Estimating parameters of the channel width–flow discharge relation using rill and gully channel junction data

Eroding channels can usually be characterized by a power relationship between channel width (W) and channel discharge (Q). This paper examines the WQ relation using a recently developed channel junction approach to extend the validity of the WQ relation and to develop a procedure for estimating the WQ exponent and proportionality coefficient. Rill and gully channel data from the literature, and new data collected in different badland areas and in a few forest mountain streams, are analysed. Analysis shows that the WQ relation for channel width collected in badlands and forests agrees with trends observed for cropland. The exponent increases with increasing channel width in a continuous fashion rather than in a step‐like way and tends to a maximum whose value ranges between 0·5 and 0·6. The proportionality coefficient can be split into two terms, one expressing the case in which an eroding channel can broaden, the other reflecting the difficulties in removing the less erodible clods or rock fragments from the channel bed. Its splitting allows the development of a more correct form of the WQ relation in agreement with modern approaches of channel geometry: one part has the dimension of a discharge and makes the power base dimensionless, while the other brings the dimension of a length, needed for the channel width, into the WQ relation. The interpretation of the two constants is supported by data collected in rainfall‐runoff simulation experiments conducted in the field. Values characterizing the two constants in some environments are also given. Nevertheless the approach is not sufficiently parameterized yet to be of practical use (e.g. in models or for estimating peak discharge in areas where rill channels have formed). Copyright © 2009 John Wiley & Sons, Ltd.     

Dimension and frequency of bar formation in a braided river

This paper presents flume and field observations of a bank-confined braided river. Morphological features, including plan form configuration, channel width, and main channel migration, were examined by a series of experiments. Repeated measurements of channel morphology, provided a basis to estimate the relationship between noncumulative frequency of bars and bar area. Additional results from the Dajia River, located in Central Western Taiwan, were presented to provide a reference data set for comparing the laboratory and field data. The results indicate that the relationship between bar length and width can be predicted by a simple best-fit power function relating to self-similarity characteristics. The Hurst index by Walsh and Hicks (2002) provides acceptable predictions of the bar length and width observed in the experiments and confirmed by the field investigations. Eexperimental and field results both show that large river width yields a uniform distribution of bar areas with the similar discharge, leading to a large value of exponent (β) in the model. The river width is confirmed to be a critical parameter in the main channel shift. A small increase in channel width likely increased rapidly the shift cycle.     

Comparison of hydraulic geometry between sand‐ and gravel‐bed rivers in relation to channel pattern discrimination

A comparison has been made between the hydraulic geometry of sand‐ and gravel‐bed rivers, based on data from alluvial rivers around the world. The results indicate a signi?cant difference in hydraulic geometry among sand‐ and gravel‐bed rivers with different channel patterns. On this basis, some diagrams for discrimination of meandering and braided channel patterns have been established. The relationships between channel width and water discharge, between channel depth and water discharge, between width–depth ratio and water discharge and between channel slope and water discharge can all be used for channel pattern discrimination. The relationship between channel width and channel depth can also be used for channel pattern discrimination. However, the accuracy of these relationships for channel pattern discrimination varies, and the depth–discharge relationship is a better discriminator of pattern type than the classic slope–discharge function. The cause for this difference has been explained qualitatively. To predict the development of channel patterns under different natural conditions, the pattern discriminator should be searched on the basis of independent or at least semi‐independent variables. The relationship between stream power and bed material grain size can be used to discriminate channel patterns, which shows a better result than the discriminator using the slope–discharge relationship. Copyright © 2004 John Wiley & Sons, Ltd.     

DYNAMIC AND KINEMATIC WAVE MODELS FOR 1-D RILL FLOW: A COMPARISON

1INTRODUCTIONInprocess-basedoverlandflowandsoilerosionmodels,surfacerunoffonahillslopeisoftenrepresentedaseitherbroadsheetfloworflowinrillswithassumedrectangularchannelcrosssections(e.g.,Bairdelal1992,NSERL1995).Inmostcasesthehydraulicsofoverlandflowiscalculatedbyusingthekinematicwavemodel,whichisasirnplificationofthedynamicwavemodel(theequationsystemofSaint-Venantequationandequationofcontinuity).Forabroadsheetoverlandflowonhillslopeduetorainfallexcess,theequationofcontinuityiswherehis…     

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.     

Application of the single point measurement in discharge estimation

The fluid flow system can be described by an equivalent electromagnetic system. In this paper a successful application of the Biot–Savart law in hydraulics is presented. Similarity between the magnetic field of a current wire and the isovel contours in a channel cross-section is used to derive the isovel patterns in an open or closed channel. Having obtained the normalized isovel contours, one can easily obtain the discharge using a single point of velocity measurement at the conduit cross-section. The estimated discharge, based on measured points and the predicted isovels on the upper half of the flow depth away from the boundaries was within ±5% of the measured and much better in comparison to the prediction of one- and two-point methods. Furthermore, the model was applied to real life channels. The prediction of the water surface velocity for the River Unon in Japan and depth-averaged velocity for the Severn River in UK show a good agreement with the measured data and analytical results.     

Energy losses in compound open channels

This paper investigates energy losses in compound channel under non-uniform flow conditions. Using the first law of thermodynamics, the concepts of energy loss and head loss are first distinguished. They are found to be different within one sub-section (main channel or floodplain). Experimental measurements of the head within the main channel and the floodplain are then analyzed for geometries with constant or variable channel width. Results show that head loss differs from one sub-section to another: the classical 1D hypothesis of unique head loss gradient appears to be erroneous. Using a model that couple 1D momentum equations, called “Independent Sub-sections Method (ISM)”, head losses are resolved. The relative weights of head losses related to bed friction, turbulent exchanges and mass transfers between sub-sections are estimated. It is shown that water level and the discharge distribution across the channel are influenced by turbulent exchanges for (a) developing flows in straight channels, but only when the flow tends to uniformity; (b) flows in skewed floodplains and symmetrical converging floodplains for small relative flow depth; (c) flows in symmetrical diverging floodplains for small and medium relative depth. Flow parameters are influenced by the momentum flux due to mass exchanges in all non-prismatic geometries for small and medium relative depth, while this flux is negligible for developing flows in straight geometry. The role of an explicit modeling of mass conservation between sub-sections is eventually investigated.     

EFFECTS OF FLOW INTENSITY, OBSTACLE ALIGNMENT AND CROSS-SECTION GEOMETRY ON SCOUR AT BRIDGE ABUTMENTS

1 INTRODUCTION Local scour at bridge piers and abutments has long concerned engineers. Scour depth estimation has attracted considerable research interest and activity, and a number of prediction methods exist at present (see, e.g., comprehensive lists of predictors given by Melville and Colleman, 2000). Several studies have been completed since the 1950s for the particular case of scour at bridge abutments. Since the beginning of the 1980s, the University of Auckland, New Zealand, …     

The Coefficient of Friction in Channel Flows

The dimensionless Darcy–Weisbach coefficient of friction is used to evaluate the drag in channel flows. A developed turbulent flow with a quadratic drag law is considered. The dependence of the coefficient of friction on the cross-section shape of the channel flow is examined. A coefficient of the channel shape is introduced, which depends on the wetted perimeter and the flow width and allows the complicated geometry of the river cross-section to be taken into account in calculating the drag. The drag estimates calculated using the suggested technique are compared with other authors' estimates for flumes and rivers.     

Parsimonious sediment transport equations based on Bagnold's stream power approach

It is increasingly recognized that effective river management requires a catchment scale approach. Sediment transport processes are relevant to a number of river functions but quantifying sediment fluxes at network scales is hampered by the difficulty of measuring the variables required for most sediment transport equations (e.g. shear stress, velocity, and flow depth). We develop new bedload and total load sediment transport equations based on specific stream power. These equations use data that are relatively easy to collect or estimate throughout stream networks using remote sensing and other available data: slope, discharge, channel width, and grain size. The new equations are parsimonious yet have similar accuracy to other, more established, alternatives. We further confirm previous findings that the dimensionless critical specific stream power for incipient particle motion is generally consistent across datasets, and that the uncertainty in this parameter has only a minor impact on calculated sediment transport rates. Finally, we test the new bedload transport equation by applying it in a simple channel incision model. Our model results are in close agreement to flume observations and can predict incision rates more accurately than a more complicated morphodynamic model. These new sediment transport equations are well suited for use at stream network scales, allowing quantification of this important process for river management applications. Copyright © 2017 John Wiley & Sons, Ltd.     

MODELLING THE SENSITIVITY OF CHANNEL ADJUSTMENTS IN DESTABILIZED SAND-BED RIVERS

Comprehensive empirical data of the response of unstable streams over a range of environmental conditions are unavailable. In this study, as a substitute for empirical data, a physically based numerical model of channel evolution is used in a range of numerical simulation experiments designed to predict the sensitivity of channel response to changes in control variables. The scope of the study is limited by the scope of the numerical model which applies to straight, sand-bed streams with cohesive bank materials that have been destabilized by sediment starvation and evolve towards equilibrium through bed degradation followed by channel widening. Results are presented for stable and unstable channel conditions. Stable channel depths are most sensitive to channel discharge, though the critical threshold shear stress for the entrainment of cohesive bank materials and discharge are both significant in determining the width. The sediment load, channel gradient, bank material cohesion, size of failed bank material aggregates and the initial bank height have sensitivities an order of magnitude smaller than discharge for both width and depth. Variations in bed material characteristics within the sand-size range are found to have little impact on simulated stable channel morphology. For unstable channels, the relative dominance of parameter sensitivities is examined in the context of an empirical-conceptual model of channel evolution proposed by Thorne and Osman (1988), to highlight the relationships between parameter dominance, time, and the processes and forms characterizing individual stages of channel evolution. Rates of change with time of width and depth sensitivity parameters for five tested independent variables (discharge, sediment supply, channel gradient, bank material cohesion and bed material size) are found to vary as a function of time, such that different stages of channel evolution are characterized by variations in the relative dominance of tested variables. The results support the hypothesis proposed by Thorne and Osman (1988) that the critical bank height required to initiate mass-wasting and widening may be regarded as a geomorphic threshold.     

Fluvial geomorphology of the Middle Reach of the Huai River

The Middle Reach of the Huai River （MRHR） flows northeast into the Hongzehu Lake. Before entering the Hongzehu Lake, the Huai River has a braided channel which is shallow and wide, and the riverbed has a negative slope. Based on the characteristics of the MRHR, this river reach can be divided into the following sections： a quasi-straight （or mildly curved） section, a bend section, and a braided section. The majority of the MRHR is quasi-straight. In this paper, several parameters are used to assess the geomorphology of the MRHR. Statistical analyses are performed to establish a relationship between the span length ＂L＂ and channel width ＂B＂ for different channel patterns. The relationship between the meandering length ＂S＂ and bankfull channel width ＂B＂ is also derived. Results indicate that the bankfull channel width ＂B＂, the bankfull cross sectional area ＂A＂ and the average flow depth ＂H＂ are mainly dependent on the dominant discharge in the channel. A relationship is derived that describes the denendencv of the curvature radius ＂R＂ on the dominant discharae ＂O＂. water surface slone ＂J＂and the turning angle ＂α＂.     

FLUVIAL PROCESSES AND SEDIMENT SCOUR RATE OF THE YELLOW RIVER UNDER ACTION OF UNSTEADY FLOWS

1 wrsoooCTIoxThe Yeuow mver crtes a huge amoun of sedimcht and the noods often cause raPid and severeerosinn and dePOsihon. The channl bed of the YelOw mver often exPeriences degIadation in the mainchannel during fioods. In some cases vigorous erosion uP to l0 meters takes place in a shOrt Period oftiIn. Such phenomenon usually occurs in the ndddie reaChs of the Yelow mver and its tributaries suchas the Wdse mVer the Beiluohe mver etc. For examPle, th6 hyPenconcentraed nood in July l…     

The variability in the morphological active width: Results from physical models of gravel‐bed braided rivers

The morphological active width, defined as the lateral extent of bed material displacement over time, is a fundamental parameter in multi‐threaded gravel‐bed rivers, linking complex channel dynamics to bedload transport. Here, results are presented from five constant discharge experiments, and three event hydrographs, covering a range of flow strengths and channel configurations for which morphological change, bedload transport rates, and stream power were measured in a physical model. Changes in channel morphology were determined via differencing of photogrammetrically‐derived digital elevation models (DEMs) of the model surface generated at regular intervals over the course of ~115 h of experimental runs. Independent measures of total bedload output were made using downstream sediment baskets. Results indicate that the morphological active width increases with total and dimensionless stream power and is strongly and positively correlated with bulk change (total volume of bed material displaced over time) and active braiding intensity (ABI). Although there is considerable scatter due to the inherent variability in braided river morphodynamics, the active width is positively correlated with independent measurements of bedload transport rate. Active width, bulk change, and bedload transport rates were all negligible below a dimensionless stream power threshold value of ~ 0.09, above which all increase with flow strength. Therefore, the active width could be used as a general predictor of bulk change and bedload transport rates, which in turn could be approximated from total and dimensionless stream power or ABI in gravel‐bed braided rivers. Furthermore, results highlight the importance of the active width, rather than the morphological active depth, in predicting volumes of change and bedload transport rates. The results contribute to the larger goals of better understanding braided river morphodynamics, creating large high‐resolution datasets of channel change for model calibration and validation, and developing morphological methods for predicting bedload transport rates in braiding river systems. Copyright © 2018 John Wiley & Sons, Ltd.     

Variation in hydraulic geometry for stable versus incised streams in the Yazoo River basin-USA

The effects of basin hydrology on hydraulic geometry of channels variability for incised streams were investigated using available field data sets and models of watershed hydrology and channel hydraulics for the Yazoo River basin,USA.The study presents the hydraulic geometry relations of bankfull discharge,channel width,mean depth,cross-sectional area,longitudinal slope,unit stream power,and mean velocity at bankfull discharge as a function of drainage area using simple linear regression.The hydraulic geometry relations were developed for 61 streams,20 of them are classified as channel evolution model(CEM) Types Ⅳ and Ⅴ and 41 of them are CEM streams Types Ⅱ and Ⅲ.These relationships are invaluable to hydraulic and water resources engineers,hydrologists,and geomorphologists involved in stream restoration and protection.These relations can be used to assist in field identification of bankfull stage and stream dimension in un-gauged watersheds as well as estimation of the comparative stability of a stream channel.A set of hydraulic geometry relations are presented in this study,these empirical relations describe physical correlations for stable and incised channels.Cross-sectional area,which combines the effects of channel width and mean channel depth,was found to be highly responsive to changes in drainage area and bankfull discharge.Analyses of cross-sectional area,channel width,mean channel depth,and mean velocity in conjunction with changes in drainage area and bankfull discharge indicated that the channel width is much more responsive to changes in both drainage area and bankfull discharge than are mean channel depth or mean velocity.     

A unifying framework for watershed thermodynamics: constitutive relationships

The balance equations for mass and momentum, averaged over the scale of a watershed entity, need to be supplemented with constitutive equations relating flow velocities, pressure potential differences, as well as mass and force exchanges within and across the boundaries of a watershed. In this paper, the procedure for the derivation of such constitutive relationships is described in detail. This procedure is based on the method pioneered by Coleman and Noll through exploitation of the second law of thermodynamics acting as a constraint-type relationship. The method is illustrated by its application to some common situations occurring in real world watersheds. Thermodynamically admissible and physically consistent constitutive relationships for mass exchange terms among the subregions constituting the watershed (subsurface zones, overland flow regions, channel) are proposed. These constitutive equations are subsequently combined with equations of mass balance for the subregions. In addition, constitutive relationships for forces exchanged amongst the subregions are also derived within the same thermodynamic framework. It is shown that, after linearisation of the latter constitutive relations in terms of the velocity, a watershed-scale Darcy's law governing flow in the unsaturated and saturated zones can be obtained. For the overland flow, a second order constitutive relationship with respect to velocity is proposed for the momentum exchange terms, leading to a watershed-scale Chezy formula. For the channel network REW-scale Saint–Venant equations are derived. Thus, within the framework of this approach new relationships governing exchange terms for mass and momentum are obtained and, moreover, some well-known experimental results are derived in a rigorous manner.     

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.     

Viscosity-excluded formulations of 2-D river flow with a new wetting and drying algorithm

An efficient method for simulating 2-D river flow is developed in which horizontal turbulent shears are omitted from the 2-D depth-averaged momentum equations. It is shown that a pseudo-viscosity can be reproduced to take into account the lost shear action, by incorporating the vertically integrated continuity equation to the momentum equations and transforming the latter into a discrete integral form. To simulate river flows with wet and dry areas, negative water depths are allowed when solving the continuity equation. The concept of negative water depth enables us to track flow boundaries with about the same accuracy but much less effort as compared with traditional numerical methods. An optimal threshold value defining dry areas is first obtained by one-dimensional theoretical analysis and then sought by trial-and-error for two-dimensional flow simulation with tolerable node-to-node spurious oscillations, while mass is best conserved. Numerical solutions using the new procedure are compared with the one-dimensional benchmark solution of the Saint Venant equations and the experimental data from a two-stage channel. Robustness of the present approach is also tested through the study of water flow in a natural river and a hypothetical channel with several bumps.     

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.