Journal of Hydraulic Engineering

Bubbles entrained in spillway plunge pools are subject to the hydrostatic force of the water column, increasing the pressure within the entrained bubbles. This phenomenon is important for the exchange of atmospheric gases such as nitrogen and oxygen, often causing dissolved gas supersaturation downstream of the plunge pool. A weighted average or effective bubble depth is introduced to predict more accurately gas transfer at spillways. A theory is developed for estimating the effective bubble depth given the spillway angle of inclination, velocity, and depth of flow at jet impact and tailwater depth. The relationship is fitted to dissolved oxygen and methane data previously reported by the authors and is successfully applied to four Bureau of Reclamation spillways for which both oxygen and nitrogen measurements were available.

A majority of river development projects that imply the creation of a lake or reservoir for hydroelectric generation, water supply, and/or recreational purposes are very frequently the object of studies that relate to the consequences of dam failure. The objective of these studies is to assess the impact of such a catastrophic event on any populated areas downstream that may be in the path of the resulting surge wave. Also, the results may be used to design protective measures so as to assure the security of the areas likely to be affected, as well as to develop emergency evacuation procedures. These studies, which frequently rely on numerical simulation, cannot be accomplished with existing models when the reservoir is composed of multiple dams and embankments disposed along its perimeter. This paper describes a simulation methodology that was developed to evaluate the response of a chain of reservoirs to a catastrophic input, generated as a result of extreme floods or failure of an upstream dam. The methodology is based on several numerical tools that assess, as accurately as possible, the risks associated with the possible failure of a reservoir within the system. Each reservoir is modeled as being composed of a main dam with several surrounding dikes or embankments. The dikes and embankments may fail at water surface elevations lower than the crest height of the main dam thus providing a measure of protection rather like a “fuse” in electrical systems. The simulation package comprises three separate analyses; the first uses the standard level pool routing procedure based on the continuity equation and a storage—outflow relationship, whereas the second and third are based, respectively, on the one (1D)- and two-dimensional (2D) unsteady formulations of the full dynamic equations. The simulation procedure incorporates the effects of crest erosion and subsequent formation of a breach in a dike leading to reservoir outflow, reduction of water surface elevations, and (possibly) protection of the main dam structure. The overall velocity field and water surface elevations as well as the discharge through the breach as a function of time have been computed. Comparison between the numerical simulations and data obtained from a reduced-scale laboratory model have, in general, validated the approach used. Varible geometry dikes in which time-dependent trapezoidal breaches could be simulated were incorporated into the physical model. This allowed different hypotheses regarding erosion and breach development to be simulated, so that a sensitivity analysis of the parameters affecting the behavior of the reservoir could be performed. Implementation of the methodology proposed here could provide useful results that would assist engineering personnel at the design stage, while also being of use to civil protection authorities who have the responsibility for the development of emergency evacuation procedures.

The three-dimensional (3D) numerical simulation of a steady, shallow turbulent flow around a groyne in a rectangular channel is presented. A method used to track a moving surface boundary and to follow its evolution, using a one-phase 3D Reynolds solver with rigid grids, by means of a transient fraction of fluid or “porosity” field is applied. Some results are compared with experimental data, such as the isolines of water depths and the mean velocity field. A comparison of the reattachment length prediction using the free-surface model and the rigid-lid assumption is given. Other results concerning the pressure field, turbulence, or shear stress distribution are presented and analyzed.

The possibility of a contaminant being accidentally or intentionally spilled in a river is a constant concern to those using the water. Methods are developed to estimate: (1) the velocity of a contaminant in a river; (2) the rate of attenuation of the peak concentration of a conservative contaminant; and (3) the time required for a contaminant plume to pass a point. The methods are based on data collected by the U.S. Geological Survey in almost a hundred different rivers representing a wide range of sizes, slopes, and geomorphic types. Although the accuracy of the predictions can be greatly increased by performing time-of-travel studies, the emphasis of this paper is on providing methods for making estimates where few data are available. It is shown that the unit-peak concentration is well correlated with travel time and that the travel time of the leading edge averages 89% of the travel time of the peak concentration.

A weakly nonlinear stability analysis of flows over erodible beds is conducted to investigate the formation of dunes. The flow is modeled with the steady vorticity transport equation and the sediment transport is described with Bagnold's bed load–transport rate formula that takes into account the effect of the dune-surface local slope. From the analysis, linear and nonlinear models are derived. Results of the models indicate that although both are able to simulate the instabilities associated with dunes, the nonlinear model predicts more reasonable dune length and development time and is less sensitive to variations of the model parameters. The physical mechanisms controlling the development and downstream migration of dunes also are examined. Predictions of the nonlinear model are in good agreement with selected experimental data.

An analytical solution is proposed for laminar mudflows and debris flows that can be modeled by a Bingham-plastic law. Two-dimensional, unsteady, nonuniform, Bingham flows released from a point source or a source of finite size (dam-break problem or mudslide problem) on a steep slope are considered. The method of matched asymptotic expansions was implemented to get a first-order solution. For the dam-break problem, the proposed model is found to be valid when the shock wave has advanced three reservoir lengths downstream. Also, it is found that the Bingham flow only propagates a finite distance downstream, with the shock depth asymptotically approaching the yield depth and the shock velocity asymptotically falling to zero. The hydrograph produced by a Bingham flow is seen to have a slower and lower flood peak and a longer and higher flow tail than that produced by Newtonian flow having the same dynamic viscosity. Comparison of the model predictions with laboratory observations shows reasonable agreement.

Water rivulets on inclined smooth plate form a stable meandering pattern under certain conditions. The bend theory for describing the meandering water rivulet includes the effect of the surface-tension force. The governing equations are the St. Venant equations of shallow water as shown in curvilinear coordinates. The resultant bend equation is nonlinear. The linear stability analysis of this equation with minute disturbance was done by the senior author. In that analysis, all the small terms (nonlinear terms) were omitted. The stable meander trajectory formed by streams has finite amplitude as derived from Cartesian sinusoidal patterns. These patterns are very similar in shape to those of meandering rivers. The pattern of meandering rivers can be expressed by sine-generated curves. The meandering river trajectory derived from the first-order sine-generated curve contains periodic deviation characteristics. This deviation is caused by either fattening and/or skewing from the first-order sine-generated curve. The approximate solution for the nonlinear analysis of the bend equation (including the surface-tension force) demonstrated that the deviations could be well formulated by the third-order sine-generated curves. Furthermore, the derived water rivulet forms of finite amplitude were verified by laboratory experimental results.

The problem of selecting a time step that exactly satisfies the Courant condition arises most commonly when the fixed-grid method of characteristics (MOC) is applied to multipipe systems. Traditionally, this problem has been solved by employing one of a variety of interpolation techniques or by allowing small adjustments in the value of wave speed. In this paper, the number of available strategies is increased substantially by allowing several new kinds of interpolation as well as blended combinations of these interpolation approaches with the wave-speed–adjustment technique. The new hybrid approaches include interpolation along a secondary characteristic line and minimum-point interpolation, which minimizes the distance from the interpolated point to the primary characteristic. An intuitively appealing technique involving direct adjustment of the wave path is rejected because it is potentially unstable. The entire flexible algorithm is implemented as a preprocessor step, uses memory efficiently, executes quickly, and provides a flexible tool for investigating the importance of discretization errors in pipeline systems. The properties of the new algorithm are analyzed theoretically and illustrated by example.

The charactertistics of combining flows past 90° junctions of rectangular closed conduit are studied to determine the various parameters such as power and energy loss coefficients, average entry angle of the branch flow, and the momentum transfer from the branch to the main conduit. Detailed pressure and velocity distribution data were obtained to understand the flow processes involved. Both the mean and fluctuating components of the velocity field were determined in the flow sections immediately downstream of the junction. The contraction coefficient of the flow and the geometry of the separation bubble were determined for a few representative cases. The results of the study indicated that the flow process in junctions of rectangular conduits and circular pipes are very different especially when the discharge ratio is large and the size of the branch conduit is very small compared to the main conduit. However, in some ranges of the discharge ratios and area ratios, the gross flow characteristics such as the dependence of energy loss coefficients on discharge ratios have similar trends. Simple empirical models are developed to determine the transfer of momentum ΔM and the contraction coefficient C_c for 90° junction of rectangular conduit flows. The predicted values ΔM and C_c for three area ratios and several discharge ratios are verified with the help of experimental data.

Optimal network design constrained by reliability is an improvement over the traditional methods for water-distribution system analysis. But the large computer time for reliability-optimization restricts its practical use for design. In this paper, a new technique is developed that applies a linear programming algorithm to optimal design constrained by reliability. The objective function and constraints are expressed by a first-order Taylor series expansion, and three submodels (a steady-state simulation model, a reliability model, and a linear optimization model) are linked in the algorithm. The optimal search is done in two steps. The first step is to search for an optimal solution and then the reliability and pressure heads, evaluated on this configuration, are compared with the constraint values. If there still exists a possibility that the cost of the system can be further decreased a new iteration is repeated. The computing burden is significantly decreased and, therefore, the proposed reliability-optimization technique can be used in planning large networks.

Spatial variability of aquifer properties and hydraulic heads are modeled as random fields, and their estimates are achieved by Kalman filtering. The state-space equation is developed from a quasi-analytical solution of a first-order approximation of the governing stochastic flow equation. In the state-space system, the effects of aquifer heterogeneity and uncertainty in recharge are lumped linearly into a random noise vector that is correlated in time. To account for the correlated system noise, we reformulate the problem in terms of an augmented–state-space system and use the resulting Kalman filtering recursions to estimate transmissivities, storativities, and hydraulic heads, simultaneously. The filter is applied to a numerical experiment in which the statistical parameters of log aquifer properties are assumed to be known. The results indicate that under mild head gradients, head measurements alone are of limited value if the objective is to estimate the spatial distribution of aquifer transmissivity and storativity. Ultimately, measurements of the aquifer properties may be required for reliable estimation of their unknown values.

A substantial proportion of natural streams in the United States and Canada are affected by ice cover during the winter. To substantiate the currently used procedures for measuring streamflow during the winter, the U.S. Geological Survey (USGS) and Water Survey of Canada (WSC) began independent, coordinated programs for research and development related to the measurement of streamflow under an ice cover. Detailed measurements of vertical velocity profiles under ice covers in field settings were collected by each agency in accordance with standardized guidelines. The data were then compiled into a joint database. This paper presents a description of the two measurement programs, describes the structure and format of the joint database, and provides preliminary summaries of the data. Ongoing research efforts by the USGS and WSC are described briefly to give examples of the use of the joint database.

An important test of the quality of a computational model is its ability to reproduce standard test cases or benchmarks. For steady open–channel flow based on the Saint Venant equations some benchmarks exist for simple geometries from the work of Bresse, Bakhmeteff and Chow but these are tabulated in the form of standard integrals. This paper provides benchmark solutions for a wider range of cases, which may have a nonprismatic cross section, nonuniform bed slope, and transitions between subcritical and supercritical flow. This makes it possible to assess the underlying quality of computational algorithms in more difficult cases, including those with hydraulic jumps. Several new test cases are given in detail and the performance of a commercial steady flow package is evaluated against two of them. The test cases may also be used as benchmarks for both steady flow models and unsteady flow models in the steady limit.