Journal of Hydraulic Engineering

A numerical model is developed to simulate the spreading of oil under, through, and over a broken ice cover floating on calm water. The oil spreading under the broken ice cover is modeled by modifying the spreading equations for oil under solid ice. Oil seepage through the broken ice is modeled as simple porous media flow. The oil spreading at the water surface near the top ice surface is modeled by considering the interfacial tension and viscous forces. The transport processes are interconnected through mass conservation during numerical computations. The results are compared with data from new experiments conducted in this study as well as experimental data from a previous study. Both axisymmetrical and unidirectional spreading are considered. The simplified model presented here agrees reasonably well with the observed data. The study provides new insight into how to model the problem of spreading when oil is released under a broken ice cover.

This paper presents an analytical approach for the partitioning of the flow cross-sectional area in steady and uniform three-dimensional channels. The mechanism and direction of energy transport from the main flow are analyzed first. Based on the availability of surplus energy from the main flow, a concept of energy transportation through a minimum relative distance toward a unit area on the wetted perimeter is proposed. This leads to a novel method to analytically divide the flow area into various parts corresponding to the channel shape and roughness composition of its wetted perimeter. The demarcated boundary or “division line” can be evaluated using a presented equation. The existence of the division lines, which are lines of zero Reynolds shear stress within the flow region, has been proven through comparison with turbulence characteristics measurements. The method is illustrated in a study of the shear stress distribution in smooth rectangular open channels. Analytical solutions, valid for all aspect ratios, are derived for the mean side wall and bed shear stresses, and they compared well with existing experimental data from various researchers.

Experiments were performed using laser-induced fluorescence (LIF) and a microconductivity probe on turbulent dense jets inclined upwards at an angle of 60° into stationary environments. Such jets are frequently used to discharge industrial wastewaters. Time-averaged LIF images show concentration profiles that vary smoothly in space but instantaneous images show considerable patchiness. Dilution at the jet impact point was found to be higher than previously reported. Downstream from the impact point, the flow becomes predominantly horizontal with a complex additional mixing process that results in ultimate dilutions considerably higher than the impact dilution. The flow is highly turbulent in the vicinity of the falling jet with large concentration fluctuations. These fluctuations decay with distance due to turbulence collapse under the influence of density stratification. The end of the mixing zone is defined as the location where the intensity of the concentration fluctuations falls to 0.05 (i.e. 5%) of their mean value. Normalized expressions for dilution, rise height, and other properties were derived and experimental coefficients are presented from which these gross flow properties could be predicted.

An algorithm is presented for computing the water surface profiles in steady-state gradually varied flows in tree-type open-channel networks. The algorithm is based on the principles of (1) decomposing the channel network into units that are as small as possible; (2) solving the smaller units using an appropriate method, such as the fourth-order Runge-Kutta method; and (3) connecting the solutions for the smaller units to obtain the final solution for the whole network using the Shooting Method. Elementary graph theoretical concepts are utilized to choose the iterative flow variables so that the small units can be solved efficiently. The algorithm is computationally more efficient than the direct method using the Newton-Raphson technique by an order of magnitude. It does not involve the solution of large matrix equations. The efficiency of the algorithm is illustrated by solving an example tree-type channel network with 42 nodes, 41 channels, and a total of 429 grid points. The proposed method will also be very useful in the design and optimization of tree-type channel networks.

This work formulates a unified set of boundary conditions to efficiently represent the majority of valve and orifice devices found in water supply, transmission, and distribution systems. A particularly useful combination of mathematical components results when a lumped inertia model is linked with a throttling device. This combination of elements, termed a pipe replacement element/valve-in-line (PREVIL), has been constructed to permit a wide range of control-valve/short-pipe combinations to be conveniently modeled with the method of characteristics. The solution is quadratic in form and explicit, regardless of the number of pipes that are connected to the boundary condition. A variety of on-off and modulating valves can be accurately handled within this framework. An additional feature developed in this treatment of pressure-reducing and pressure-sustaining valves, flow controllers, and other similar devices permits a more realistic representation of these important control devices. The response time of the regulating valve on opening or closing can be readily approximated so that a greater range of control behavior can be simulated. Application of the combined boundary condition is illustrated in a pipe network.

The cross-sectional mean velocity is an important variable in open-channel hydraulics, whereas the maximum velocity in a channel cross section is mentioned very little. However, the maximum velocity in a channel cross section might be as important as the cross-sectional mean velocity. This is because the measurable maximum velocity can be considered as a “signal,” from which one can know the range of the velocity in a channel cross section. This study explored the relation between the cross-sectional mean and maximum velocities in a natural river by using velocity data collected from the Mississippi River. The relation of the maximum velocity to the cross-sectional mean velocity on different straight reaches in the Mississippi River is perfectly linear. The relation of the maximum velocity to the cross-sectional mean velocity on different river bends is still linear and changes with the r_c/B value slightly. The conclusions are preliminary because of the limited amount of data.

The five computation steps of CASTOR—a simplified dam-break, flood-wave model—are described. The first step uses a simple relation to determine peak discharge at the dam. Second, a dimensionless graph gives peak discharge at the distance x from the dam. Afterwards the uniform-flow equation is used to compute peak water elevation, peak velocity, and wave arrival time. The validation of these last three steps is obtained on a set of 15 dams and 440 channel cross sections by comparison to the results of the model RUBAR 3, which solves Saint Venant equations. The deviation is less than 30% for peak water depth and 50% for other results in more than 90% of the cross sections. Such statistically justified results might be used independently from CASTOR. The example of the Lawn Lake Dam failure is treated by CASTOR; except for a point where the topography changed during the flood, peak water depth shows a deviation less than 20%.

The drag coefficient for dispersed particles settling in a fluid is related to the particle Reynolds number with the same function as that used for a single particle falling in a clear fluid, after taking into account the effects of concentration both on the effective density of particles and on the viscosity of fluid-sediment mixture. A new method is developed for evaluating the settling velocity of natural sediment particles dispersed in a fluid; it agrees well with the available experimental data. The differences among various empirical expressions are illustrated using the present relationship.

A one-dimensional (1D) flow, resulting from a sudden rise or decline in the water stage of a flood channel in a composite aquifer, which consists of two different regions separated by a linear discontinuity parallel to the channel, is considered. Governing equations are solved analytically for appropriate initial and boundary conditions. The obtained solution allows the determination of water level fluctuations in both regions of the composite aquifer and the time-dependent flow rate to (or from) the aquifer. It is shown that three other solutions found in the literature (solutions for uniform finite aquifer with impervious boundary, uniform finite aquifer with recharge boundary, and uniform semiinfinite aquifer) are special cases of the proposed solution, and they are unified in one form. The proposed solution is a relatively simple means of predicting the variations in the water levels in the aquifer as well as evaluating the time-dependent flow rate. It may also be used for the identification of the aquifer properties and for numerical model validation.