Flow in Compound Channel with Abrupt Floodplain Contraction

Flooding rivers usually present transition reaches where the floodplain width can significantly vary. The present study focuses on an abrupt floodplain contraction (mean angle 22°) in order to determine whether one-dimensional (1D) models, developed for straight and slightly converging geometry, are equally valid for such a geometry. Experiments on a contraction model were carried out in an asymmetric compound channel flume. Severe mass and momentum transfers from the floodplain towards the main channel were observed, giving rise to a noteworthy transverse slope of the water surface and different head loss gradients in the two subsections. Three 1D models and one 2D simulation were compared to experimental measurements. Each 1D model incorporates a specific approach for the modeling of the momentum exchange at the interface boundary between the main channel and the floodplain. The increase of the lateral mass transfer generates moderate errors on the water level values but significant errors on the discharge distribution. Erroneous results arise because of incorrect estimations of both momentum exchange due to lateral mass transfers and boundary conditions which are imposed by the tested 1D models.     

Boundary Shear Distribution in Straight Ducts and Open Channels

A semianalytical model was developed to predict boundary shear distribution in straight, noncircular ducts and open channels. The model was developed using a simplified streamwise vorticity equation, which involves only secondary Reynolds stress terms. These terms are representative of transverse turbulence anisotropy and nonhomogeneity. Transverse anisotropy is modeled using a universal function. Shear stresses are incorporated into the model by applying the momentum transfer model. An empirical model was employed to calculate the effect of the channel boundary on shear stresses. The final equation was applied to calculate boundary shear distribution in triangular ducts and trapezoidal open channels. The model predictions were well correlated with experimental data.     

Turbulence Measurements of Dye Concentration and Effects of Secondary Flow on Distribution in Open Channel Flows

This paper presents simultaneous turbulence measurements of velocity and tracer concentration using a combination of laser Doppler anemometer (LDA) and laser induced fluorescence (LIF) in rectangular and compound channels. Secondary flow, Reynolds stresses, Reynolds fluxes, and dye concentration distributions were measured near the water surface in both channels. An investigation of the effect of secondary flow on passive contaminant diffusion processes was carried out with relatively weak secondary flow in the rectangular channel and relatively strong secondary flow in the compound channel. The results show that the secondary flow clearly influences the spreading of the tracer concentration and the location of concentration peak, being different from the injection location. The transport rate of solute due to the secondary flow is not significant in the rectangular channel case but significant in the compound channel case. The transverse eddy viscosity is demonstrated to be equal to the transverse eddy diffusivity. The transverse eddy diffusivity near the water surface is larger than the vertical one. The Fickian law is valid in most regions investigated, but there are some regions where the Reynolds flux and concentration gradients are locally of the same sign due to the influence of secondary flow on the concentration distribution.     

Calculating Shear Stress at Channel-Overbank Interfaces in Straight Channels with Vegetated Floodplains

A series of eight experiments was performed in a physical model of a compound channel to quantify the apparent shear stress at the interface between a main channel and both a vegetated and unvegetated floodplain. Data were analyzed using a turbulence-based method for calculating the apparent shear stress as a function of the fluctuation in channel velocities. A predictive expression was developed to permit the estimation of the apparent shear stress at the boundary of a main channel and floodplain as a function of the bed shear stress, average velocity, and depth in both the main channel and floodplain and the blockage caused by floodplain vegetation.     

Shear Stress in Smooth Rectangular Open-Channel Flows

The average bed and sidewall shear stresses in smooth rectangular open-channel flows are determined after solving the continuity and momentum equations. The analysis shows that the shear stresses are function of three components: (1) gravitational; (2) secondary flows; and (3) interfacial shear stress. An analytical solution in terms of series expansion is obtained for the case of constant eddy viscosity without secondary currents. In comparison with laboratory measurements, it slightly overestimates the average bed shear stress measurements but underestimates the average sidewall shear stress by 17% when the width–depth ratio becomes large. A second approximation is formulated after introducing two empirical correction factors. The second approximation agrees very well (R2>0.99 and average relative error less than 6%) with experimental measurements over a wide range of width–depth ratios.     

Depth-Averaged Shear Stress and Velocity in Open-Channel Flows

Turbulent momentum and velocity always have the greatest gradient along wall-normal direction in straight channel flows; this has led to the hypothesis that surplus energy within any control volume in a three-dimensional flow will be transferred toward its nearest boundary to dissipate. Starting from this, the boundary shear stress, the Reynolds shear stress, and the velocity profiles along normal lines of smooth boundary may be determined. This paper is a continuous effort to investigate depth-average shear stress and velocity in rough channels. Equations of the depth-averaged shear stress in typical open channels have been derived based on a theoretical relation between the depth-averaged shear stress and boundary shear stress. Equation of depth mean velocity in a rough channel is also obtained and the effects of water surface (or dip phenomenon) and roughness are included. Experimental data available in the literature have been used for verification that shows that the model reasonably agrees with the measured data.     

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.     

Bed-Shear Stress in Turbulent Wave-Current Boundary Layers

An approach for calculating turbulent flows in a wave-current boundary layer over a slowly varying bed is presented. Waves are periodic in time with several harmonics. In this paper, we adopt a time invariant eddy viscosity model, in which the eddy viscosity is linearly proportional to the distance from the bed. The boundary-layer flow field is solved analytically in terms of Fourier components. The approach allows fast computations and can be easily included in a phase resolving wave propagation model. As a part of the results, bottom shear stress and the spatial variation of the boundary layer thickness are also obtained. Present results compare well with experimental data and can explain the asymmetries in the bottom shear stress under sawtooth shaped waves.     

Velocity and Turbulence Measurements for Two Overbank Flow Events in River Severn

Field measurements of velocity and turbulence have been carried out in a study reach of the River Severn at Lower Farm near Shrewsbury during overbank flow. Acoustic Doppler velocity meters have been used for the field measurements of velocity and turbulence, particularly in the interface region between river channel and floodplain. The values of local shear velocity and roughness length for the reach under study were calculated using measured velocity data. The distributions of turbulent intensities, and the Reynolds stresses are also presented. The variation of horizontal shear stress in the vertical direction deviates from linear for the main channel/floodplain interaction region due to the existence of a lateral shear and momentum transfer from the floodplain towards the main channel. Comparisons are made between the field data and previous experimental data from the Flood Channel Facility.     

Investigation of Twin Vortices near the Interface in Turbulent Compound Open-Channel Flows Using DNS Data

The direct numerical simulation of turbulent flows in a compound open channel is described. Mean flows and turbulence structures are provided, and are compared with numerical and measured data available in the literature. The simulated results show that twin vortices are generated near the interface of the main channel and the floodplain and that their maximum magnitude is about 5% of the bulk streamwise velocity. Near the interface, the simulated wall shear stress reaches a maximum, contrary to experimental data. A quadrant analysis shows that both sweeps and ejections become the main contributor to the production of Reynolds shear stresses near the interface. Through the conditional quadrant analysis, it is demonstrated how the directional tendency of dominant coherent structures determines the production of Reynolds shear stress and the pattern of twin vortices near the interface. In addition, the time-dependent characteristics of three-dimensional vortical structures in a compound open-channel flow were investigated using direct numerical simulation (DNS) data.     

Semianalytical Model for Shear Stress Distribution in Simple and Compound Open Channels

Semianalytical equations were derived for distribution of shear stress in straight open channels with rectangular, trapezoidal, and compound cross sections. These equations are based on a simplified streamwise vorticity equation that includes secondary Reynolds stresses. Reynolds stresses were then modeled and their different terms were evaluated based on the work of previous researchers and experimental data. Substitution of these terms into the simplified vorticity equation yielded the relative shear stress distribution equation along the width of different channel cross sections. In compound channels the effect of additional secondary flows due to the shear layer between the main channel and the flood plain were also considered. Comparisons between predictions of the model and experimental data, predictions of other analytical or three dimensional numerical models with advanced turbulent closures, were made with good agreement.     

Analytic Stage-Discharge Formulas for Flow in Straight Prismatic Channels

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.     

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.     

Overbank Flow in Symmetrically Narrowing Floodplains

Experimental data are presented for flow in compound channels with symmetrically narrowing floodplains. In such a geometry, the flow behavior presents similarities with the more complex flow in a meandering compound channel, yet without the curvature effects, because of mass transfers between the floodplains and the main channel, and secondary currents induced in the main channel. An estimation of the momentum transfer generated by the mass transfer is found significant compared to the frictional losses. It mainly depends on the geometrical parameters and is practically independent of the friction slope. Free-surface profile computations are performed with the exchange discharge model (EDM) to incorporate the effects of the momentum transfer in terms of an additional head loss. Agreement was found between measured and computed water surfaces, thus validating the EDM approach.     

Sediment Transport in River Models with Overbank Flows

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.     

Bank Profile of Threshold Channels: A Simplified Approach

A simplified model is presented for the computation of shape and dimensions of the cross section of a self-formed straight threshold channel with noncohesive uniform sediments. The model is based on the equilibrium of the individual sediment particles lying on the channel bed under the threshold condition, due to the hydrodynamic force acting on it. The transverse momentum diffusion, caused by the Reynolds stresses, is assumed as a function of the transverse distance from the center. Channel dimensions predicted by this model are in agreement with those obtained from previous models. However, the model slightly underestimates the experimental data.     

Test of a Method to Calculate Near-Bank Velocity and Boundary Shear Stress

Detailed knowledge of the flow and boundary shear stress fields near the banks of natural channels is essential for making accurate calculations of rates of near-bank sediment transport and geomorphic adjustment. This paper presents a high-resolution laboratory data set of velocity and boundary shear stress measurements and uses it to test a relatively simple, fully predictive, numerical method for determining these distributions across the cross-section of a straight channel. The measurements are made in a flume with a fairly complex cross-section that includes a simulated, cobble-roughened floodplain. The method tested is that reported by Kean and Smith in Riparian Vegetation and Fluvial Geomorphology in 2004, which is modified here to include the effects of drag on clasts located in the channel. The calculated patterns of velocity and boundary shear stress are shown to be in reasonable agreement with the measurements. The principal differences between the measured and calculated fields are the result of secondary circulations, which are not included in the calculation. Better agreement with the structure of the measured streamwise velocity field is obtained by distorting the calculated flow field with the measured secondary flow. Calculations for a variety of narrower and wider configurations of the original flume geometry are used to show how the width-to-depth ratio affects the distribution of velocity and boundary shear stress across the channel.     

Turbulence Characteristics in Gradual Channel Transition

A field study was conducted to determine the effects of a channel transition on turbulence characteristics. Detailed three-dimensional (3D) flow measurements were collected at a cross section that is located downstream of a gradual channel expansion. These measurements were obtained via an acoustic doppler velocimeter and include the 3D velocity field, the mean local velocities, the turbulent intensities, the frictional characteristics of the flow, the secondary velocity along the transverse plane, and the instantaneous shear stress components in the streamwise and transverse directions. Analysis of the 3D flow data indicates that the turbulent flow on the outer bank of the channel is anisotropic. Such anisotropy of turbulence, which is attributed to the gradual expansion in the channel and bed roughness, yields the development of a secondary flow of Prandtl’s second kind as reported in 1952. In particular, it was found that turbulent intensities in the vertical and transverse directions on the outer bank section are different in magnitude creating turbulence anisotropy in the cross-sectional plane and secondary flows of the second kind. Turbulent intensities increase toward the free surface indicating the transfer of a higher-momentum flux from the channel bed to the free surface, which contradicts common wisdom. Results for the normalized stress components in the streamwise and transverse direction show similar behavior to the intensities. Moreover, the nonlinear distribution of stresses is indicative of the oscillatory nature of the flow induced by the secondary flows of Prandtl’s second kind. A similar behavior was found for flows in straight rectangular channels over different roughness. Finally, a comparison between the secondary current velocity with the mainstream velocity indicates that secondary flow of Prandtl’s second kind is present within the right half of the measured cross section.     

Flow Velocity and Pier Scour Prediction in a Compound Channel: Big Sioux River Bridge at Flandreau, South Dakota

The two-dimensional (2D) depth-averaged river model Finite-Element Surface-Water Modeling System (FESWMS) was used to predict flow distribution at the bend of a compound channel. The site studied was the Highway 13 bridge over the Big Sioux River in Flandreau, South Dakota. The Flandreau site has complex channel and floodplain geometry that produces unique flow conditions at the bridge crossing. The 2D model was calibrated using flow measurements obtained during two floods in 1993. The calibrated model was used to examine the hydraulic and geomorphic factors that affect the main channel and floodplain flows and the flow interactions between the two portions. A one-dimensional (1D) flow model of the bridge site was also created in Hydrologic Engineering Centers River Analysis System (HEC-RAS) for comparison. Soil samples were collected from the bridge site and tested in an erosion function apparatus (EFA) to determine the critical shear stress and erosion rate constant. The results of EFA testing and 2D flow modeling were used as inputs to the Scour Rate in Cohesive Soils (SRICOS) method to predict local scour at the northern and southernmost piers. The sensitivity of predicted scour depth to the hydraulic and soil parameters was examined. The predicted scour depth was very sensitive to the approach-flow velocity and critical shear stress. Overall, this study has provided a better understanding of 2D flow effects in compound channels and an overall assessment of the SRICOS method for prediction of bridge pier scour.     

Flow Interaction of Meandering River with Floodplains

A series of laboratory test results are presented concerning the boundary shear stress, shear force, and discharge characteristics of compound meandering river sections composed of a rectangular main channel and one or two floodplains disposed off to its sides. Five dimensionless parameters are used to form equations representing the total shear force percentage carried by floodplains. A set of smooth and rough sections is studied with an aspect ratio varying from 2 to 5. Apparent shear forces on the assumed vertical, diagonal, and horizontal interface plains are found to be different from zero at low depths of flow and change sign with an increase in depth over the floodplain. A variable-inclined interface is proposed for which apparent shear force is calculated as zero. Equations are presented giving proportion of discharge carried by the main channel and floodplain. The equations agree well with experimental and river discharge data. Using the variable-inclined interface, the error between the measured and calculated discharges for the meandering compound sections is found to be the minimum when compared with that using other interfaces.