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This paper proposes an analytical model to predict the lateral distribution of streamwise velocity for flow in a curved channel with vertical sides, based on the depth-integrated Navier–Stokes equations. The model includes the effects of bed friction, lateral turbulence and secondary flows, where the additional secondary flow is approximated by a linear function of the lateral distance, as demonstrated by the limited data which are available. Two analytical solutions for the depth-averaged velocity are obtained, one for a flat bed and another for a bed with a transverse slope. Two parameters (denoted by m and n herein), which define the secondary flow, have been examined to analyze how they affect the velocity distribution in these two cases. Comparison of the analytical results with the limited experimental data available shows that the proposed model predicts the lateral distributions of depth-averaged velocity well. Further studies are needed to validate the values of the model parameters ( m and n ) for bends with different geometric properties.

Six distinct “views” of river hydraulics are presented, beginning with what influences us today, given our shared history, to what we can learn from others as they tackled research topics in their day. Other views relate to how we regard rivers through laboratory studies, the computer screen or in nature at full scale, and to how we might view research problems in the future. Interspersed with these various views are 10 questions that are frequently asked of river engineers, along with some possible answers. In attempting to answer these particular questions, some insights gained from a career in river hydraulics research are offered as a guide to others, both in practice or academe, as they raise some further issues which are worth reflecting on. This paper is particularly aimed at emerging hydraulic researchers and young engineers who are embarking on a career in river hydrodynamics.

In this paper, the authors present experimental results of overbank flow in compound channels with nonprismatic floodplains and different convergence angles. The depth-averaged velocity, the local velocity distributions, and the boundary shear stress distributions were measured along the converging flume portion for different relative depths. The momentum balance is used to analyze the force acting on the flow in the main channel and for the whole cross section. Using the experimental data, various terms in the momentum equation are also calculated. The apparent shear forces on the vertical interface between the main channel and floodplains are evaluated for compound channels with nonprismatic floodplains, and the results are then compared with the prismatic cases. The energy balance in nonprismatic compound channels is also investigated by using the water surface elevation.

This paper presents a method for predicting the lateral distribution of depth-averaged streamwise velocity in straight prismatic open channels with emergent vegetation. The approach is fully consistent with the original Shiono and Knight method of analysis, and extends it to include the drag force due to vegetation, modelled as an additional momentum ‘sink' term, with the blockage effect of the vegetation modelled by way of a porosity analogy. An analytical solution to the depth-integrated Reynolds-averaged Navier–Stokes equation is given which includes the effects of bed friction, drag force, lateral turbulence and secondary flows, governed by four coefficients f, CD, λ and Γ respectively. The analytical results are shown to predict the lateral distributions of depth-averaged velocity well for three sets of experimental data: one for inbank flow in a partially vegetated channel and two for overbank flows in compound channels with partially vegetated floodplains. The analytical solution is also shown to give identical results to numerical simulations of the same governing Reynolds-averaged Navier–Stokes equation applied to some experiments undertaken in the UK Flood Channel Facility. The lateral distribution of bed shear stress is also obtained through the Darcy–Weisbach friction factor, thus providing a basis for modelling flood conveyance, fluvial processes and eco-environmental impacts in natural rivers.

The following work explores the possibility of applying an evolutionary algorithm (NSGA-II) to automate the calibration procedure of a quasi 2-D numerical model. Seven rivers are examined, with discharges and flow depths ranging from 6 to 450 m 3 /s and 0.49 to 3.69 m, respectively. The calibration procedure is based on matching lateral distributions of depth-mean velocity, for which data exist. The results are compared with simulations undertaken by an expert user using traditional calibration techniques. The new approach compares favourably with the expert user and is able to provide an insight into the optimum calibration parameters, from which further scientific knowledge could be developed.

This paper considers whether the application of principal component analysis to a free overfall in an open channel can yield any further insights into the variables which govern the relationship between the depth of flow at the start of the free overfall and the critical depth. It is shown that for a channel of rectangular cross-section, the width, the end depth, the square root of bed slope and the square root of the critical slope can be considered to be the primary variables of interest. While a possible relationship between these variables is suggested, it is noted that the precise form of the relationship is beyond the abilities of principal component analysis.

Modelling the boundary shear stress distribution using a depth-averaged approach such as the Shiono and Knight method can give inaccurate results due to poor representation of secondary current cells. The perturbations in the experimental boundary shear stress distributions were analysed to develop an improved modelling approach to capture the secondary current cells effects. This approach is applied to a variety of experimental data, and accurate results were obtained for both the depth-averaged velocity and boundary shear stress distributions. The outcome indicates that the standard calculation of the boundary shear stress can overestimate the shear values. The proposed modelling approach is applied to compute sediment transport based on equations using the boundary shear stress. The analytical sediment transport results could not predict the experimental values despite the improvement in the boundary shear stress distribution, mainly due to limitations of the sediment equations.

In this paper, genetic programming (GP) is used as an effective model induction tool to solve a classic problem in open channel flow: the free overfall. By applying GP to experimental data of circular channels with a flat bed and employing a model selection procedure, a reliable expression in the form of is found for calculating the critical depth (hc) and end-depth ratio (EDR). Further effort is made to verify the applicability and superiority of this expression for channels with other cross sections. This global expression not only outperforms other expressions in estimating the critical depth, it is also dimensionally correct (unlike some other applications of GP) and can be used for channels with any cross-section and any flow regime.

Roughness plays an essential role in water level estimation for rivers, watercourses and drains. It reduces the discharge capacity through energy expenditure from boundary-generated turbulence as well as physical blockages caused by vegetation. Today's practitioners are constantly challenged with identifying, quantifying and simulating these processes to provide vital information for a range of flood risk management tasks. This paper introduces the roughness advisor, one of a series of tools embedded in the recently developed Environment Agency's conveyance and afflux estimation system. The roughness advisor provides an extensive database of roughness information from a diverse set of sources (>700) and presents it in a structured manner to enable users readily to select from a range of in-channel and floodplain vegetation and bed material types. Traditionally, flow resistance datasets are based on average values of Manning's n for whole river sections. Here, the notion of a local unit roughness nl is introduced and its performance is demonstrated through flow prediction for a range of channel types. Further applications are used to compare the unit roughness with the traditional Manning n, to trial a boulder roughness approach and to describe the sensitivity and relative importance of roughness in the calculation of channel flow.

The Shiono and Knight Method (SKM) is known as a capable tool to model flow in prismatic compound channels. This research explores whether SKM can be used to predict depth-averaged velocity and boundary shear stress in compound channels with non-prismatic floodplains. For this reason SKM was modified and used in combination with an extensive experimental data set of depth-averaged velocity and boundary shear stress measurement to investigate the issue over three various floodplain converging angles and relative depths. The modeling results indicate a good agreement between the experimental data and the modified SKM. Also, based on the momentum balance and using the experimental data on compound channel with non-prismatic floodplains lateral variations of the depth-averaged apparent shear stress, the Reynolds shear stress, and the secondary flow were investigated. The results reveal that the Reynolds shear stress is significant at the interface between the main channel and floodplains and secondary flow ha...

Natural rivers are commonly characterized by a main channel for primary flow conveyance and a floodplain, often partially covered with vegetation such as shrubs or trees, to carry extra flow during floods. The hydraulic resistance due to vegetation on the floodplain typically causes a further reduction of flow velocity and increases the velocity difference between the main channel and the floodplain. As a consequence a strong lateral shear layer leads to the exchange of mass and momentum between the main channel and floodplain, which in turn affects the overall channel conveyance and certain fluvial processes. The prediction of the lateral velocity distribution is important for many flood alleviation schemes, as well as for studies on sediment transport and dispersion in such channels. The present paper proposes a method for predicting the depth-averaged velocity in compound channels with partially vegetated floodplains, based on an analytical solution to the depth-integrated Reynolds-Averaged Navier-Stokes equation with a term included to account for the effects of vegetation. The vegetation is modelled via an additional term in the momentum equation to account for the additional drag force. The method includes the effects of bed friction, drag force, lateral turbulence and secondary flows, via four coefficients f, CD, λ & Γ respectively. The predicted lateral distributions of depth-averaged velocity agree well with the experimental data. The analytical solutions can also be used to predict the distribution of boundary shear stresses, which adds additional weight to the method proposed.

Some practical and theoretical concepts related to the use of an acoustic Doppler current profiler (ADCP) in a small river are examined. The importance of understating the limitations of the measurement equipment and a system for locating the exact position of the ADCP are discussed. Details of a new measurement protocol which is suitable for small rivers are presented. Small samples of data measured in the River Blackwater are used to illustrate the concepts outlined in the paper. It is concluded that ADCPs can be successfully used in small rivers provided sufficient care is taken over their deployment and subsequent data analysis. However, in some cases it is acknowledged that additional modifications to the ADCP may need to be undertaken as illustrated in the paper.

Stream power can be an extremely useful index of fluvial sediment transport, channel pattern, river channel erosion and riparian habitat development. However, most previous studies of downstream changes in stream power have relied on field measurements at selected cross-sections, which are time consuming, and typically based on limited data, which cannot fully represent important spatial variations in stream power. We present here, therefore, a novel methodology we call CAFES (combined automated flood, elevation and stream power), to quantify downstream change in river flood power, based on integrating in a GIS framework Flood Estimation Handbook systems with the 5 m grid NEXTMap Britain digital elevation model derived from IFSAR (interferometric synthetic aperture radar). This provides a useful modelling platform to quantify at unprecedented resolution longitudinal distributions of flood discharge, elevation, floodplain slope and flood power at reach and basin scales. Values can be resolved to a 50 m grid. CAFES approaches have distinct advantages over current methodologies for reach- and basin-scale stream power assessments and therefore for the interpretation and prediction of fluvial processes. The methodology has significant international applicability for understanding basin-scale hydraulics, sediment transport, erosion and sedimentation processes and river basin management. Copyright © 2008 John Wiley & Sons, Ltd.

The Shiono and Knight method (SKM) is a simple depth-averaged flow model, based on the RANS equations which can be used to estimate the lateral distributions of depth-averaged velocity and boundary shear stress for flows in straight prismatic channels with the minimum of computational effort. However, in order to apply the SKM, detailed knowledge relating to the lateral variation of the friction factor (f), dimensionless eddy viscosity (λ) and a sink term representing the effects of secondary flow (Γ) are required. In this paper a multi-objective evolutionary algorithm is used to study the lateral variation and value of these parameters for simple trapezoidal channels over a wide range of aspect ratios through the model calibration process. Based on the available experimental data, four objectives are selected and the NSGA-II algorithm is applied to several datasets. The best answer for each set is then selected based on a proposed methodology. Rules relating f, λ and Γ to the wetted parameter ratio (Pb/Pw) for a variety of situations have been developed which provide practical guidance for the engineer on choosing the appropriate parameters in the SKM model.

Tests were carried out to investigate bridge afflux phenomena for bridge constrictions in a compound channel flume. The flume had different roughness configurations in the main channel and floodplains. All tests were undertaken for the condition of no eccentricity and no entrance rounding. The normal crossing (ø = 0°) and two different skew angles (ø = 30° and 45°) were tested for different arch and flat soffit type bridge models. For each set of experiments, the Froude number for normal depth, afflux ratio and blockage ratio (area of bridge below water level to total flow area) were obtained based on an analogical method developed previously. These quantities were analysed to obtain a simple practical afflux equation. This afflux equation was also applied to field data collected by the US Geological Survey and the results were compared with those obtained using the more complex methods such as HEC-2, WSPRO and USBPR.

This paper presents a method to predict depth-averaged velocity and bed shear stress for overbank flows in straight rectangular two-stage channels. An analytical solution to the depth-integrated Navier–Stokes equation is presented that includes the effects of bed friction, lateral turbulence, and secondary flows. The Shiono and Knight method accounts for bed shear, lateral shear, and secondary flow effects via three coefficients, f , λ , and Γ , respectively. A novel boundary condition at the internal wall between the main channel and the adjoined floodplain is proposed and discussed along with other conventional boundary conditions. The analytical solution using the novel boundary condition gives good prediction of both lateral velocity distribution and bed shear stress when compared with experimental data for different aspect ratios.

This paper illustrates a new approach to obtaining analytical stage–discharge formulae for both zonal and total discharges in straight prismatic channels of any shape, based on the concepts of a zero–shear force interface and an analytical solution for the lateral variation of depth-averaged velocity. The analytical solution for velocity is derived from the depth-integrated form of the Navier–Stokes equations, and includes the effects of bed friction, lateral turbulence, and secondary flows/planform vorticity. The analytical formulae for stage discharge are given for both simple and compound trapezoidal channels, together with formulae that permit the boundary shear force to be determined for every linear element on the wetted perimeter. These stage–discharge and shear force formulae depend on the channel geometry and on three hydraulic parameters related to the bed friction factor f, lateral eddy viscosity λ and depth-averaged secondary flow Γ, as required in the original Shiono and Knight method. The analytical results show good agreement with experimental data. Ways of extending this approach to more complex shaped channels are outlined.

This paper reviews a model, developed by Shiono and Knight [Shiono K, Knight DW. Two-dimensional analytical solution for a compound channel. In: Proceedings of the 3rd international symposium on refined flow modelling and turbulence measurements, Tokyo, Japan, July 1988. p. 503–10; Shiono K, Knight DW. Turbulent open channel flows with variable depth across the channel. J Fluid Mech 1991;222:617–46 [231:693]], which yields analytical solutions to the depth-integrated Navier–Stokes equations, and includes the effects of bed friction, lateral turbulence and secondary flows. Some issues about the original model developed by Shiono and Knight (1988, 1991) are highlighted and discussed. Based on the experimental data concerning the secondary flow, two assumptions are proposed to describe the contribution of the streamwise vorticity to the flow. Two new analytical solutions are compared with the conventional solution for three simple channel shapes and one trapezoidal compound channel to highlight their differences and the importance of the secondary flow and planform vorticity term. Comparison of the analytical results with the experimental data shows that the general SKM predicts the lateral distributions of depth-averaged velocity well.

Estimating water level underpins almost all river flood risk management (FRM) tasks from identifying routine channel maintenance actions to developing comprehensive sustainable FRM measures. Research over the past 50 years has seen considerable advances in estimating flow capacity; however, much of this knowledge has not been transferred into industry practice. This paper introduces the Conveyance and Afflux Estimation System (CES/AES) software, the primary output from two UK Environment Agency Research projects, which aim to bridge this gap between science and practice. The focus is the conveyance element, which provides a means for estimating flow capacity for a range of channel types, flow conditions and vegetation and substrate cover. An overview of the methodology and testing is given, together with a practical example of its use in decision making. The method is applied to 16 river sites from the United Kingdom, New Zealand, Argentina and Ecuador, exhibiting model performance for a wide range of channel and flow conditions. Simulations of depth-averaged velocities at four sites are compared with observations, improving confidence in the underlying methods. The CES/AES toolset is also used in assessing flood risk versus ecological objectives for a small UK river, where vegetation is of significant conservation value but impacts flow capacity.

Analytic stage–discharge formulae are derived for flow in straight trapezoidal channels, based on the 2D analytic velocity distribution in open channels given by Shiono and Knight [Shiono K, Knight DW, Turbulent open-channel flows with variable depth across the channel. J Fluid Mech 1991;222:617–46]. A simple hand-calculation method is provided. Legendre incomplete elliptic integrals of the first and second kinds and a binomial series expansion are used in the derivation of these analytic formulae, together with physically based hydraulic parameters, such as local friction factor ( f ), dimensionless eddy viscosity ( λ ) and secondary flow ( Γ ). The stage–discharge results obtained from the formulae are shown to be in good agreement with experimental data, as are the corresponding analytic velocity and boundary shear stress distributions. The influences of f , λ and Γ on the stage–discharge relationship are also discussed.

Three analytic stage-discharge formulas, suitable for hand calculation, have been derived for prismatic open channels. The three types of prismatic geometry investigated are: simple rectangular, symmetric, and asymmetric rectangular compound channels. The formulas include three key parameters that govern the local friction factor, eddy viscosity, and secondary flow. The discharge results and the corresponding analytic depth-averaged velocity and bed shear stress distributions show good agreement with the experimental data, even when constant parameter values are assumed. The influence of these three parameters on the stage-discharge relationships is explored.

Some significant flood events that have occurred in various European countries in the last decade are described. They are used to illustrate the widespread nature of flooding, its economic impact and the resultant loss of life. The underlying hydro-meteorological causes of each flood are outlined, followed by a brief chronology of the flood event and the subsequent consequences. The flood events have been drawn from countries with differing climatic conditions, and from river basins that differ in both size and topography. The selection includes floods from the following countries: the Czech Republic, France, Germany, Hungary, Poland, Switzerland and the UK. The events include examples of both flash floods and slower basin-wide floods. The important lessons that may be drawn from these events are highlighted, as are the economic impacts such floods might have in the future due to climate change.

Understanding the hydraulics of flow in a compound channel with vegetated floodplains is very important for determining the stage-discharge curve and for supporting the management of fluvial processes. In this paper, the flow patterns over different types of vegetation, such as tree, shrub, and grass, are described, based on an experimental study. For vegetation on the floodplain, the authors choose plastic grass, duck feathers, and plastic straws as model grass, shrubs, and trees, respectively. A 3D acoustic Doppler velocimeter was used to measure the local flow velocities for different types of vegetation on the floodplain, and the total discharge and flume slope were measured independently. In the cases of nonvegetated floodplains, all measured streamwise velocity distributions followed the logarithmic distribution, but for vegetated floodplains, they followed an S-shaped profile, exhibiting three zones. For all cases, the fluctuating velocity followed a normal distribution. The influence of different types of vegetation on the distributions of the secondary currents, turbulence intensities, and Reynolds shear stresses were also analyzed.

The Shiono and Knight method (SKM) offers a new approach to calculating the lateral distributions of depth-averaged velocity and boundary shear stress for flows in straight prismatic channels. It accounts for bed shear, lateral shear, and secondary flow effects via 3 coefficients— f,λ , and Γ —thus incorporating some key 3D flow feature into a lateral distribution model for streamwise motion. The SKM incorporates the effects of secondary flows by specifying an appropriate value for the Γ parameter depending on the sense of direction of the secondary flows, commensurate with the derivative of the term Hρ(UV )d . The values of the transverse velocities, V , have been shown to be consistent with observation. A wide range of boundary shear stress data for trapezoidal channels from different sources has been used to validate the model. The accuracy of the predictions is good, despite the simplicity of the model, although some calibration problems remain. The SKM thus offers an alternative methodology to the mo...

Several sets of experimental data on conveyance capacity, the division of flow between a main river channel and its floodplains, boundary shear, and sediment transport in overbank flow are presented. The strengths and weaknesses of various 1-D modelling approaches are highlighted. The coherence method (COHM) of Ackers [J. Hydraul. Res. 31 (1993) 509] and the weighted divided channel method (WDCM) of Lambert and Myers [Proc. Inst. Civil Engineers Water Maritime Energy 130 (1998) 84] are shown to be two useful 1-D methods for dealing with overbank flows. They are relatively simple to apply, and give not only the stage–discharge relationship, but also the division of flow between the main channel and the floodplains. Their general validity has been extended by testing the two methods against data sets other than those used in their original formulation.A modified version of the WDCM is presented that gives better predictions for homogeneously roughened channels. It is shown that the WDCM does not give good p...

Flooding in the USA and elsewhere, as well as issues related to climate change, have again alerted politicians and scientists to the dangers that floods pose. This article, written by international river experts from several countries, is aimed at giving readers an insight into what engineers are currently doing to understand the underpinning science, to improve hydrodynamic flow models and to develop better flood risk management procedures. It reviews fluvial flooding from a European perspective, describes recent R&D studies in the UK, China & Japan and highlights the need for more international collaboration.

Some laboratory sediment-transport experiments are described in which a compound channel with a mobile-bed composed of uniform sand with a d50 of 0.88 mm was subjected to overbank flows. The main river channel was monitored to determine the effect of floodplain roughness on conveyance capacity, bed-form geometry, resistance, bed-load transport, and dune migration rate. The floodplain roughness was varied to simulate a wide range of conditions, commensurate with conditions that can occur in a natural river. For a given discharge, the main river channel bed was found to adjust itself to a quasi-equilibrium condition governed by the lateral momentum transfer between the floodplain and main channel flows and the local alluvial resistance relationship appropriate for the proportion of total flow in the main river channel. The sediment transport rate was found to reflect all these influences. The data are summarized in equation form for comparison with other experimental studies and for checking numerical river simulation models.

Some small-scale laboratory results are presented concerning sediment transport rates and stage–discharge relationships in compound channels. The sediment transport data confirm the hypothesis of Ackers (Proceedings of the Institution of Civil Engineers, Water, Maritime & Energy, 1992, 96, No. 6, 167–178) that the bed load concentration generally increases up to bankfull flow, then peaks at around this discharge, before declining again with increasing overbank discharge. Experimental data concerning velocity and boundary shear stress distributions, the interaction between the floodplain and the main channel, and alluvial resistance are also presented. Simple empirical relationships summarise the discharge, sediment transport rate, division of flow, resistance, and boundary shear force data, to aid comparison with other experimental studies and numerical river simulation models that simulate the geomorphological response of rivers to flood events.

The prediction of the stage-discharge relationship for rivers in flood is described by a finite element model of depth-averaged turbulent flow, calibrated using (hree hydraulic coefficients governing local bed friction, lateral eddy viscosity and depth-averaged secondary flow. The resulting lateral distributions of depth-averaged velocity are subsequently integrated to yield the stage-discharge relationship. The calibration of the model involves the establishment of simplifying hypotheses for certain coefficients in order to give the correct depth-mean velocity and boundary shear, both across the channel and with stage. Comparisons against some experimental data from the UK Flood Channel Facility, for channels with trapezoidal and compound cross-sections, help develop the calibration philosophy for both inbank and overbank flows. Numerical experiments with the coherence method for a hypothetical river are used to extend the model calibration to rivers with homogeneous and heterogeneous roughness. Applicat...

Ten years ago a landslide in the mountains of Ecuador killed over 100 people. It also blocked a mountain river, creating a temporary flood reservoir that, a month later, burst through the debris and caused extensive flood damage downstream. The geomorphology of the whole valley was substantially altered and it become unstable, not helped by continued local aggregate mining. This paper reports on the delicate, long-term operation to monitor and stabilise the Paute river valley, including shaving two million m3 off a mountain and installing a novel system of drop structures on the river bed.

This paper highlights the similarities between a number of studies which have applied the concept of Shannon's entropy to Hydraulic Engineering. The entropy concept is further developed in an attempt to predict the transverse distribution of boundary shear stress in circular open channels. The approach is also extended and applied to circular channels with a flat bed and trapezoidal channels, and the Lagrange multipliers, λ, found by recourse to empirical equations. Doubts are expressed concerning the value of the entropy approach to such problems.

The critical depth of flow (hc) and the brink depth (hb), for a circular pipe with and without a horizontal bed are used to estimate the channel discharge. The brink depth ratio (hb/hc) for a given cross section geometry is shown to be a constant for subcritical flow. The brink depth ratios for various channel geometries and bed slopes are presented in a form readily accessible to engineers. Two worked examples, one for an irrigation channel and the other for a larger circular sewer, show how the discharge Q can be obtained from measurement of the brink depth.

Some large scale experiments concerning equilibrium sand channels with overbank flow are described. The experiments were undertaken in the UK Flood Channel Facility (FCF) configured into a straight compound channel with fixed banks, a mobile main channel composed of uniform sand with a d50 of around 0.8mm, and two symmetric floodplains. The main channel alluvial resistance changed with flow depth and discharge in a complex way arising from the effects of both bedforms and the floodplain/main channel interaction processes. Overall, zonal and local resistance coefficients for this type of channel are reviewed and the data discussed in relation to practical modelling of alluvial channels with overbank flow.

This paper tackles a practical problem in flood routing, the estimation of the speed of propagation of the flood wave. It is well known that this propagation speed varies with the discharge in quite a complex manner for natural rivers. The principal innovative step in this paper is the identification of a relatively simple conceptual model of river geometry to obtain two methods for generating realistic wave speeds from a standard river cross-section survey. These are verified against data from two rivers in the UK, showing good agreement with wave speeds deduced from long-term flow records. This work is expected to be of particular value in building forecasting models of ungauged or partially gauged river systems, as it removes the need for long concurrent records to estimate wave speeds.

The distribution of boundary shear stress in circular conduits flowing partially full, with and without a smooth flat bed simulating deposited sediments, has been examined experimentally ranging from 0.375 < F < 1.96 (F = Froude number) and 65,000 < R < 342,000 (R = hydraulic radius), using the Preston tube technique. The invert level of the flat bed and the water depth have been varied to simulate a wide range of possible flow conditions that may occur in culverts, sewers, and hydropower tunnels. The distribution of boundary shear stress around the wetted perimeter is shown to be highly sensitive to changes in cross-sectional shape. The results have been analyzed in terms of the variation of local/global shear stress versus perimetric distance, and the percentage of the total shear force acting on the wall or bed of the conduit. The %SFw results (%SFw = the percentage of the average wall shear force of the overall shear force) have been shown to agree well with Knight's empirical formula for prismatic channels. The influence of secondary flows on the distribution of boundary shear stress and the implications of this for sediment transport have also been examined.

Recent large-scale experiments in the UK Flood Channel Facility concerning equilibrium sand channels are described. The experiments involved free-formed channels and straight sediment channels with fixed banks, using a uniform sand with a d 50 of around 0.8 mm. Inbank, bankfull and overbank flows were investigated, and an overview of the experimental procedures, results and implications for practitioners is given. Some of the operational difficulties, successes and lessons learnt from these novel experiments are also reviewed. Some practical lessons are drawn concerning the application of rational regime theories to alluvial channels, channel morphology and sediment transport rates.

(1999). Variable parameter Muskingum-Cunge method for flood routing in a compound channel. Journal of Hydraulic Research: Vol. 37, No. 5, pp. 591-614.

An investigation of energy losses due to boundary friction, secondary flow, turbulence, expansions and contractions in meandering compound channels with overbank flow is described.The compound meandering channel was divided into three sub-areas, namely the main channel below the bankfull level, the meander belt width above the bankfull level and a region outside the meander belt above the bankfull level, and turbulence data obtained by a Laser Doppler anemometer system.The energy loss due to the shear stress on the horizontal plane at the bankfull level was estimated using the measured Reynolds stresses and sectional averaged velocity, and the energy loss due to secondary flow below the bankfull level was then estimated.Both energy losses were found to make a significant contribution to the total energy loss in the lower layer for shallow overbank flow.The energy losses due to the contraction and expansion in the meander belt were evaluated and found to be a significant component of the total energy loss ...

The simple Variable Parameter Muskingum-Cunge (VPMC) method is still frequently used for flood routing. However, difficulties arise in the selection of an appropriate “reference” discharge for evaluating the routing parameters and in the small volume loss that can occur. Several commonly used schemes for the VPMC method are compared through a series of numerical experiments that cover different channel bed slopes and different space/time steps. The tests show that 4-point schemes are better than 3-point schemes, that a certain amount of volume loss (up to 8%) still occurs in all schemes, and that an empirical relationship exists between the volume loss and channel bed slope (S). A new scheme for the VPMC method is presented, with the routing parameters (c and D) being modified to take into account the longitudinal hydrostatic pressure gradient term. This scheme improves the routed hydrographs, not only with regard to the sensitivity of the outflow peak for given space and time steps, but also with regard ...

Discharge measurements for overbank flow were carried out in a two-stage meandering channel with various bed slopes, sinuosities, and water depths. The effect of bed slope and sinuosity on discharge was found to be significant. A simple design equation for the conveyance capacity, based on dimensional analysis, is proposed. This equation may be used to estimate the stage-discharge curve in a meandering channel with overbank flow. Predictions of discharge using existing methods and the proposed method are compared and tested against the new measured discharge data and other available overbank data. The strengths and weaknesses of the various methods are discussed.

A new solution to the stable-channel paradox has been derived based on the contribution of secondary flow to the redistribution of boundary shear stress. This new solution was then combined with the entropy-based bank profile equations, the flow-continuity condition, an appropriate frictional resistance relation, and a sediment transport relation to develop a new geometric model for straight stable alluvial channels. Furthermore, the effect of nonuniform boundary particle sizes was introduced to make the new geometric model applicable to a wide range of both laboratory experiments and natural alluvial rivers. A FORTRAN program was developed to compute the design procedure. The comparisons between the cross-sectional shapes, depths, and widths calculated by the new geometric model and field and laboratory data show that the proposed geometric model is in reasonable agreement with the data both for well-graded and for nonuniform bed materials.

A new approach has been developed for designing the shape and dimensions of the cross section of a straight threshold channel based on the concepts of entropy and probability. A formula for the lateral distribution of transverse slopes, and hence the cross-sectional bank profile, was derived by the entropy-maximisation principle and the calculus of variations. The bank profile is a new type of simple parabolic curve. The results of numerical experiments based on the approach of boundary shear stress distribution support the conclusion that the entropy-based channel bank profile is at threshold. Bank profile equations are coupled with an appropriate frictional relationship to obtain a new design method. Channel dimensions and bank profiles predicted by this method are compared with those given by other design methods. The predicted channel dimensions are in reasonable agreement with laboratory experimental data.

The value of integrating mathematical modelling with experimental work in both the laboratory and field is illustrated through the development of a software tool that deals with key practical issues related to rivers in flood. The Conveyance Estimation System software (www.river-conveyance.net) is aimed primarily at estimating the stage-discharge relationship, the distribution of depth-averaged velocity and boundary shear stress across channels of any prismatic shape for both inbank and overbank flows. The practical problems in obtaining data and the theoretical issues in identifying relevant flow parameters for stream wise and planform vorticity, turbulence shear stresses and frictional resistance are highlighted. The significance of these and their relevance to other hydraulics problems are noted. The issues involved in moving from data to theory (or vice-versa), then to practical application, are described in general terms, beginning with how to develop a model as a research tool, testing it against different data sets, through to using the model in practice with embedded tools. The tools deal with uncertainties in estimates and give guidance on roughness coefficients in natural channels.

A new rational regime theory for stable alluvial channels is developed in this paper. Based on the concepts of stream power and fluvial process probability, a basic regime equation with a modified aspect ratio relationship is analytically derived. Most existing explicit regime equations can be transformed into the format of the proposed basic regime equation. A relationship for the basic regime coefficient is derived after introducing the concept of a 'fluvial processes index'. A suitable resistance relationship and a sediment transport formula are then coupled with the basic regime equation to determine depth, width and slope of the regime channel. The new regime theory is compared with existing regime equations and is also appied to field data and laboratory data. The predicted channel dimensions are in good agreement with observed values.

A philosophy for calibrating a numerical simulation river model for overbank flow using three calibration coefficients related to local friction factors, eddy viscosities and secondary flows is described. A comparison is made against some data from the UK Flood Channel Facility (FCF) and comments made as to the inherent difficulty of calibrating such a depth-averaged model. The model is also applied to the simulation of sediment transport fluxes and the results are compared with those obtained using the coherence method.

Two-stage open-channel flow is physically modeled using air as the working fluid in a straight, wide, smooth, closed duct of compound cross section. Time-averaged velocity and boundary shear-stress measurements are analyzed and presented in a form pertaining to the lateral shear-layer mechanism.

This paper examines the feasibility of applying a mobile, large scale particle image velocimetry (LS-PIV) system to a 300 m reach of a small river in order to estimate the discharge. Detailed velocity measurements at a number of locations were carried out using an acoustic Doppler current profiler (ADCP) and acoustic Doppler velocimetry (ADV) for inbank, bankfull and overbank flows. The lateral distributions of the velocity index k (i.e., the ratio of the depth-averaged velocity to the surface velocity) were found to be influenced by the secondary currents, channel vegetation and flow conditions. An attempt is made to quantify the relationship between secondary flow and the velocity index. Appropriate conclusions and advice relating to the practical use of a LS-PIV system as applied to a small river are given.

Mean flow distributions of primary velocity and boundary shear stress were measured in a wide closed duct with a range of asymmetric compound cross-sections. The cross-sectional geometries included three different wall angles, vertical, 1:1 and 1:2 (vertical:horizontal) at the interface between the shallow and deep subsections. Results are presented for the effect of relative depth and wall angle upon primary velocity, boundary shear stress and friction factors. The particularly detailed boundary shear stress measurements indicate the presence of secondary flow on the flood plain even at the lowest relative depths, where it would not normally be identified by coarser spacing of the data.