Journal of Hydraulic Engineering

A two-dimensional (2D) depth-averaged model of turbulent flows has been developed in a boundary-fitted curvilinear coordinate system. Based on the finite-volume method (FVM), the convection terms are discretized by the Roe's scheme of second-order accuracy, as well as the Power-law scheme. The governing equations are solved in a collocated grid system by the efficient fractional two-step implicit algorithm that is regarded superior to the SIMPLEC algorithm. The “time marching” technique has been used to obtain a steady-state solution as a limiting case. The new model has been applied to several problems including pure convection of a sharp step profile, side discharge into an open channel, flow in a meandering channel, and flow in a Parshall flume with supercritical outflow. Comparison with the available data shows that the model is efficient and robust.

A semi-Lagrangian method for the solution of the unsteady advection-diffusion equation in complex geometries is presented. The domain is discretized into a set of control volumes defined by an orthogonal, boundary-fitted coordinate system. A splitting strategy is employed that decouples the advective and diffusive processes. The advective update is realized by calculating back trajectories along characteristic lines and then, at the feet of these trajectories, the value of the transported field is calculated by interpolation. The interpolated values are calculated using a tensor product cubic spline function. The method is simple to program and produces results of high accuracy. Numerical errors are considerably lower than for conventional Eulerian schemes. In one-dimensional and rectangular two-dimensional domains, the present method gives comparable results to the well-known semi-Lagrangian scheme. However, the new method allows for greater flexibility in handling complex domains.

A boundary-fitted numerical model adopting the general conservation of mass and momentum equation is applied to free surface water flow over a two-dimensional topography. A three-layer near-wall k-ε turbulence model is used to partly account for the effect of the separated-reattaching region in front of each sand wave. A modification of the streamline curvature is introduced to achieve a proper response to the degree of anisotropy between the normal stresses. The geometric shape of the train of sand waves is simulated by introducing a general curvilinear coordinate system. The numerical results were compared with the available experimental data reported by Raudkivi in 1963 and 1966, and more recently by Van Mierlo and De Ruiter, in 1988, and overall agreement has been satisfactory. Detailed calculations indicate that the two-equation k-ε model with careful modifications can yield good predictions for the sand-wave problem. The present model provides a basis for the extended study of bed-load transport and resistance to flow arising from the movement of sediment bedforms.

Five models are investigated for determining the percentage delivery of sediment to streams for shallow landslides that evolve into debris flows. Models I–III are based on debris flow run-out distance, Model IV on snow avalanche run-out distance. For these it is assumed that percentage delivery is 100% for slopes above 10° and zero for slopes below 4°. For intermediate slopes, delivery is based on the run-out distance estimate. Model V, derived from field data, estimates percentage delivery directly without the need for slope conditions. The model performances are investigated using 100 hypothetical hillslopes and a limited database on landslide sediment delivery in Idaho. Model IV performs best but Model I is a close second and its design (run-out distance varying with elevation drop) may be preferable for modeling purposes. Model II (run-out distance varying with debris flow slope and volume) provides a conservative upper limit on percentage delivery. Parallel use of models to provide bounds on the percentage delivery estimate is recommended. The assumption of no deposition at slopes above 10° is found to be not entirely correct and requires further research.

Some analytical solutions are derived for the one-dimensional, vertically integrated, time-dependent equations describing turbid underflows. The system of equations is hyperbolic, therefore, the method of characteristics may be used to transform the partial differential equations to a system of ordinary differential equations, which may then be integrated for the solution. The resulting analytical solutions provide a valuable tool which may be used not only to verify a numerical method, but also to gain insight into the behavior of the equations. It is also shown that the two-dimensional equations cannot be transformed into a system of ordinary differential equations and therefore cannot be integrated exactly. However, the characteristic decomposition of the equations yields important information about the physics of the turbidity equations and also provides insight into the appropriate construction of numerical techniques for solving the multidimensional equations.

Jet-induced mixing is often used to prevent stagnation in shallow service reservoirs. This paper describes a nonorthogonal boundary-fitted model for simulating flows in reservoirs of arbitrary shape. The numerical model solves the curvilinear shallow water equations that are expressed in terms of the depth-averaged contravariant velocity components and free surface elevation. Results are presented for the case of jet-forced flow in a circular reservoir where the inlet and outlet stems are diametrically opposite. Excellent agreement is obtained with alternative analytical and numerical schemes, at inlet Reynolds numbers equal to 10 and 25. A further comparison is given between numerical simulations and experimental measurements of the steady-state velocities in a circular reservoir where the inlet and outlet stems are diametrically asymmetric. Although the present application concerns steady jet-forced circulation, the contravariant shallow water equations should be suitable for modeling wind-driven circulation or tidal flows.

Full recognition of the physical coupling of water and sediment phases of alluvial flows leads to the need for a concurrent solution of the water-routing and sediment-routing components in mobile-bed river modeling. In this paper the coupled and uncoupled methods of alluvial stream modeling are compared. A newly developed coupled model of one-dimensional riverine water and sediment flow, called COUPFLEX, is briefly introduced. Several schemes in discretization of the sediment continuity equation, often used in uncoupled approaches, are mentioned. Two elaborate flume tests on river degradation are briefly described. Experimental data is used to compare the performance of COUPFLEX with that of the uncoupled approaches. This comparison highlights the advantages of the coupled method over the traditional uncoupled method. Performing several numerical tests, some aspects of numerical modeling of alluvial flows are briefly dealt with. These include problems resulting from the use of equilibrium relations in nonequilibrium situations; the dominant role of empirical sediment transport and hydraulic resistance formulas in the accuracy of the answers from any alluvial flow model; significance of the computational time step; violation of the sediment mass conservation law; and the use of approximate water-routing models.

The main flow features of subcritical junction flows are explored, based on an extended hydraulic model study. The flow conditions chosen resulted in flows that are governed by the Froude similarity law. So-called simple junctions with junction angles of 30°, 60°, and 90° were tested. The main emphasis was made in determining the characteristics of the lateral flow and the flow contraction in the tailwater branch. Further, expressions for the momentum correction coefficients, the lateral wall pressure force, and the ratio of flow depths in the lateral and upstream branches were provided. A rational approach for the momentum contribution of the lateral branch is presented and applied for the prediction of the backwater effect across a simple junction. The complex flow pattern is further documented with selected photographs such that a rather complete description of junction flow is now available.

The generalized laws of degradation and spreading of the boundaries of a submerged round jet discharging under oblique and vertical impingements into a channel have been investigated and derived. The laser Doppler anemometry (LDA) technique was adapted for measurement of mean velocities without any interference in the flow, and was utilized for the investigation of the complex three-dimensional circulating flow that was experienced in the channel. In the experiments, the inclination of the jet was varied from 45° to 90° to the bed of the channel, while differing ratios of channel width and depth to jet diameter were studied for various Froude numbers of the flow. The experimental results have been analyzed and compared with Glauret's theory for a radial wall jet as a first approximation neglecting gravity forces when small compared with turbulent forces. The research provides practical information for determining an efficient form of stilling basin for high velocity discharge from pipe outlets.

In modeling dam-break floods in natural channels, the practicing engineer must decide whether to use a one-dimensional (1D) or a two-dimensional (2D) numerical model. Here in the examination of what might be considered a 2D problem, it is clearly illustrated that a 1D formulation provides an excellent solution. The solution is based on a formulation of the St. Venant equations developed for rectangular channels of varying widths, which are applied to the experimental dam-break study conducted in a converging-diverging flume. Numerical solutions based on a conservation formulation solved with the characteristic dissipative Galerkin (CDG) finite-element method are compared to results obtained with a conventional nonconservation formulation, solved by the “box” (four-point implicit) finite-difference method. For subcritical dam-break problems, it is shown that the quality of the result does not depend upon the particular numerical solution technique used. Although the four-point implicit scheme was unable to provide solutions in tests where both subcritical and supercritical flow occurred, the CDG results shows that any conservative, shock capturing 1D scheme would work well on this type of problem.

Settling basins are used on irrigation and hydropower channels to remove objectionable sediment of a specified size and quantity. They are formed by widening the approach channel and lowering its floor through an expansion transition, so as to reduce the mean velocity of flow into the basin. However, various combinations of width, depth, and length of the basin are possible to achieve a desired removal efficiency in a given situation. Taking the cost of the straight and prismatic portion of the basin as the criterion, equations have been developed for its best width, depth, and length. The design example of Maneri Bhali Stage II Project in Uttar Pradesh, India, has been worked out by the proposed method and the results are compared with the actual dimensions provided.