EXPERIMENTAL STUDY ON BED SCOUR IN A 90° CHANNEL BEND

1 INTRODUCTION Scouring in the bend ways leads to deep sections at the toe of the outer bank of the bend. The presenceof secondary currents and the greater depths at the outer bank cause high velocity along the outer bank.The high velocity and shear stres…     

Channel erosion along the Carmel river,Monterey county,California

Historic maps, photographs, and channel cross-sections show that the channel of the Carmel River underwent massive bank erosion, channel migration, and aggradation in a major flood in 1911, then narrowed and incised by 1939. The channel was stable until 1978 and 1980, when bank erosion affected some reaches but not others. The narrowing and incision were in response to a lack of major floods after 1914 and construction in 1921 of a dam that cut off sediment supply from the most actively eroding half of the basin. Localized erosion in 1978 and 1980 occurred during low magnitude events along reaches whose bank strength had been reduced by devegetation. These events illustrate that the stability of a fluvial system can be disrupted either by application of a large erosive force in a high magnitude event (the 1911 flood) or in a low magnitude event, by reducing the resistance to erosion (bank devegetation). The Carmel River is a potentially unstable system. Its discharge and slope characteristics place it near the threshold between meandering and braided. On the Lower Carmel, the presence of bank vegetation can make the difference between a narrow, stable meandering channel and a wide shifting channel with braided reaches.     

Minimum froude number and the equilibrium of alluvial sand rivers

Rivers adjust towards an equilibrium condition, the stability of which depends upon a set of controlling factors expressed by the Froude number. As alluvial river channels approach stable conditions, the Froude number of the channel flow will tend to attain a minimum value which reflects minimum bed material motion and maximum channel stability, under the constraints imposed by water discharge, sediment load, and particle size. Computer simulations for sand bed rivers show that the Froude number of the flow tends to a minimum value when the equilibrium river tends to a certain hydraulic geometry. Evidence from 57 alluvial sand material rivers and stable canals shows that this simulated hydraulic geometry with minimum Froude number corresponds to the natural equilibrium state.     

Relationship between the equilibrium morphology of river islands and flow-sediment dynamics based on the theory of minimum energy dissipation

River islands are vital geomorphic units in alluvial rivers, and the variation of their morphology and position plays a significant role in regulating flow-sediment transport and channel stability. Based on the theories of minimum energy dissipation theory of fluid movement and river morphodynamics, this study uses the river islands in anabranching channels to analyze the relationship between the shape coefficient of river island and the flow-sediment dynamics under stable equilibrium conditions...     

Analytical findings for power law cross-sections: Uniform flow depth

Analytical results concerning open channel flows are presented, assuming that the cross-section is defined by a power law relationship between the channel width and the channel depth. Explicit equations to compute the normal flow depth are derived by considering the liquid discharge, the channel roughness height and the cross-section geometry (based on knowledge of the power law exponent, the reference width, and the reference depth) as known quantities.Such equations are deduced by writing the physical quantities as a power expansion in the power law exponent and expressing the wetted perimeter using a Gauss hypergeometric function. With the designed procedure, an accurate estimations of the integrals required to invert the uniform flow formula are obtained, at least for cross-sections characterized by aspect ratios of technical interest.Two relationships are proposed between the normal depth and the flow discharge. The first relationship is shown to work well for any discharge, provided that the width to depth ratio is sufficiently large. If this is not the case, the second procedure must be used for non-dimensional discharge larger than a given threshold, while the former procedure remains valid under the threshold.     

Flow resistance equation for rills

In this paper, a new flow resistance equation for rill flow was deduced applying dimensional analysis and self‐similarity theory. At first, the incomplete self‐similarity hypothesis was used for establishing the flow velocity distribution whose integration gives the theoretical expression of the Darcy–Weisbach friction factor. Then the deduced theoretical resistance equation was tested by some measurements of flow velocity, water depth, cross section area, wetted perimeter, and bed slope carried out in 106 reaches of some rills shaped on an experimental plot. A relationship between the velocity profile, the channel slope, and the flow Froude number was also established. The analysis showed that the Darcy–Weisbach friction factor can be accurately estimated by the proposed theoretical approach based on a power–velocity profile.     

Dynamics of river–aquifer interactions along a chalk stream: the River Lambourn,UK

This paper describes the spatial and temporal pattern of groundwater flow accretion to the River Lambourn, a 234 km² chalk catchment of the West Berkshire Downs, UK, which has been largely unaffected by groundwater abstraction. Variations in the discharge measured at four fixed gauges in the catchment, coupled with information on the length of flowing channel over the period 1983–2001, are used to describe regional patterns in flow accretion. Mean catchment accretion generally exceeds 0·15 m³ s⁻¹ km⁻¹, but there are significant differences between perennial reaches indicating how the combination of local structural controls and seasonal changes in the drainage net affect flow accretion. Data from current meter surveys were used to determine the spatial variability in flow accretion: 505 paired observations along 12 reaches between 1 and 2·95 km in length indicated a consistent spatial trend in accretion. Accretion was high in upstream and downstream channel reaches, and in middle reaches where dry valleys intersected the main valley. A flow accretion index was developed to describe the relationship of flow accretion in each of the 12 study reaches to catchment discharge. The relationship varied from a strong positive correlation with catchment discharge (two reaches), a weak positive correlation (three reaches), a strong negative correlation (two reaches), to no relationship to catchment discharge (four reaches). The results highlight the need to reconsider the usual assumption of uniform, or uniformly increasing, flow accretion in chalk catchments. Moreover, they emphasize the importance of catchment topography, and illustrate how flow accretion in individual reaches may vary between high and low groundwater levels. Copyright © 2005 John Wiley & Sons, Ltd.     

Non-linear laminar flow into well partially penetrating a porous aquifer of finite thickness

In steady state condition, non-linear laminar flow of fluid into a well partially penetrating a porous aquifer of finite thickness is considered. The influence of such a flow on discharge and its dependence on related physical quantities are investigated. It is observed that the discharge into the well decreases as the depth of the well is decreased and the region of non-linear laminar flow is widened, which is quite obvious from physical considerations. As a particular case, result for a fully penetrating well has been deduced.     

Suspended sediment dynamics at high and low storm flows in two small watersheds

A record spanning almost 20 years of suspended sediment and discharge measurements on two reaches of an agricultural watershed is used to assess the influence of in‐channel sediment supplies and bed composition on suspended sediment concentrations (SSC). We analyse discharge‐SSC relationships from two small streams of similar hydrology, climate and land use but widely different bed compositions (one dominated by sand, the other by gravel). Given that sand‐dominated systems have more fine sediment available for transport, we use bed composition and the relative proportion of surface sand and gravel to be representative of in‐channel sediment supply. Both high flow events and lower flows associated with onset and late recessional storm flow (‘low flows’) are analysed in order to distinguish external from in‐channel sources of sediment and to assess the relationship between low flows and sediment supply. We find that SSC during low flows is affected by changes to sediment supply, not just discharge capacity, indicated by the variation in the discharge‐SSC relationship both within and between low flows. Results also demonstrate that suspended sediment and discharge dynamics differ between reaches; high bed sand fractions provide a steady supply of sediment that is quickly replenished, resulting in more frequent sediment‐mobilizing low flow and relatively constant SSC between floods. In contrast, SSC of a gravel‐dominated reach vary widely between events, with high SSC generally associated with only one or two high‐flow events. Results lend support to the idea that fine sediment is both more available and more easily transported from sand‐dominated streambeds, especially during low flows, providing evidence that bed composition and in‐channel sediment supplies may play important roles in the mobilization and transport of fine sediment. In addition, the analysis of low‐flow conditions, an approach unique to this study, provides insight into alternative and potentially significant factors that control fine sediment dynamics. Copyright © 2007 John Wiley & Sons, Ltd.     

Shaping and maintaining a medium-sized main channel in the Lower Yellow River

This paper studies relations between bankfull discharge,lateral cross section variation and the incoming flow and sediment condition in the Lower Yellow River using measured data from 1950 to 2003.Since 1950 the bankfull discharge has obviously decreased and the ratio of channel width to flow depth has increased.The critical annual average incoming sediment coefficient（defined as the ratio of sediment concentration to discharge） and discharge at the Huayuankou station are approximately 0.012 and 1,850 m³s^-1,respectively,for no accumulative deposition occurring in the reach from Huayuankou to Lijin.On this basis,a mathematical model is used to study the scale of the main channel in the Lower Yellow River and its corresponding bankfull discharge under possible incoming flow and sediment conditions in the near future.The main factors influencing the scale of the main channel are analyzed,and measures to shape and maintain a medium-sized channel are discussed.The results show the effect of various water and sediment combinations released from the Xiaolangdi Reservoir on the shaping of the main channel and suggest that under recent incoming flow and sediment conditions,it is possible to shape and maintain a medium-sized channel with a bankfull discharge of approximate 4,000 m³ s^-1.     

Planform dynamics of braided streams

The high dynamism and complexity of braided networks poses a series of open questions, significant for river restoration and management. The present work is aimed at the characterization of the morphology of braided streams, in order to assess whether the system reaches a steady state under constant flow conditions and, in that case, to determine how it can be described and on which parameters it depends. A series of 14 experimental runs were performed in a laboratory physical model with uniform sand, varying the discharge and the longitudinal slope. Planimetric and altimetric configurations were monitored in order to assess the occurrence of a steady state. A set of parameters was considered, such as the braid‐plain width and the number and typology of branches and nodes. Results point out that a relationship exists between braiding morphology and two dimensionless parameters, related to total water discharge and stream power. We found that network complexity increases at higher values of water discharge and a larger portion of branches exhibits morphological activity. Results are then compared to the outputs of a simple one‐dimensional model, that allows to easily predict the average network complexity, once the bed topography is known. Model computations permit also the investigation of the effect of water discharge variations and to compare different width definitions. The at‐a‐station variability of planimetric parameters shows a peculiar behaviour, both regarding number of branches and wetted width. In particular, the analysis of the relationship between width and discharge highlighted relevant differences in comparison to single thread channel. Copyright © 2009 John Wiley & Sons, Ltd.     

Velocity-discharge relationships in three lowland rivers

The use of different functional forms to describe the variation of velocity with discharge is explored for four cross-sections, nine short reaches (100-250 m), and three long reaches (2-7 km) in three lowland rivers in Lincolnshire. The traditional log-linear relationship applies to more than half the cases, the degree of correlation never falling below 0-9. Although probably more valid from a physical standpoint, the log-quadratic relationship-is only moderately successful, one problem being the position of the vertex relative to bankfull discharge. Alternative formulations based on a kinematic routing model and a partitioned log-linear model have restricted application. Rates of change of velocity with discharge are relatively high in these lowland rivers, not only at-a-station but also downstream. One explanation is that velocity becomes particularly sensitive to local slope and within-channel vegetation conditions as discharge decreases, resulting in rather low velocities at small discharges. Cross-sectional and reach-based results are compared for neighbouring stretches of river. Velocities in short reaches do not differ appreciably from those at nearby cross-sections or from those in long reaches with a length of less than 3 km. By integrating within-reach variability and avoiding the need to chose a representative cross-section, velocity measurement over short reaches is probably preferable to that at cross-sections as a basis for at-a-station hydraulic geometry.     

Simulation of flow geometry in a riffle-pool stream

The nature of the flow in most natural streams is gradually varied rather than uniform. This is particularly true of streams with coarse gravel bed material organized into relatively stable riffle and pool features. In spite of this, there are few applications of the gradually varied flow models (e.g. the Bernoulli equation) to such streams. This paper presents some initial results of a simulation of flow patterns in two riffle-pool reaches, using an open channel flow profile computation method based on an equation defining an energy balance between successive cross-sections separated by an incremental distance.     

Multiple temporal scale relationships of bankfull discharge with streamflow and sediment transport in the Yellow River in China

This paper presents a study on the characteristics of multiple time scales of bankfull discharge and its delayed response to changes of flow conditions using continuous wavelet analysis for data from selected hydrological stations in the Yellow River basin. Results showed that bankfull discharge series had one or two dominant time scales. For example, the Huayuankou station in the lower reach of the Yellow River had two dominant time scales of 19-20 years and 545 years. The dominant time scales of the bankfull discharge series were generally consistent with the dominant time scales of water discharge and sediment concentration series, indicating that the channel morphology inherits the characteristics of the hydrological system in terms of multiple time scales. In addition, the wavelet coefficients of the bankfull discharge series had a phase difference in relation to those of the sediment concentration series, with a delay time that varied from 3 to 16 years at different sites. This delay time or relaxation time is a result of the delayed response of bankfull discharge to flow conditions, which was significant for channel adjustments in response to changes of flow conditions. The findings of the multiple time scales and the delayed response are of importance for further study of channel morphology of fluvial systems.     

特征差分法在水位推流上的应用

本文阐述了在符合明渠非恒定流一维定床条件的水文测站,应用变化的特征差分格式,将两断面实测水位过程线推算为流量过程线的原理、方法和应用实例,对理论推算的流量过程和实测流量过程进行了比较分析。从泗洪站和运河站的成果看出,推流和实测过程线基本吻合,精度较高。因此可以明显看出,应用本法推流,不但安全可靠,具有节约人力、物力等经济效益,还可提高测验精度、防止高洪期流量的错测、漏测,保证洪水资料的连续和完整。在湖泊水量平衡计算中,同样可以借助两组水尺获得的水位资料进行推流,无需设置专用流量站。     

Effects of vegetation on channel morphodynamics: results and insights from laboratory experiments

A series of laboratory experiments demonstrates that riparian vegetation can cause a braided channel to self‐organize to, and maintain, a dynamic, single‐thread channel. The initial condition for the experiments was steady‐state braiding in non‐cohesive sand under uniform discharge. From here, an experiment consisted of repeated cycles alternating a short duration high flow with a long duration low flow, and uniform dispersal of alfalfa seeds over the bed at the end of each high flow. Plants established on freshly deposited bars and areas of braidplain that were unoccupied during low flow. The presence of the plants had the effect of progressively focusing the high flow so that a single dominant channel developed. The single‐thread channel self‐adjusted to carry the high flow. Vegetation also slowed the rate of bank erosion. Matching of deposition along the point bar with erosion along the outer bend enabled the channel to develop sinuosity and migrate laterally while suppressing channel splitting and the creation of new channel width. The experimental channels spontaneously reproduced many of the mechanisms by which natural meandering channels migrate and maintain a single dominant channel, in particular bend growth and channel cutoff. In contrast with the braided system, where channel switching is a nearly continuous process, vegetation maintained a coherent channel until wholesale diversion of flow via cutoff and/or avulsion occurred, by which point the previous channel tended to be highly unfavorable for flow. Thus vegetation discouraged the coexistence of multiple channels. Varying discharge was key to allowing expression of feedbacks between the plants and the flow and promoting the transition from braiding to a single‐thread channel that was then dynamically maintained. Copyright © 2010 John Wiley & Sons, Ltd.     

Channel change,bankfull and effective discharges on a vertically accreting,meandering, gravel‐bed river

Along the lower reaches of the Waipaoa River, New Zealand, cross‐section survey data indicate there was a 23 per cent decrease in bankfull width and a 22 per cent reduction in channel cross‐section area between 1948 and 2000, as the channel responded to increased inputs of fine (suspended) sediment following deforestation of the headwaters in late C19 and early C20. We determined the bankfull discharge within a ～39 km long reach by routing known discharges through the one‐dimensional MIKE 11 flow model. The model runs suggest that the bankfull discharge varies between ～800 and ～2300 m³ s^?1 and that the average recurrence interval is 4 ± 2 years on the annual maximum series; by contrast, the effective flow (360 m³ s^?1) is equaled or exceeded three times a year. The variability in bankfull discharge arises because the banks tend to be lower in places where flood flows are constricted than in reaches where overbank flow is dispersed over a wide area, and because scour has counteracted aggradation in some locations. There is no downstream variation in Shields stress, or in relative shear stress, within the study reach. Bankfull shear stress is, on average, five times greater than the shear stress required to initiate motion. At the effective discharge it is more than twice the threshold value. The effective discharge probably has more relevance than the bankfull discharge to the overall picture of sediment movement in the lower reaches of the Waipaoa River but, because width is constrained by the stability and resistance of the bank material to erosion during high flows that also scour the bed, the overall channel geometry is likely determined by discharges at or near bankfull. Copyright © 2006 John Wiley & Sons, Ltd.     

The channel-geometry method: Guidelines and applications

All river engineering schemes require flood discharge estimates as part of the design and appraisal process. Unfortunately, continuous measurement of flood discharges is limited to those river sites with instrumented gauging stations, which constitute only a small proportion of channel reaches where information is required. Therefore, considerable research effort has been devoted to the development of reliable indirect techniques of flood discharge estimation. Research on the interrelationship of stream channel geometry and river discharge has provided the basis for an indirect method of flood estimation – the channel-geometry method – which employs river channel dimensions alone to estimate discharge characteristics at ungauged river sites. Channel-geometry equations are developed empirically by relating streamflow data from gauging stations and channel dimensions measured from natural river reaches in the vicinity of the gauge, and take the form of power function relations. Once regional channel-geometry equations have been defined, a channel width or channel capacity measurement is the only variable needed to estimate the flood flow characteristics at a specified river site. The method is useful as an alternative to traditional catchment-based approaches or as a rapid reconnaissance technique. In addition to the application for flood discharge prediction, channel-geometry equations could prove helpful in the management of river channels, first, by providing a basis for assessing local deviations in the channel form–discharge relation, deviations which could be employed as indicators of the sensitivity of particular stretches of river channel to change, and secondly, in the computation of natural channel dimensions for use in river channel design and river restoration.     

Recent variation in reach‐scale bankfull discharge in the Lower Yellow River

Bankfull discharge is a key parameter in the context of river engineering and geomorphology, as an indicator of flood discharge capacity in alluvial rivers, and varying in response to the incoming flow and sediment regimes. Bankfull channel dimensions have significantly adjusted along the Lower Yellow River (LYR) due to recent channel degradation, caused by the operation of the Xiaolangdi Reservoir, which has led to longitudinal variability in cross‐sectional bankfull discharges. Therefore, it is more representative to describe the flood discharge capacity of the LYR, using the concept of reach‐averaged bankfull discharge. Previous simple mean methods to estimate reach‐scale bankfull discharge cannot meet the condition of flow continuity or account for the effect of different spacing between two sections. In this study, a general method to calculate cross‐sectional bankfull discharge using the simulated stage‐discharge relation is outlined briefly, and an integrated method is then proposed for estimating reach‐scale bankfull discharge. The proposed method integrates a geometric mean based on the log‐transformation with a weighted average based on the spacing between two consecutive sections, which avoids the shortcomings of previous methods. The post‐flood reach‐scale bankfull discharges in three different channel‐pattern reaches of the LYR were estimated annually during the period from 1999 to 2010 using the proposed method, based on surveyed post‐flood profiles at 91 sedimentation sections and the measured hydrological data at seven hydrometric sections. The calculated results indicate that: (i) the estimated reach‐scale bankfull discharges can effectively represent the flood discharge capacity of different reaches, with their ranges of variation being less than those of typical cross‐sectional bankfull discharges; and (ii) the magnitude of the reach‐scale bankfull discharge in each reach can respond well to the accumulative effect of incoming flow and sediment conditions. Finally, empirical relationships for different reaches in the LYR were developed between the reach‐scale bankfull discharge and the previous four‐year average discharge and incoming sediment coefficient during flood seasons, with relatively high correlation coefficients between them being obtained, and the reach‐scale bankfull discharges in different reaches predicted by the delayed response model were also presented for a comparison. These relations for the prediction of reach‐scale bankfull discharges were validated using the cross‐sectional profiles and hydrological data measured in 2011. Copyright © 2013 John Wiley & Sons, Ltd.     

An appraisal of the velocity-reversal hypothesis for stable pool-riffle sequences in the river severn,England

The ‘velocity-reversal hypothesis’ is the linchpin for a number of recent conceptual models pertaining to sediment sorting and the maintenance of pool-riffle sequences in gravel-bedded streams. The literature in support of the hypothesis together with published adverse criticism is reviewed. It is concluded that convincing evidence for the ubiquitous occurrence of such a reversal in a range of channel geometries is currently unavailable. Continuity considerations indicate that riffles need to be considerably wider than pools for a reversal in the mean velocity to occur under conditions of subcritical flow, high stage, and stable morphology. These observations are substantiated by a detailed study of the hydraulic geometry of stable pool-riffle sequences in the River Severn, England. Neither the sectionally-averaged velocity nor the near-bed shear velocity is sensibly greater in the pools than over the riffles during bankfull or near bankfull flow. Instead a tendency towards equalization of the values of average hydraulic variables is noted as discharge increases. A detailed investigation of the three-dimensional character of the flow is required to demonstrate whether the entrainment forces within pools can locally exceed those over neighbouring riffles. Unusual behaviour of the energy gradient over riffles during moderate discharges is related to backwater effects as mediated by the spacing of the riffles. The hydraulic data are used to comment on the stability of the test reaches in the context of the development of the River Severn in the vicinity of Shrewsbury.