direct application of its findings. Copyright © 2002 John Wiley & Sons, Ltd.     

A test of equilibrium theory and a demonstration of its practical application for predicting the morphodynamics of the Yangtze River

Taking the width/depth ratio of a river channel as an independent variable, a variational analysis of basic flow relationships shows that alluvial‐channel flow adjusts channel geometry to achieve stationary equilibrium when the condition of maximum flow efficiency (MFE) is satisfied. As a test of the veracity of MFE and to examine if this theory of self‐adjusting channel morphodynamics can be practically applied to large river systems, this study examines the degree of correspondence between theoretically determined equilibrium channel geometries and actual measurements along the middle and lower Yangtze River. Using four different forms of the Meyer‐Peter and Müller bedload relation and relations of flow continuity and resistance we show that the Meyer‐Peter and Müller bedload relation modified on the basis of MFE theory predicts channel dimensions most accurately when applied to the middle and lower Yangtze River. This provides convincing evidence supporting MFE equilibrium theory. Copyright © 2014 John Wiley & Sons, Ltd.     

Lithological and fluvial controls on the geomorphology of tropical montane stream channels in Puerto Rico

An extensive survey and topographic analysis of five watersheds draining the Luquillo Mountains in north‐eastern Puerto Rico was conducted to decouple the relative influences of lithologic and hydraulic forces in shaping the morphology of tropical montane stream channels. The Luquillo Mountains are a steep landscape composed of volcaniclastic and igneous rocks that exert a localized lithologic influence on the stream channels. However, the stream channels also experience strong hydraulic forcing due to high unit discharge in the humid rainforest environment. GIS‐based topographic analysis was used to examine channel profiles, and survey data were used to analyze downstream changes in channel geometry, grain sizes, stream power, and shear stresses. Results indicate that the longitudinal profiles are generally well graded but have concavities that reflect the influence of multiple rock types and colluvial‐alluvial transitions. Non‐fluvial processes, such as landslides, deliver coarse boulder‐sized sediment to the channels and may locally determine channel gradient and geometry. Median grain size is strongly related to drainage area and slope, and coarsens in the headwaters before fining in the downstream reaches; a pattern associated with a mid‐basin transition between colluvial and fluvial processes. Downstream hydraulic geometry relationships between discharge, width and velocity (although not depth) are well developed for all watersheds. Stream power displays a mid‐basin maximum in all basins, although the ratio of stream power to coarse grain size (indicative of hydraulic forcing) increases downstream. Excess dimensionless shear stress at bankfull flow wavers around the threshold for sediment mobility of the median grain size, and does not vary systematically with bankfull discharge; a common characteristic in self‐forming ‘threshold’ alluvial channels. The results suggest that although there is apparent bedrock and lithologic control on local reach‐scale channel morphology, strong fluvial forces acting over time have been sufficient to override boundary resistance and give rise to systematic basin‐scale patterns. Copyright © 2010 John Wiley and Sons, Ltd.     

Self‐adjustment in rivers: Evidence for least action as the primary control of alluvial‐channel form and process

Least action principle (LAP) in rivers is demonstrated by maximum flow efficiency (MFE) and is the foundation of variational mechanics based on energy and work rather than Newtonian force and momentum. Empirical evidence shows it to be the primary control for the adjustment of alluvial channels. Because most rivers flow with imposed water and sediment loads down valley gradients they have largely inherited, they self‐regulate energy expenditure to match the work they are required to do to remain stable. Overpowered systems develop a variety of channel patterns to expend excess energy and remain stable. Australia offers an opportunity to study low‐energy rivers closely adjusted to very low continental gradients. The anabranching Marshall and single‐thread Plenty Rivers flow down nearly straight channels with average H numbers [ratio between excess bed shear and width/depth (W/D) ratio] close to the optimum of 0.3 for stationary equilibrium. Ridge‐form divisions of the original channel width create anabranches that radically alter W/D ratios relative to bed shear, the same being true for short‐wide islands on the large low‐gradient Yangtze River in China. In contrast, Mount Chambers Creek in Australia's tectonically more active Flinders Ranges is accreting an alluvial fan with unstable distributary channels exhibiting H numbers well below the optimum. LAP also explains profound biases in Earth's stratigraphic record. Because meandering is an energy‐shedding mechanism, sinuous rivers sequester relatively little sediment resulting in all sequences being just a few tens of metres thick. In contrast, low‐energy braided disequilibrium systems can sequester sediment piles over a kilometre in thickness and tens of kilometres wide. LAP provides a new paradigm for river research by identifying the attractor state controlling river channel evolution. It links advances in theoretical physics to fluvial geomorphology, stratigraphy and hydraulic engineering and opens opportunities for diverse investigations in Earth system science. Copyright © 2016 John Wiley & Sons, Ltd.     

At‐a‐station hydraulic geometry relations, 1: theoretical development

This paper, the first of two, hypothesizes that: (1) the temporal variation of stream power of a river channel at a given station with varying discharge is accomplished by the temporal variation in channel form (flow depth and channel width) and hydraulic variables, including energy slope, flow velocity and friction; (2) the change in stream power is distributed among the changes in flow depth, channel width, flow velocity, slope, and friction, depending on the boundary conditions that the channels has to satisfy. The second hypothesis is a result of the principle of maximum entropy and the theory of minimum energy dissipation or its simplified minimum stream power. These two hypotheses lead to families of at‐a‐station hydraulic geometry relations. The conditions under which these families of relations can occur in the field are discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

Spatial variability of three‐dimensional Reynolds stresses in a developing channel bend

Experimental results of the mean flow field and turbulence characteristics for flow in a model channel bend with a mobile sand bed are presented. Acoustic Doppler velocimeters (ADVs) were used to measure the three components of instantaneous velocities at multiple cross sections in a 135° channel bend for two separate experiments at different stages of clear water scour conditions. With measurements at multiple cross sections through the bend it was possible to map the changes in both the spatial distribution of the mean velocity field and the three Reynolds shear stresses. Turbulent stresses are known to contribute to sediment transport and the three‐dimensionality inherent to flow in open channel bends presents a useful case for determining specific relations between three‐dimensional turbulence and sediment entrainment and transport. These measurements will also provide the necessary data for validating numerical simulations of turbulent flow and sediment transport. The results show that the magnitude and distribution of three‐dimensional Reynolds stresses increase through the bend, with streamwise‐cross stream and cross stream‐vertical components exceeding the maximum principal Reynolds stress through the bend. The most intriguing observation is that near‐bed maximum positive streamwise‐cross stream Reynolds stress coincides with the leading edge of the outer bank scour hole (or thalweg), while maximum cross stream‐vertical Reynolds stress (in combination with high negative streamwise‐cross stream Reynolds stress near the bend apex) coincides with the leading edge of the inner bank bar. Maximum Reynolds stress and average turbulent kinetic energy appear to be greater and more localized over the scour hole before final equilibrium scour is reached. This suggests that the turbulent energy in the flow is higher while the channel bed is developing, and both lower turbulent energy and a broader distribution of turbulent stresses near the bed are required for cessation of particle mobilization and transport. Copyright © 2010 John Wiley & Sons, Ltd.     

The fate of suspended sediment and particulate organic carbon in transit through the channels of a river catchment

Particulate organic matter (POM) transiting through rivers could be lost to overbank storage, stored in‐channel, added to by erosion or autochthonous production, or turned over to release greenhouse gases to the atmosphere (either while in the water column or while stored in the channel). In the UK, a net loss of POM across catchments has been recorded, and the aim here was to investigate the balances of processes acting on the POM. This study considered records of suspended sediment and POM flux in comparison to stream flow, velocity, stream power, and residence time for the River Trent (English Midlands, 8,231 km²). We show that for the lower two thirds (106 km) of the River Trent, 2% is lost to overbank storage; 10% is lost to the atmosphere in the water column; and 31% is turned over while in temporary storage. Permanent in‐channel storage is negligible, and for the lower course of the river, material stored in‐channel will have a residence time of the order of hundreds of days between the last flood hydrograph of one winter and the first winter storm of the next winter (usually in the same calendar year). When considered at the scale of the UK, 1% POM in transit would be lost to overbank sedimentation; 5% turned over in the water column, and 14% turned over while in temporary storage. In the upper third of the study river channel, there is insufficient stream power to transport sediment and so in‐channel storage or in‐channel turnover over to the atmosphere dominate. The in‐channel processes of the River Trent do not conform to that expected for river channels as the headwaters are not eroding or transporting sediment. Therefore, the source of sediment must be lower down the channel network.     

Transporting capacity of overland flow on plane and on irregular beds

In this paper the transporting capacity of thin flows, in the laminar and transitional flow regime, is studied. Experiments were carried out on irregular as well as on plane beds, using two totally different set-ups. The results of these two types of experiment were convergent. In both cases, sediment concentration was clearly related to grain shear velocity and unit stream power, expressed as the product of mean velocity and slope (Yang, 1973). The data agreed with those of Kramer and Meyer (1969). For a sandy bed, the unit stream power relationship was able to predict reasonably well the sediment concentrations measured on a mulched surface. For laminar and transitional flows, both the unit stream power and the shear velocity are related in the same way to slope and unit discharge. The unit stream power is a parameter which in particular can be very easily measured and might therefore become useful in obtaining a quick estimate of the transporting capacity of a thin flow. However, before a sediment transport equation for thin flows can be developed, more information is needed about the influence of the flow regime and grain size and density.     

Flow hydraulics and geomorphic effects of glacial‐lake outburst floods in the Mount Everest region,Nepal

Glacial‐lake outburst floods (GLOFs) on 3 September 1977 and 4 August 1985 dramatically modified channels and valleys in the Mount Everest region of Nepal by eroding, transporting, and depositing large quantities of sediment for tens of kilometres along the flood routes. The GLOF discharges were 7 to 60 times greater than normal floods derived from snowmelt runoff, glacier meltwater, and monsoonal precipitation (referred to as seasonal high flow floods, SHFFs). Specific stream power values ranged from as low as 1900 W m^?2 in wide, low‐gradient valley segments to as high as 51 700 W m^?2 in narrow, high‐gradient valley segments bounded by bedrock. Along the upper 16 km of the GLOF routes, the reach‐averaged specific stream power of the GLOFs was 3·2 to 8·0 times greater than the reach‐averaged specific stream power of the SHFFs. The greatest geomorphic change occurred along the upper 10 to 16 km of the GLOF routes, where the ratio between the GLOF specific stream power and the SHFF specific stream power was the greatest, there was an abundant supply of sediment, and channel/valley boundaries consisted primarily of unconsolidated sediment. Below 11 to 16 km from the source area, the geomorphic effects of the GLOFs were reduced because of the lower specific stream power ratio between the GLOFs and SHFFs, more resistant bedrock flow boundaries, reduced sediment supply, and the occurrence of past GLOFs. Copyright © 2003 John Wiley & Sons, Ltd.     

Feedbacks between erosion and sediment transport in experimental bedrock channels

Natural bedrock rivers flow in self‐formed channels and form diverse erosional morphologies. The parameters that collectively define channel morphology (e.g. width, slope, bed roughness, bedrock exposure, sediment size distribution) all influence river incision rates and dynamically adjust in poorly understood ways to imposed fluid and sediment fluxes. To explore the mechanics of river incision, we conducted laboratory experiments in which the complexities of natural bedrock channels were reduced to a homogenous brittle substrate (sand and cement), a single sediment size primarily transported as bedload, a single erosion mechanism (abrasion) and sediment‐starved transport conditions. We find that patterns of erosion both create and are sensitive functions of the evolving bed topography because of feedbacks between the turbulent flow field, sediment transport and bottom roughness. Abrasion only occurs where sediment impacts the bed, and so positive feedback occurs between the sediment preferentially drawn to topographic lows by gravity and the further erosion of these lows. However, the spatial focusing of erosion results in tortuous flow paths and erosional forms (inner channels, scoops, potholes), which dissipate flow energy. This energy dissipation is a negative feedback that reduces sediment transport capacity, inhibiting further incision and ultimately leading to channel morphologies adjusted to just transport the imposed sediment load. Copyright © 2007 John Wiley & Sons, Ltd.     

Nondimensional sediment transport capacity of sand soils and its response to parameter in the Loess Plateau of China

Soil erosion is a major contributor to land degradation in the Loess Plateau in China. To clarify the sediment transport capacity of overland flow influenced by hydraulic parameters, such as shear stress, sand shear stress (hydraulic gradient partition method and hydraulic radius partition method), mean flow velocity, Froude number, stream power, and unit stream power, indoor experiments with eight-unit-width flow discharges from 0.0667 × 10⁻³ to 0.3333 × 10⁻³ m²·s⁻¹, six slope gradients from 3.49 to 20.79%, and two kinds of sand soils (d₅₀ = 0.17 and 0.53 mm) were systematically investigated. A nondimensional method was adopted in data processing. Results showed that there was a partition phenomenon of relation curves because of the different median grain diameters. The correlation between the nondimensional stream power and nondimensional sediment transport capacity was the highest, followed by the correlation between the nondimensional unit stream power and nondimensional sediment transport capacity. However, there was a poor correlation between the flow intensity indices of velocity category and nondimensional sediment transport capacity. Nondimensional stream power, nondimensional unit stream power, and nondimensional shear stress could predict sediment transport capacity well. Ignoring the partition phenomenon of the relation curves, stream power could be used to predict sediment transport capacity, with a coefficient of determination of .85. Furthermore, a general flow intensity index was obtained to predict sediment transport capacity of overland flow. Finally, an empirical formula for predicting sediment transport capacity with a coefficient of determination of .90 was established by multiple regression analyses based on the general flow intensity index. During the analysis between measured sediment transport capacities in present study and predicted values based on Zhang model, Mahmoodabadi model, and Wu model, it was found that these three models could not accurately predict sediment transport capacities of this study because different models are estimated on the basis of different experimental conditions.     

Controls of alluvial cover formation,morphology and bedload transport in a sinuous channel with a non-alluvial boundary

The alluvial cover in channels with non-alluvial beds is a major morphologic feature in these rivers and has important geomorphic and ecologic functions. Although controls on the extent of the alluvial cover have been previously researched, little is known about the role of channel meanders in shaping the three-dimensional morphology and bedload transport rates in these rivers. Flume experiments were conducted in a fixed-bed sinuous channel scaled from an engineered urban river. A fully graded sediment supply mixture was fed into the bare channel at rates ranging between 0.3 and 1.2 times the estimated channel capacity under constant discharge. The three-dimensional morphology and surface texture of the alluvial cover were captured using photogrammetry, and the sediment output was periodically measured and sieved. A stable alluvial cover was achieved under all sediment supply conditions that coincided with a sediment transport equilibrium. The sediment supply rate controlled the final areal extent, mass and volume of the alluvial cover, while cover developed as a periodic series of stable bars ‘fixed’ by the channel planform. The alluvial cover development followed consistent trajectories relative to angular position around bends but developed to a greater degree and higher elevation with increasing sediment supply. The stable cover extent had a logarithmic relationship with the relative sediment supply, while the final mass, volume and bar height had linear relationships. The final channel morphology was characterized by fine-textured point bars with flat tops and steep margins connected by coarse riffle features. The outside of banks between bend apexes remained bare, even at sediment supply conditions exceeding the channel capacity. The length of the exposed outer banks followed predictable linear relationships with the total cover extent. Insights from this study can provide guidance for the management of channels with non-alluvial boundaries and provide validation for models of sinuous bedrock channel abrasion. © 2020 John Wiley & Sons, Ltd.     

The form and function of headwater streams based on field and modeling investigations in the southern Appalachian Mountains

Headwater streams drain the majority of most landscapes, yet less is known about their morphology and sediment transport processes than for lowland rivers. We have studied headwater channel form, discharge and erosive power in the humid, moderate‐relief Valley and Ridge and Blue Ridge provinces of the Appalachian Mountains. Field observations from nine headwater (<2 km² drainage area), mixed bedrock–alluvial channels in a variety of boundary conditions demonstrate variation with respect to slope‐area channel initiation, basic morphology, slope distribution, hydraulic geometry, substrate grain size and role of woody debris. These channels display only some of the typical downstream trends expected of larger, lowland rivers. Variations are controlled mainly by differences in bedrock resistance, from the formation level down to short‐wavelength, outcrop‐scale variations. Hydrologic modeling on these ungauged channels estimates the recurrence of channel‐filling discharge and its ability to erode the channel bed. Two‐year recurrence discharge is generally larger and closer to bankfull height in the Valley and Ridge, due to low soil infiltration capacity. Discharge that fills the channel to its surveyed bankfull form is variable, generally exceeding two‐year flows at small drainage areas (<0·5 km²) and being exceeded by them at greater drainage areas. This suggests bankfull is not controlled by the same recurrence storm throughout a channel or physiographic region. Stream power and relative competence are also variable. These heterogeneities contrast relations observed in larger streams and illustrate the sensitivity of headwater channels to local knickpoints of resistant bedrock and armoring of channels by influx of coarse debris from hillslopes. The general lack of predictable trends or functional relationships among hydraulic variables and the close coupling of channel form and function with local boundary conditions indicate that headwater streams pose a significant challenge to landscape evolution modeling. Copyright © 2005 John Wiley & Sons, Ltd.     

Field evidence for the control of grain size and sediment supply on steady‐state bedrock river channel slopes in a tectonically active setting

We exploit a natural experiment in Boulder Creek, a ~ 30 km² drainage in the Santa Cruz mountains, CA, USA to explore how an abrupt increase in the caliber of bedload sediment along a bedrock channel influences channel morphology in an actively uplifting landscape. Boulder Creek's bedrock channel, which is entirely developed on weak sedimentary rock, has a high flow shear stress that is about 3.5 times greater where it transports coarse (~ 22 cm D₅₀) diorite in the lower reaches in comparison with the upstream section of the creek that transports only relatively finer bedload (~2 cm D₅₀) derived from weak sedimentary rocks. In addition, Boulder Creek's channel abruptly widens and shallows downstream and transitions from partial to nearly continuous alluvial cover where it begins transporting coarse diorite. Boulder Creek's tributary channels are also about three times steeper where they transport diorite bedload, and within the Santa Cruz mountains channels in sedimentary bedrock are systematically steeper when >50% of their catchment area is within crystalline basement rocks. Despite this clear control of coarse sediment size on channel slopes, the threshold of motion stress for bedload, alone, does not appear to control channel profile slopes here. Upper Boulder Creek, which is starved of coarse sediment, maintains high flow shear stresses well in excess of the threshold for motion. In contrast, lower Boulder Creek, with a greater coarse sediment supply, exerts high flow stresses much closer to the threshold for motion. We speculate that upper Boulder Creek has evolved to sustain partial alluvial cover and transfer greater energy to the bed via bedload impacts to compensate for its low coarse sediment supply. Thus bedload supply, bedrock erosion efficiency, and grain size all appear to influence channel slopes here. Copyright © 2017 John Wiley & Sons, Ltd.     

Ecological and environmental instream flow requirements for the Wei River—the largest tributary of the Yellow River

Instream flows are essential determinants of channel morphology, riparian and aquatic flora and fauna, water quality estuarine inflow and stream load transport. The ecological and environmental instream flow requirements (EEIFR) should be estimated to make the exploitation and utilization of water resources in a highly efficient and sustainable way and maintain the river ecosystem good health. As the largest tributary of the Yellow River, the Wei River is the ‘Mother River’ of Guanzhong region in Shaanxi province. It plays a great role in the development of West China and the health of the ecosystem of the Yellow River. The objective of this study is to estimate the EEIFR for improving the Wei River's ecological and environmental condition and develop the river healthily. Concerning the main ecological and environmental functions of the Wei River in Shaanxi Province, the EEIFR for each section of the Wei River including minimum instream flow requirements (IFR) for aquicolous biotopes maintenance, IFR for channel seepage, channel evaporation, stream self‐purification and sediment transportation were estimated in this paper. The methods to estimate the instream flow requirements for stream self‐purification and instream flow requirements for sediment transportation were proposed. The temporal scale of typical years include the year with the probability 25% of occurrence (high‐flow year), the year with the probability 50% (normal‐flow year) and the year with the probability 75% (low‐flow year). The results show that the EEIFR for the Wei River mainly include instream flow requirements for self‐purification and sediment transportation in each typical year. From high‐flow year to low‐flow year, the annual EEIFR for each reach decrease, except those for the reach from Linjiacun to Weijiabao, and from Linjiacun at the upper reaches to Huaxian at the lower reaches, and the annual reach EEIFR decrease in a sequence. Copyright © 2007 John Wiley & Sons, Ltd.     

Tree establishment on bars in low‐order gravel‐bed mountain streams

In many large alluvial rivers, trees often recruit and survive along laterally accreted sediments on bars. This produces a gradient of tree ages and composition with distance from the active channel. However, in low‐order, gravel‐bed mountain streams, such as the stream investigated in this study, it is suggested that vertical accretion results in sediment deposition patterns on bars that are often highly patchy. Consequently, tree species and ages are also heterogeneously distributed, rather than having distinct linear or arcuate banding patterns with distance from the channel. In addition, overall age patterns of trees on these bars follow the distribution of floods, with numerous young trees and few older trees. Recruitment is fairly continuous on these bars and is not correlated with high water years, suggesting that even flows close to bankfull levels are capable of transporting fine sediment to the bars on which trees establish. This pattern of sediment deposition/erosion and the resulting tree recruitment and survival seem to be a result of valley confinement and the lack of lateral accretion in these smaller, mountainous channels. Copyright © 2011 John Wiley & Sons, Ltd.     

洞庭湖城陵矶水道水力几何形态的研究

根据１９５１－１９８８年洞庭湖城陵矶站的水文测验资料,运用Ｌ．Ｂ．Ｌｅｏｐｏｌｄ河床力几何形态原理,建立洞庭湖出口－城陵矶水道河相关系式,研究该水道水力几何形态的特点及变化。研究表明,与河流水道相比,洞庭湖出口水道河宽指数ｂ随流量的变化较小,而水深指数ｆ及流速指数ｍ随流量的变化较大,河床横面具有窄深的特点。     

Enlargement and evolution of a semi‐alluvial creek in response to urbanization

The impact of urbanization on stream channels is of interest due to the growth of cities and the sensitivity of stream morphology and ecology to hydrologic change. Channel enlargement is a commonly observed effect and channel evolution models can help guide management efforts, but the models must be used in the proper geologic and climatic context. Semi‐alluvial channels characterized by a relatively thin alluvial layer over clay till and a convex channel profile in a temperate climate are not represented in currently available models. In this study we: (i) assess channel enlargement; and (ii) propose a channel evolution model for an urban semi‐alluvial creek in Toronto, Canada. The system is 90% developed with an imperviousness of approximately 47%. Channel enlargement is assessed by comparing 50 year old construction surveys, a recent survey of a relic channel, low‐precision surveys of channel change over a 15 year period, and high‐precision surveys over a three year period. The enlargement ratio of the channel since 1958 is 2.6, but could be as high 8.2 in comparison with the pre‐urban channel. When the increase in flow capacity is considered, the enlargement ratio is 1.9 since 1958 and up to 6.0 in comparison with the pre‐urban channel. Channel enlargement continues in the contemporary channel at an estimated rate of 0.23 m²/year. A five stage model is presented to describe channel evolution in the lower reaches. In this model the coarse lag material from glacial sources provides a natural resilience to the bed and incision occurs only after the increased flows from urbanization are combined with higher slopes as a result of channel straightening or avulsions. Further research should be done to assess stream behaviour close to an identified geologic control point. Copyright © 2018 John Wiley & Sons, Ltd.     

Dynamics of bedload transport in Turkey brook,a coarse-grained alluvial channel

Automatic and continuously recording samplers are deployed in a Hertfordshire gravel-bed stream to show that bedload transport is related to stream power. The pattern is similar to that already established for North American channels but, because the record is so detailed, it is possible to identify the cause of the considerable scatter that is normal in such relationships. A major factor is the occurrence of rhythmic pulses in bedload discharge that are not matched by similar fluctuations in hydraulic variables. It is suggested that these pulses reflect downstream differences in the concentration of mobile particles in a slow-moving traction carpet, and that they may be likened to kinematic waves. The record also reveals that the threshold of sediment transport—always presumed hithero to be associated with incipient motion—is related to the cessation of bedload transport in a river flood. Indeed, the mean value of stream power at the finish of bedload transport is only 20 percent of that prevailing at the moment of incipient sediment motion. Because of this, there is an inevitably poor correlation between actual bedload transport rates and those predicted by bedload equations which rely upon a single traction threshold. These new data show that the general inverse relationship between bedload discharge and water-depth : grain-size ratio proposed by Bagnold (1977, 1980) is not universal. Transport efficiency for this gravel-bed stream is typically 0.05 per cent of available stream power, which compares with 1.6 per cent for a river moving both gravel and sand, and 5 per cent for another channel where bedload is composed predominantly of sand-sized particles. It is argued that coarse and fine-grained alluvial channels may need to be considered separately. By allowing for differences in traction threshold at the beginning and end of bedload events, and by averaging bedload discharge flood by flood in order to smooth out the effect of pulses, it is possible to achieve a reasonably good prediction of average bedload transport rate in terms of stream power.     

Erosion, sediment transportation and accumulation in rivers

The present paper analyses the interrelation between erosion, sediment transportation and accumulation proposed by N. I. Makkaveyev （1908-1983） and its further development in modem studies of river channel processes in Russia. Spatio-temporal linkages between erosion and accumulation are defined considering channel processes at different scales - river longitudinal profile, channel morphological patterns, alluvial bedforms （bars, dunes） and individual sediment particles. Relations between river geomorphic activity, flow transportation capacity and sediment budgets are established （sediment input and output; channel bed erosion and sediment entrainment into flow - termination of sediment transport and its deposition）. Channel planforms, floodplain segments separated by the latter and alluvial channel bedforms are shown to be geomorphic expressions of sediment transport process at different spatial and temporal scales. This paper is dedicated to the 100th anniversary of N. I. Makkaveyev, Professor of the Moscow State University, author of the book ＂River channel and erosion in its basin＂ （1955）. That book is regarded in Russia as the pioneering work which initiated the complex hydrological and geographical studies of channel processes and laid a basis for the theory of unified fluvial erosion-accumulation process.