Showing papers in "Journal of Hydraulic Engineering in 1986"

Open‐channel Flow Measurements with a Laser Doppler Anemometer

Abstract: A powerful two‐color Laser Doppler Anemometer (LDA) system, with direct digital signal processing has been used to measure accurately the longitudinal and vertical velocity components in two‐dimensional, fully‐developed open‐channel flow over smooth beds. The law of the wall and the velocity defect law were re‐examined because the log‐law has been often applied to open channels without detailed verification. It was found that the log‐law can be applied strictly only to the near‐wall region. In this region, the von K´rm´n constant κ and the integral constant A are truly universal, having values of κ=0.412 and A=5.29 irrespective of the Reynolds and Froude number. As the Reynolds number becomes larger, the deviation from the log‐law cannot be neglected in the outer region. This deviation can be expressed well by Coles' wake function which involves a Reynolds‐number dependent parameter Π. The distributions of eddy viscosity and mixing length were evaluated and found to depend on Π. All the data including the...

Stable Channels with Mobile Gravel Beds

Abstract: Regime type equations for mobile gravel-bed rivers are presented based on data obtained from 62 stable gravel-bed river reaches in the United Kingdom. Multiple regression techniques are applied to derive equations relating reach average and riffle values of width, mean and maximum depth, slope, velocity, sinuosity and riffle spacing to bankfull discharge, bed and bank material characteristics, valley slope, bank vegetation type and an independent estimate of bankfull bed load transport rates. Although discharge has a dominant control on channel geometry, these equations indicate that bed load discharge also has a significant influence, particularly with regard to channel slope. Bank vegetation has a major control on width and velocity while depth, velocity and slope are storngly affected by bed material size. Reasons for these results are considered in terms of the physical processes controlling channel adjustment. The application of these regime equations is discussed, and particular consideration is given to the design of sinuous channels with a pool-riffle bed topograph.

Functional Trends of Scour at Bridge Piers

Abstract: The functional trends of the local scour depth at a bridge pier in subcritical flow are discussed and related to flow and sediment parameters leading to a framework within which the scour depth under given conditions can be estimated. The local scour depth is shown to depend primarily on the shear velocity or mean velocity ratio to the value at the beginning of sediment movement, u*/u*c or U/Uc, the grading of sediment and flow depth relative to pier width. The functions presented are based on laboratory data.

Free‐Surface Air Core Vortex

Abstract: A Rankine vortex model is used as the basis for an equation for critical submergence of intakes. The equation relates critical submergence to Froude number, circulation number, Reynolds number, and Weber number. The Froude and circulation numbers are the major controlling parameters. The model accounts for the effect of eddy viscosity on vortex-core characteristics. The equation for critical submergence is in agreement with experimental results. Criteria for neglect of surface tension and kinematic viscosity are established.

Mathematical Modeling of Suspended Sediment in NonUniform Flows

Abstract: A two-dimensional vertical mathematical model for suspended sediment is presented. The model is based on the width-integrated convection-diffusion equation for the sediment particles including settling effects. The local fluid velocities and mixing coefficients are described by a new so-called Profile model, which is based on the application of flexible profiles to represent the vertical distribution of the basic variables. Measured and computed velocities of strongly nonuniform flows were used for calibration of the Profile model. A stochastic approach is introduced to represent the sediment input at the bed. A bed concentration or an upward sediment flux can be specified (optional). The convection-diffusion equation is solved by a finite-element method, which proved to be better than a finite-difference method. An extensive sensitivity analysis is presented to show the influence of the main controlling parameters of the model. Finally, a verification analysis is presented using flume and field data of dredged trenches.

Meander flow model. i: development

Abstract: A model for simulating the flow and bed topography in a meandering alluvial channel is developed. The basis is a solution to the equations for conservation of mass and momentum and for lateral stability of the streambed. The bed‐stability equation is a transverse force balance for bed‐sediment particles relating the transverse bed slope to primary flow variables. The main controlling parameters are the channel's width‐depth ratio, radius‐width ratio, resistance characteristics (or gradient), and sediment Froude number. An innovative feature is the use of a simple mass‐flux balance (mass conservation) to link the equation for bed stability to the momentum equations. The mass‐flux balance relates the net lateral transport of flow volume to the streamwise variation of transverse bed slope. Thereby, the equations governing the secondary‐current velocity and the transverse bed slope become those of a damped oscillating system subjected to a driving force, the change in channel curvature. The model is tested wi...

Hydraulics of Vertical Slot Fishways

Abstract: This paper presents the results of an experimental study on the hydraulics of vertical slot fishways. Seven designs, including some conventional designs, were tested. A conceptual uniform flow state has been defined for which a linear relation has been found between the dimensionless flow rate and relative flow depth. Non-uniform flow of the M1 and M2 types has been analyzed using the Bakhmeteff-Chow method. Some observations have also been made on the velocity profiles at the slot and circulation patterns in the pools.

A Model for Flow Over Two‐Dimensional Bed Forms

Abstract: When non‐cohesive sediment is set in motion by a unidirectional flow, waves of sand often result; moreover, these waves typically are asymmetrical with steep lee faces that produce flow separation. Behind each wave, a wake region forms which grows in height and decays in strength with distance downstream, producing a near‐bottom acceleration. The no‐slip condition at the bed, however, requires an internal boundary layer to form beneath the wake region which retards the flow there. The interaction of these flow processes produces a local maximum in the boundary shear stress downstream of a bump, even over an otherwise flat bed. Because the erosion rate is proportional to the stress divergence for bed load and weak suspended load transport, erosion will occur upstream of this point and desposition will occur downstream of it, thus influencing the bottom shape. Herein, the equations of motion are solved for the accelerating internal boundary layer beneath a wake. The resulting velocity and boundary shear str...

Behavior of Density Currents on an Incline

Abstract: Investigation of the behavior of salt solution released down a sloping surface in a tank of freshwater is reported here. Analysis indicates that the dense layer spreads in all directions at a rate proportional to the entrainment coefficient. Observations and measurements revealed a variety of phenomena depending strongly on the buoyancy flux, Richardson number, and the angle of incline. At small slope (∼<1/10) flow was found to be subcritical with negligible entrainment. As the slope increases, flow becomes supercritical and periodic interfacial instabilities appear. Growth and subsequent breakup of these instabilities were found to be the main mechanism for entrainment. Mean layer velocity away from the source can be estimated from the initial conditions and the angle of incline.

Sediment Control by Submerged Vanes

Abstract: A procedure is developed for a rational design of a system of submerged vanes for depth control in alluvialriver channels. The vanes are vertical, smallaspect ratio foils installed on the channel b...

Turbulence Modeling of Flood Plain Flows

Abstract: A numerical model capable of predicting flow characteristics in a compound channel is described. The model solves the continuity and momentum equations along with the transport equations of kinetic energy of turbulence and the dissipation rate. Closure is achieved with the aid of algebraic relations for turbulence stresses. The model is capable of treating compound channels formed by regular geometrical sections of main channel and flood plain segments. The width of the main channel, the width of the total section, the depth of flow in flood plain, the total depth, channel slope and boundary roughness of main channel section and flood plain section can all be varied. The model predictions of total flow rate, shear stress distributions around the wetted perimeter, and the percentage of flow and shear force carried by the different sections were compared with published experimental data. Reasonable agreement between data and predictions was obtained.

Flow and Bed Profile in Meandering Sand-Silt Rivers

Abstract: Mathematical models for defining three-dimensional flow and bed topography in sinuous channels with suspendable bed material are presented. It is shown theoretically that the secondary flow in sinuous channels shows a reduction in its magnitude below that of a uniformly-curved channel, and also displays a phase-lag relative to the channel plan-form. The model for bed topography is derived by considering the sediment balance for bed load and suspended load, the transport rate and direction, all of which are governed by the three-dimensional flow. A laboratory test supports the model. The present study has made it possible to predict the large-scale bed topography of meandering sand-silt rivers, including such features as the magnitude and the location of local scour and point-bar deposits.

Practical Aspects of Accurate Tidal Computations

Abstract: Alternating direction implicit (ADI) methods are widely used for the approximation of shallow water equations. For calibration the size of the timestep is often based upon the so-called propagation factor. This factor gives only a minor indication of the numerical propagation speed of the tidal wave. It is shown that the numerical propagation speed depends entirely on the geometry and the bathymetry combined with the spatial gridsize and the timestep. Another factor that influences the propagation of the tidal wave in a computational model is the numerical simulation of intertidal flats. Numerical examples are given.

Structure of 3‐D Flow in Rectangular Open Channels

Abstract: A parameter estimation method has been developed for a system of three‐dimensional mathematical model of flow in open channels, which does not require (primary flow) velocity data. It has broadened the applicability and effectiveness of the model in scientific investigations into the complex interaction among the primary and secondary flows, shear stress distribution, channel characteristics (roughness, slope, and geometry), and other related variables governing all transport processes in open channels. The method was applied to a study of 3‐D structure of flow in rectangular open channels. The interaction among the primary and secondary flows and the shear stress distribution was investigated under various values of Manning's n, width‐to‐depth ratio and slope of the channels. The result has answered quantitatively many questions which arise in open channel hydraulics.

Cohesive Sediment Transport Model

Abstract: A mathematical model has been developed which simulates the transport of cohesive sediment. The model solves the complete, three-dimensional version of the diffusion-advection equation using a splitting method in conjunction with a characteristics technique and a mixed explicit-implicit finite difference approach. The effects of the flocculation, deposition, consolidation, erosion and slump of the sediment are incorporated in the model, which can also handle irregular layouts. Application of the model to a harbor siltation problem indicated that the large input data requirements can be satisfied economically and that the scheme yields realistic results. The application also provided an insight into possible ways of operating the model for different field situations.

Bed load transport of sediment mixtures

Abstract: Experiments were conducted on alluvial beds of four sediment mixtures having different arithmetic mean diameters and standard deviations. The bed load transport rates of individual fractions were measured. Einstein's method, Proffitt and Sutherland's method, and Misri's method of calculation of the bed load transport of individual fractions for sediment mixtures were checked with carefully collected laboratory data. By analyzing the data on lines similar to those of Misri, et al, their method of calculation of the bed load transport rate for individual fraction is modified to make it applicable over a wide range of parameters. The relationship between the dimensionless grain shear stress and the dimensionless bed load transport rate developed by Misri, et al., for uniform sediments was made applicable to sediment mixtures by introducing a multiplying correction factor. The parameters affecting this correction factor were identified and a relationship obtained for the same by analysis of an extreme amount of laboratory and river data. Use of this factor along with the transport law for uniform sediments enables determination of the rate of bed load transport of the individual fractions of a mixture.

Diffusion Wave Modeling of Catchment Dynamics

Abstract: A diffusion wave method for catchment dynamics is presented. The method has better convergence sproperties than kinematic wave models which use off-centered derivatives in their numerical formulations. Unlike the off-centered schemes, the diffusion wave scheme is formulated by matching physical and numerical diffusivity. This results in an effective control of numerical diffusion and leads to simulations which are essentially independent of grid size. The diffusion method is further extended to the realm of dynamic waves by including the Froude number dependence sof the physical diffusivity. The resulting formulation is believed to represent as complete a description of the wave dynamics as is possible within the framework of diffusion wave theory. Numerical experiments show that the diffusion wave theory. Numerical experiments show that the diffusion wave method has better convergence properties than existing kinematic better convergence sproperties than existing kinematic better convergence properties than existing kinematic wave models featuring uncontrolled numerical diffusion.

Velocity Distribution Coefficients for Grass‐Lined Channels

Abstract: Relations are developed for use in estimating the momentum and energy coefficients of flow over submerged grass channel linings. The proposed relations have their basis in Prandtl’s mixing length approach to momentum transfer but are reduced by curve fitting to a form suitable for direct computer solution. The independent variables are those routinely calculated in grass-lined open channel design.

Turbulent Structure in a River Bend

Abstract: A field experiment was carried out in a river bend and velocity components were measured in the longitudinal, lateral and vertical directions at various cross sections within the bend; the bed topography was determined. Isovels, equal contours of the lateral mean velocity, of the Reynolds shear stress and normal stresses were obtained. No meandering of these parameters occurred within the bend and mean velocity profiles were not logarithmic.

Simple Model of Sediment‐Laden Flows

Abstract: A theoretical model of sediment‐laden flow is applied to dilute openchannel suspensions. It is found that the effect of the sediment is manifested in terms of a reduced depth and coefficient of resistance, and an increased mean velocity of flow. In particular, an expression for the effect of sediment on the wake strength parameter Π of the velocity profile can be derived. The expression predicts results that are in agreement with the measurements of a previous study. Another prediction of the theory concerns the level of turbulence. The ratio of the power consumed by the flow in holding the sediment in suspension to the power supplied to the flow by the work of the downstream pull of gravity on the sediment is used to form a dimensionless ratio. If this ratio is less than unity, i.e., sufficiently fine sediment, the turbulence is intensified; otherwise, it is damped.

Errors in Stormwater Modeling—A Quantitative Assessment

Abstract: Inaccuracies in stormwater modeling can be caused by a number of factors such as errors in input data, model simplifications, parameter uncertainties, and numerical problems. This paper compares several simple, commonly used approaches to the most advanced method currently available. The advanced method develops a rainfall/runoff model which features rainfall with high spatial resolution and time‐varying loss rates, and computes surface hydrographs for every subcatchment and fully dynamic conduit routing. Twenty‐seven rainfall events, obtained from high resolution radar measurements, are applied to a hypothetical 729 ha (1,800 acres) catchment.

Suspended load transport of sediment mixtures

Abstract: Careful experiments were conducted on alluvial beds of four sediment mixtures having different arithmetic mean diameters and standard deviations. The suspended load transport rates of individual fractions were measured and compared with both Einstein's and Holtroff's methods of calculation of suspended load for individual fractions. These methods were found to be unsatisfactory in the present range of sediment parameters. A relationship is found to exist between the dimensionless shear stress and the suspended transport rate for uniform sediment. To make this relation applicable to nonuniform sediments, a corrective multiplying factor for shear stress is introduced. The dimensionless parameters which govern this correction factor are identified and a relation for the same obtained. In this manner the relation can be applied to individual size portions of a sediment mixture.

Applications of Sediment Pick‐Up Function

Abstract: Two applications are presented of a recently proposed empirical sediment pick-up function. The first application deals with bed load transport which is computed as the product of the pick-up rate and the saltation length. Comparison with measured bed-load transport rates shows encouraging results. The second application deals with suspended load transport. The classical problem of sediment concentration profiles developing in a steady uniform flow which is initially free of sediment, is studied.

Hydraulic Uncertainties in Flood Levee Capacity

Abstract: This paper explores hydraulic uncertainty in flood levee capacity, which results from the inability of mathematical models and/or empirical equations to describe completely the physical flow process of floods. The hydraulic uncertainty is evaluated through a first‐order analysis of uncertainties of Manning's equation. This study shows that the roughness coefficient and the friction slope dominate the variation in hydraulic uncertainty in that they account for 95% of the hydraulic uncertainty. A procedure is developed for determining the hydraulic effect of friction slope uncertainty.

Structure of 3-d flow in rectangular open channels

Abstract: A parameter estimation method has been developed for a system of three-dimensional mathematical models of flow in open channels, which does not require (primary flow) velocity data. It has broadened the applicability and effectiveness of the model in scientific investigations into the complex interaction among the primary and secondary flows, shear stress distribution, channel characteristics (roughness, slope, and geometry), and other related variables governing all transport processes in open channels. The interaction among the primary and secondary flows and the shear stress distribution was investigated under various values of Manning's n, width-to-depth ratio and slope of the channels. The result has answered quantitatively many questions which arise in open channel hydraulics.

Hydraulic Design Algorithms for Pipe Networks

Abstract: A general methodology is presented for use in the design of water distribution networks The proposed approach is conceptually useful for certain applications The approach is based on recasting the basic set of hydraulic network equations in terms of selected design parameters for specified operating conditions The reformulated, network equations are then solved using a modified linear method In order to demonstrate the feasibility of the approach, two different algorithms are developed and applied to an example network

Armoring and Sorting Simulation in Alluvial Rivers

Abstract: Formulations for bed armoring and hydraulic sorting of bed sediments in alluvial streams are developed, and an application to Missouri River bed evolution is presented. A relation for the areal coverage factor for armoring on a plane bed is first formulated as a function of degradation depth and bed-material characteristics, and is then modified by introducing correction factors for the effect of bed forms and the stochastic nature of sediment motion. For the simulation of hydraulic sorting, bed sediments are assumed to be mixed homogeneously in a mixed-layer depth approximately equal to average bed-form height, and the composition of mixed-layer materials is adjusted to satisfy the continuity equation for each sediment size fraction. These formulations are applied in a 20-year simulation of bed degradation in the middle Missouri River reach downstream of Gavins Point Dam. It is found that the simulated bed-sediment composition, including the two-layer structure comprising the top armor coat and the underlying finer sediments, is in good agreement with the observed Missouri River bed characteristics.

Washload and Fine Sediment Load

Abstract: Washload and fine sediment load should not be used synonymously. In streams with large concentrations of fines, the sediment size D\d1\d0 may be much smaller than 0.0625 mm. The fluid becomes very viscous at low concentrations of clays and the reduced settling velocity inhibits the exchange of sediment particles between the bed and the suspension. The sediment transport capacity under those conditions remains very poorly defined. In coarse bed streams, sands and fine gravel can be considered as washload as long as the sediment transport capacity remains larger than the availability of sediment. Intermittently, different conditions prevail when the upstream supply exceeds the transport capacity.