Journal of Hydraulic Engineering

The standard one‐dimensional equations of unsteady sediment‐transport are examined, and multiple time (or length) scales are identified. The existence of multiple scales may lead to a singularly perturbed behavior that should be taken into account in any general numerical model. Previous models, which reduce the number of conservation equations solved simultaneously from three to two, are seen to be unable to satisfy exactly either a general boundary condition or a general initial condition. Implications for numerical modeling are explored. Numerical results for the model problem of sediment‐deposition upstream of a dam illustrate the analytical argument.

The stability and convergence characteristics of a four‐point implicit finite‐difference scheme due to Preissmann, which has been widely used in open‐channel flow modeling, are examined. The analysis is made for a general linear hyperbolic system of n first‐order equations, but is restricted to the homogeneous or frictionless case. In particular, the effect of a weighting factor in space, as well as in time, is considered. The specific case of unsteady sedimenttransport modeling, which conventionally results in a third‐order system, is discussed with particular reference to its singularly perturbed nature. Recommendations for practical computations are made.

Significant advances in the state‐of‐the art of dam‐breach flood wave modeling have occurred during the past decade. A comparative evaluation of several leading models representative of the current state‐of‐the‐art included a comprehensive literature survey and application of the selected models to several case study data sets. A dynamic routing model should be used whenever obtaining a maximum practical level of accuracy is required and adequate manpower, time, and computer resources are available. The National Weather Service (NWS) Dam‐Break Hood Forecasting Model (DAMBRK) is the optimal choice of model for most practical applications. Some applications require the capability to perform an analysis as expeditiously as possible. The NWS Simplified Dam‐Break Flood Forecasting Model (SMPDBK) is the optimal choice of model for most of these types of applications.

The last few decades have witnessed accelerated developments in hydraulics in China. These developments were prompted by construction of large‐scale hydraulic projects and thermal power plants. A brief account of these developments is given, covering such areas of specialization as sediment transport, high‐velocity flow, river hydraulics, cooling of thermal effluents, hydraulic machinery, and hydraulic transients. In each case, selected references are given. Special attention is called to some strange flow phenomena at hyperconcentrations of sediment, innovations for the enhancement of energy dissipation, a new arrangement for the intake structure for the cooling water of thermal power plants, and mathematical modeling of alluvial rivers, with change in sediment composition taken into account.

The three‐parameter nonlinear Muskingum method for flood routing is analyzed. Analytical solutions for simplifying cases and approximate integral solutions for general cases are derived. Its accuracy depends mainly on the parameter k. Unlike the linear case, the weighting factor is much less significant. A comparison with the linear case using four sets of inflow‐outflow data shows that the nonlinear method is less accurate than its linear counterpart. Also, the accuracy varies from one nonlinear version to another.

Sediment‐driven density currents exist in most secondary sedimentation basins and cause the usual hydrodynamic flow pattern in these basins to deviate substantially from uniformity. The mathematical model introduced here allows one to predict, by direct computation, the behavior of the bottom current and the surface return flow, and simultaneously to determine their distributional effects on the sedimentation process itself. The model consists of conservation equations for fluid mass and momentum and sediment volume, supplemented by a modified form of the $k‐\epsilon$ turbulence closure model. This paper emphasizes the description of features of the model and the presentation of results for a set of flows that may occur in a typical circular secondary clarifier. These results include the flow pattern, concentration distribution of sediment, the percentage of solids removal, and some examination of turbulence quantities in the basin. Some model sensitivity studies are reported.

Recent pipeline experiments performed in Saskatchewan show the existence of a shear layer in which the solids concentration decreases linearly with height. This finding has already been used to calculate the velocity distribution within a constant-stress shear layer. The analysis has now been extended to obtain the solids discharge per unit breadth of bed. The result agrees with the modified Meyer-Peter and Muller equation and with the writer's sand data. For larger nylon particles the solids discharge per unit breadth fell below that expected on the basis of the sand data; and the new analysis shows the reason for this apparent anomaly. It also shows that a shear layer several grain-diameters thick will not be uncommon in open-channel flow. Contrary to the conventional wisdom, the new analysis predicts that the threshold-of-motion curve on the Shields diagram must approach a constant value at sufficiently small abscissae, a finding which appears to be in accord with recent experimental evidence.