Overbank Flow in Compound Channels with Nonprismatic Floodplains

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.     

Flow Resistance and Momentum Flux in Compound Open Channels

New formulations are presented for flow resistance and momentum flux in compound open channels. As implemented in the St. Venant equations, these formulations facilitate a physically enhanced approach to evaluating conveyance, roughness, stage-discharge relationship, and unsteady flood routing in compound open channels. An analysis using steady flow data from the well-controlled experiments at the large-scale Flood Channel Facility, HR Wallingford, demonstrates the ability of the present approach to properly resolve the discontinuity of overall roughness across the main-channel bankfull level. Also, the proposed formulations are shown to be conducive to obviating the long-standing computational difficulty in unsteady flood routing due to small flow depths over flat and wide floodplains. The present work should find general applications in one-dimensional computation of river flows.     

Behavior of Meandering Overbank Channels with Graded Sand Beds

Measurements of velocity distributions, depth variation, and sediment transport have been made under bankfull and overbank flow conditions in meandering channels with a graded sand bed, using the large-scale U.K. Flood Channel Facility. The overbank conditions depend upon the relative strength of opposing secondary circulation cells generated by shear at the channel crossover and centrifugal forces around the meander bend. Generally the shear-generated secondary flow either reversed or weakened the centrifugal circulation around the next downstream bend. This led to considerable modification of the main channel bed morphology, which, in turn, altered flow distributions. Measurements of the lateral distribution of bed load were made using a ?-scale Helley–Smith sampler. This demonstrated that the bed load was generally concentrated within a limited width of the channel and tended to take the shortest route through the meanders. Comparisons of observed and calculated bed material load gives an indication of how secondary circulation around meanders, under both bankfull and overbank conditions, affects the predictive performance of formulas derived for predominantly one-dimensional flow.     

Lateral Depth-Averaged Velocity Distributions and Bed Shear in Rectangular Compound Channels

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.     

Flow Characteristics of Skimming Flows in Stepped Channels

Skimming flows in stepped channels are systematically investigated under a wide range of channel slopes (5.7°?θ?55°). The flow conditions of skimming flows are classified into two flow regimes, and the hydraulic conditions required to form a quasi-uniform flow are determined. An aerated flow depth of a skimming flow is estimated from the assumption that the residual energy at the end of a stepped channel coincides with the energy at the toe of the jump formed immediately downstream of the stepped channel. In a quasi-uniform flow region, the friction factor of skimming flows is represented by the relative step height and the channel slope. The friction factor for the channel slope of θ=19° appears to have a maximum. The residual energy of skimming flows is formulated for both nonuniform and quasi-uniform flow regions. Further, a hydraulic-design chart for a stepped channel is presented.     

Flow Patterns in Compound Channels with Vegetated Floodplains

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.     

Three-Dimensional Hydrodynamics of Meandering Compound Channels

The velocity field in meandering compound channels with overbank flow is highly three dimensional. To date, its features have been investigated experimentally and little research has been undertaken to investigate the feasibility of reproducing these velocity fields using computer models. If computer modeling were to prove successful in this context, it could become a useful prediction technique and research tool to enhance our understanding of natural river dynamics. In particular, an accurate computer prediction of the velocity field could benefit studies of channel morphology and pollution transport. In this paper, a meandering channel experiment from the U.K. Flood Channel Facility is simulated using computational fluid dynamics and the predicted velocities compared with the experimental data. Particular attention is paid to the reproduction of the secondary velocities and the helical motion of the water flowing within the main channel. Sensitivity tests of mesh design, discretization scheme, and roughness height are reported, together with the turbulence characteristics of the flow.     

Upstream Discharge Distribution in Compound-Channel Flumes

Common inlet design for compound-channel flumes does not ensure a proper upstream discharge distribution. As the total head in the upstream tank is the same for both main-channel and floodplain subsections, the velocity in the upstream section is also the same in both subsections. The floodplain discharge is therefore too large and a mass transfer towards the main channel occurs along the flume. This Technical Note investigates how long a compound-channel flume must be to ensure that equilibrium between subsection discharges is achieved. The required length is found to be significant compared to the actual length of experimental flumes reported in the literature.     

Gravitational and Shear Instabilities in Compound and Composite Channels

Linear analysis of gravitational instabilities in the presence of a shear layer and shear instabilities in the presence of a free surface is performed. This study is relevant to shallow mixing layers, such as flow in compound and composite channels and inflows at channel junctions. The variations of the channel bed, velocity profile, Froude number, and friction coefficients with the transverse (lateral) coordinate are considered. It is found that there is a threshold Froude number above which the flow is unstable with respect to gravity waves and below which the flow is unstable with respect to shear waves for a certain range of the bed friction number. For values of Froude number larger than the threshold value, the influence of the shear layer and channel walls on the characteristics of the gravitational instability is strong when the channel and the shear layer are of comparable width. This influence reduces as the channel becomes wider and disappears in the limit when the channel width becomes infinite. When the Froude number is below the threshold value, free surface deformation in the form of gravitational waves exerts a strong stabilizing influence on the shear instability. In particular, the value of the critical bed friction number decreases when either the Froude number of the fast stream (main channel) or the slow stream (flood plain) increases. That is, shallow mixing layers become more stable as the Froude number increases. Comparisons of the linear stability calculations with experimental data show reasonable agreement.     

Three-Dimensional Modeling of Negatively Buoyant Flow in Diverging Channels

Diverging channels, also known as diffusers, represent common natural and industrial outlets to lakes, reservoirs, and rivers. If the outflow in a diffuser has a larger density than the ambient water, the inflow may plunge and form a density underflow. In this paper, a three-dimensional numerical study was conducted to gain insight into the mechanism of negatively buoyant flows in diffusers with a sloping bottom. Of particular interest is the formation of separated flows such as wall-jet and free-jet flows. Various cases of plunging and the associated density current in a diffuser with different divergence angles and inflow densimetric Froude numbers are considered. The model successfully simulates the formation of attached flow, wall jets, and free jets in a negatively buoyant environment. The onset, evolution, and stabilization of a stall and the subsequent development of a wall jet in a negatively buoyant flow are investigated in detail. Computed results also show favorable agreement with some published experimental data on density current generated by the plunging of cold water in ambient warm water in a diverging channel.     

Hydraulically Efficient Power-Law Channels

A power-law channel is a generalized form of a channel and includes parabolic and triangular cross sections. For an exponent m<0.5 in the power law, the relative wetted perimeter has been estimated from a series expansion truncated to four terms. For values of the exponent m ≥ 0.5 the relative wetted perimeter has been estimated using an appropriate non-linear interpolation expression. A table to estimate relative wetted perimeter based on these expressions is presented for design purposes. With these expressions for relative wetted perimeter, and using the Lagrange method of undetermined multipliers, for any given maximum side slope, the area and/or wetted perimeter is minimized subject to the equality constraint of a uniform flow (Mannings) equation. Using this technique, for any given side slope, the exponent of the power-law channel can be determined and hydraulically efficient power-law channels can be designed. Optimized power-law channels are compared with trapezoidal and parabolic channels. The existing parabolic design of the Pehur High Level Canal, Pakistan is compared with an optimum power-law channel.     

Interacting Divided Channel Method for Compound Channel Flow

A new method to calculate flow in compound channels is proposed: the interacting divided channel method (IDCM), based on a new parametrization of the interface stress between adjacent flow compartments, typically between the main channel and floodplain of a two-stage channel. This expression is motivated by scaling arguments and allows for a simple analytical solution of the average flow velocities in different compartments. Good agreement is found between the analytical model results and laboratory data from the literature.     

Depth-Averaged Velocity Distribution in Straight Trapezoidal Channels

In trapezoidal channels that are not “wide,” the banks exert form drag on the fluid and thereby control the depth-averaged velocity distribution. As such, commonly used equations for predicting depth-averaged velocities in wide channels are not well suited for predicting depth-averaged velocities in trapezoidal channels. Using data from three previous studies, we developed two models for predicting depth-averaged velocity distributions in straight trapezoidal channels. The data used to develop the models had a range of discharges (8.05–4,248?L/s), velocities (0.16–1.03?m/s), bottom widths (0.305–3.62?m), flow depths (0.0518–0.805?m), and bank slopes (1.0–3.0, horizontal/vertical). The first model requires measured velocity data for calibrating the model coefficients, whereas the second model uses prescribed coefficients. The first model yielded velocity distributions with coefficients of determination (r2) from 0.84 to 0.90 and we recommend its use when possible because it yields predictions that are more accurate. The second model also yielded good results (r2 = 0.86 and 94% of the predicted velocities were within 20% of the observed values).     

Simulation of Flow and Mass Dispersion in Meandering Channels

This paper reports the development of an enhanced two-dimensional (2D) numerical model for the simulation of flow hydrodynamics and mass transport in meandering channels. The hydrodynamic model is based on the solution of the depth-averaged flow continuity and momentum equations where the density of flow varies with the concentration of transported mass. The governing equation for mass transport model is the depth-averaged convection and diffusion equation. The dispersion terms arisen from the integration of the product of the discrepancy between the mean and the actual vertical velocity distribution were included in the momentum equations to take into account the effect of secondary current. Two laboratory experimental cases, flow in mildly and sharply curved channels, were selected to test the hydrodynamic model. The comparison of the simulated velocity and water surface elevation with the measurements indicated that the inclusion of the dispersion terms has improved the simulation results. A laboratory experiment study of dye spreading in a sine-generated channel, in which dye was released at the inner bank, centerline, and outer bank, respectively, was chosen to verify the mass transport model. The simulated concentration field indicated that the Schmidt number can be used as a calibration parameter when dispersion is computed using a 2D approach with a simplified turbulence model.     

Prediction of the Asymptotic Water Depth in Rough Compound Channels

We report on a curious result related to the computation of the asymptotic depth in rough compound channels by one-dimensional approaches. Such approaches, which are widely used in practice, utilize one of a number of well-established methods for estimating the equivalent composite/compound roughness. It was found that many of these methods yield predictions of the asymptotic water depth which erroneously depend on the initial, control, depth. Only one of the methods examined was found not to exhibit this unsatisfactory behavior. We explain the results by analysis of the governing equations.     

Velocity Distribution of Turbulent Open-Channel Flow with Bed Suction

This study investigates theoretically and experimentally the velocity distributions of turbulent open channel flow with bed suction. A velocity profile with a slip velocity at the bed surface and an origin displacement under the bed surface is proposed and discussed. Based on this assumption, a modified logarithmic law is derived. The measured experimental velocity distribution verifies the accuracy of the theoretically derived profile. The data show a significant increase in the near bed velocity and a velocity reduction near the water surface, resulting in the formation of a more uniform velocity distribution. The values of the origin displacement, slip velocity and shear velocity are found to increase with increasing relative suction. The measured data show the occurrence of two flow regions in the suction zone: a transitional region in which the velocity readjusts rapidly; and an “equilibrium” region.     

Velocity Distribution and Energy Dissipation along Stepped Chutes Lined with Wedge-Shaped Concrete Blocks

Stepped channels lined with wedge-shaped concrete blocks may constitute a low-cost alternative to provide overtopping protection of embankment dams if the discharge capacity of existing spillways is not adequate or even to be used as the main spillway of newly built embankment dams. This paper addresses the velocity distribution and the energy dissipation, downstream of the inception point, on stepped chutes lined with wedge-shaped concrete blocks. An experimental setup was developed with two flumes designed with a relative scale of 1∶2.5. Air concentration was measured with an optical probe in several cross sections of both flumes. The velocity profiles along chutes lined with wedge-shaped blocks with the upper face sloping downstream were analyzed. The measurements’ accuracy was checked by comparing discharges indicated by a facility flowmeter and obtained by the integration of velocity and air concentration profiles. The effect of the steps-slope in the energy dissipation is studied. Values of the Darcy-Weissbach friction factor are proposed for this type of chute lining, for transition flows, and for skimming flows.     

Maximum Velocity and Regularities in Open-Channel Flow

Maximum velocity in a channel section often occurs below the water surface. Its location is linked to the ratio of the mean and maximum velocities, velocity distribution parameter, location of mean velocity, energy and momentum coefficients, and probability density function underpinning a velocity distribution equation derived by applying the probability and entropy concepts. The mean value of the ratio of the mean and maximum velocities at a given channel section is stable and constant, and invariant with time and discharge. Its relationship with the others in turn leads to formation of a network of related constants that represent regularities in open-channel flows and can be used to ease discharge measurements and other tasks in hydraulic engineering. Under the probability concept, the ratio of mean and maximum velocities being constant means that the probability distribution underpinning the velocity distribution and other related variables is resilient, and that the same probability distribution is governing various phenomena observable at a channel section and explains the regularities in open-channel flows.     

Momentum Exchange in Straight Uniform Compound Channel Flow

Transverse exchange of momentum between the channel and the floodplain in straight uniform compound channel flow is considered in this paper. This process results in the so-called “kinematic effect,” a lowering of the total discharge capacity of a compound channel compared to the case where the channel and the floodplain are considered separately. The mechanisms responsible for the momentum exchange are considered. The transverse shear stress in the mixing region is modeled using a newly developed effective eddy viscosity concept, that contains: (1) the effects of horizontal coherent structures moving on an uneven bottom, taking compression and stretching of the vortices into account and (2) the effects of the three-dimensional bottom turbulence. The model gives a good prediction of the transverse profiles of the streamwise velocity and the transverse shear stress of the flood channel facility experiments. Characteristic features of the lateral profile of the eddy viscosity are also well predicted qualitatively, but in a quantitative sense there is room for improvement. Secondary circulations are shown to be of minor importance in straight uniform compound channel flows.