Journal of Hydraulic Engineering

Field measurements of oxygen transfer at four types of hydraulic structures are compared to predictions by 12 equations in the literature. The hydraulic structures were divided into weirs, spillways (gated and ungated), gated sills, and gated conduit outlets. For weirs, it was found that Avery and Novak's equation provides the best prediction of oxygen transfer. Rindels and Gulliver's equation and Wilhelms's equation provide the best prediction for spillways and gated sills, respectively. No equation provided an acceptable prediction of oxygen transfer at gated conduit outlets, probably because of the variety of hydraulic conditions that exist in these structures. The prediction of the transfer of other compounds from these equations also was discussed. It appears that it is currently possible to predict the transfer of another volatile compound from these oxygen transfer equations at these types of hydraulic structures, as long as the dimensionless Henry's law constant is greater than 10. The uncertainty of the prediction, however, would increase.

A pilot study was conducted to evaluate existing rock-sizing techniques for stabilizing transition toes of embankments. The U.S. Bureau of Reclamation and the U.S. Army Corps of Engineers (Campbell) procedures were applied and determined to be conservative in sizing riprap. Embankment-overtopping tests were conducted placing 8.9, 13.0, and 19.8-cm-diameter stones at the slope transition. An alternative method was developed for sizing toe rock based upon the unit discharge, embankment slope, and flow concentration. The results indicate that an embankment toe can be stabilized with a smaller median stone size than previously anticipated. These results were verified for unit discharges of 0.54 m³/s/m or less.

Numerical models that assume hydrostatic pressure are usually sufficiently accurate for applications in civil engineering where the vertical component of the velocity is relatively small. Nevertheless, the vertical momentum, and, hence, the nonhydrostatic pressure component, cannot be neglected when the bottom topography of the domain changes abruptly, as in cases of short waves, or when the flow is determined by strong density gradients. In this paper a numerical method for the three-dimensional (3D) quasi-hydrostatic, free-surface flows is outlined. The governing equations are the Reynolds-averaged Navier-Stokes equations with the pressure decomposed into the sum of a hydrostatic component and a hydrodynamic component. The momentum equations, the incompressibility condition, and the equation for the free surface are integrated by a time-splitting method in such a fashion that the resulting numerical solution is mass conservative and stable at a minimal computational cost. Several applications serve to illustrate the effect of the deviation from the hydrostatic pressure.

A mathematical model of three-dimensional (3D) free surface flows has been applied to simulate the curved channel flows and mass transport. In the horizontal plane, a channel-fitted curvilinear coordinate system is used, whereas in the vertical plane, the σ-transformation is adopted to track the free surface and variable bed topography. To reduce the numerical diffusion, the second-order upwind scheme of Roe is incorporated to discretize the convection terms. The standard k-ε model has been modified to take account of some anisotropic effects appearing in shallow curved channels, i.e., streamline curvature and the damping effects of free surface and solid walls. The governing equations are solved in a collocated grid system by a fractional three-step implicit algorithm. Two test cases from curved flumes have been studied: (1) A 270° channel bend with a sloped outer bank; and (2) a meandering channel with mass transport. The results are compared with the available data, which shows generally good agreement.

An efficient semi-implicit finite-element model for stratified coastal seas is proposed. Nine-node Lagrangian quadratic isoparametric elements are employed for spatial discretization in the horizontal domain and a three-mode Lagrangian interpolation formula is used to approximate the vertical gradients of the two horizontal velocity components. The distinguishing feature of the proposed numerical scheme is that only nodal values on the same vertical line are coupled, resulting in a drastic reduction of computer time. The model is applicable even in situations where there are great variabilities in the water depth in the computational domain, which leads to orders of magnitude difference in the thicknesses of the different water layers in the water body. The model is first verified by a test case for which analytic solutions are available and then applied to simulate the flow in a stratified sea for which solution by a combined finite-difference–Galerkin method is available in the literature for comparison.

An unsteady two-dimensional (2D) reservoir hydrodynamics and transport model is employed to simulate contaminated density currents in the Shasta Reservoir after a chemical spill into the Sacramento River, Calif. Three flow regimes (plunging flow, underflow, and interflow) and their occurrence are captured by the laterally averaged model. Transport and mixing processes in the temperature-stratified reservoir are analyzed through simulations of flow velocities, water temperature, and contaminant concentration. Flow behavior of the contaminant plume is described by plunge distance, separation depth, intruding thickness, and the spatial and temporal dilution of chemicals. Simulation results are compared with field data for water temperature and contaminant concentration collected in the reservoir during the emergency response to the spill. Relatively good agreement between field measurements and predicted reservoir stratification and chemical dilution is obtained. It is shown that the aeration system installed in the reservoir contributed to the downstream reduction of chemical concentration to a nondetectable level shortly after the spill. The 2D simulations and analyses improve understanding and predictions of the movement of a conservative contaminant plume in a stratified reservoir. The results can assist in contamination control and remediation after a toxic chemical spill, guide field sampling during the spill, and provide information useful for water quality management.

Although a one-dimensional (1D) mathematical model based on the nonequilibrium transport of sediment is rational in principle, its application to rivers requires empirical determination of a key coefficient in the basic equation of transport, this is known as the adjustment coefficient. It also requires, as all 1D models do, empirical and rather arbitrary apportioning of the computed total scour or deposition to the wetted perimeter. In this paper an attempt is made to avoid both. The equation of sediment transport is written for a vertical stream tube of infinitesimal width for which the adjustment coefficient has been rationally determined. A procedure of lateral integration is then applied to obtain the global values of the said coefficient for the entire cross section and the distribution of deposition/erosion to the wetted perimeter. The shape of the cross section is thus determined along with the amount of deposition/erosion. Results obtained with this model compare favorably with those of depth-integrated two-dimensional (2D) computations and physical model testing, both carried out for the dam neighborhood of the Three Gorges Project.

Numerical computations are conducted of the flow across a turbulent mixing layer in an open channel of small depth using three turbulence models: a single-length-scale model, a modified single-length-scale model, and a two-length-scale model. The performance of these turbulence models is evaluated by comparing the numerical results with the available experimental data. The single-length-scale turbulence model is shown to be biased toward the small-scale turbulence. The coefficients of this single-length-scale turbulence model have been modified in an attempt to improve the performance of the model. The results of the modified single-length-scale model are in agreement with the laboratory data but not with the field data. The two-length-scale turbulence model, by treating the small-scale and the large-scale turbulence as separate components, has produced results in better agreement with the experimental data than those obtained by the single-length-scale model treating both components together as a whole.

Linear dynamic wave and diffusion wave analytical solutions are obtained for a small, abrupt flow increase from an initial to a higher steady flow. Equations for the celerities of points along the wave profiles are developed from the solutions and are related to the kinematic wave and dynamic wave celerities. The linear solutions are compared systematically in a series of case studies to evaluate the differences caused by inertia. These comparisons use the celerities of selected profile points, the paths of these points on the x-t plane, and complete profiles at selected times, and indicate general agreement between the solutions. Initial diffusion wave inaccuracies persist over relatively short time and distance scales that increase with the wave diffusion coefficient and Froude number. The nonlinear monoclinal wave solution parallels that of the linear dynamic wave, but is applicable to arbitrarily large flow increases. As wave amplitude increases, the monoclinal rating curve diverges from that for a linear wave, and the maximum Froude number and energy gradient along the profile increase and move toward the leading edge. A monoclinal-diffusion solution for the diffusion wave equations is developed and dynamic wave-diffusion wave comparisons are made over a range of amplitudes with the same case studies used for linear waves. General dimensionless monoclinal-diffusion profiles exist for each depth ratio across the wave, whereas corresponding monoclinal wave profiles exhibit minor, case-specific Froude number dependence. Inertial effects on the monoclinal profiles occur near the leading edge, increase with the wave amplitude and Froude number, and are responsible for the differences between the dimensionless profiles.

This paper describes the experimental and numerical study of the vortex formation during the passage of a solitary wave over a rectangular structure submerged in water. The transient patterns of the separated flow (R= 82,000) behind the block are visualized by tracing the motion of injected dye in a laboratory flume. The related numerical solution is calculated by using the stream function-vorticity formulation in a transient boundary-conformed grid system to satisfy the full nonlinear free-surface conditions. Both experimental and numerical results illustrate that a large vortex is first formed at the rear of the block, accompanied by a secondary eddy below it, as the solitary wave hits this block. Then the vortex is bulgy but decays with time, and the secondary eddy continues to grow in both size and strength as the primary vortex diffuses. The time development of these calculated flow patterns, including vortex shedding and vorticity transportation, agrees quite well with experimental observations.

Scour at bridges is generally estimated as a deterministic value. Other loads at bridges, such as vessel impact and wind loads, are determined as probabilistic values. In an effort to use probabilistic estimates as a tool in decision making, a probabilistic framework was developed for estimating scour using deterministic methods given in the Hydraulic Engineering Circular (HEC-18). Uncertainties in the HEC-18 model, in determination of the parameters and in estimating the hydraulic variables for a large event storm, were included in the analysis. The probabilistic framework can then be used as the basis for determining the likelihood of achieving various scour depths, probabilities of failure for various foundation designs, pile depths necessary to achieve a specified probability of failure for a design bridge life span, and for comparing designs based on various storm events. The Bonner Bridge in North Carolina is used as an example. Pile depths appropriate for various design life spans are calculated based on both 100- and 500-year storm events.

Dimensional analysis of the variables influencing local scour at skewed piers brings into issue the generality of skew factors apparently related only to skew angle, α, and pier aspect ratio, L/b, for a particular pier shape. This note discusses this issue and provides insights into flow-field and scour-geometry changes at skewed piers. It shows that the skew factor, K_α, as used in pier-scour equations to account for the influence on scour depth of pier orientation (skew) to flow, is influenced by parameters in addition to skew angle and pier aspect ratio. The parameters define the local flow field around the pier and determine the eventual scour depth and form in ways not fully taken into account by existing relationships for K_α. Those relationships, however, retain their usefulness as upper-bound envelopes for estimating K_α values for piers in comparatively shallow flows, especially for α less than about 45°.

This technical note describes an experimental study of the free overfall from a rectangular channel with differing slopes and bed roughnesses. The relationship between the upstream critical depth and brink depth is explored and found to be influenced by both slope and channel-bed roughness, with roughness having a greater effect at steeper slopes. Two empirical equations are proposed for calculating this relationship, the first requiring only the channel slope to be known, and the second requiring a knowledge of channel slope and roughness. The accuracy of the two equations when used in a method for flow measurement are compared. The first relationship, in which the effects of slope and roughness are aggregated, provides a useful estimate of channel discharge if only the channel slope is known. If both bed roughness and slope are known then the second relationship can be used to calculate channel discharge with greater accuracy.