Journal of Hydraulic Engineering

A characteristics-based, upwind, explicit numerical scheme is developed for one-dimensional (1D) unsteady flow modeling of natural rivers and implemented into the U.S. National Weather Service (NWS) FLDWAV model in combination with the original four-point implicit scheme. The new explicit scheme is extensively tested and compared with the implicit scheme. The study shows that the new explicit scheme provides improved versatility and accuracy in some situations, such as particularly large dam-break waves and other unsteady flows with near critical mixed-flow regimes. A technique for implicit-explicit multiple routing is introduced to incorporate the advantages of using both schemes within an application of the FLDWAV model.

The diffusive wave simplification of the unsteady, open-channel flow equations is a commonly used approach for flood routing applications. Among the many routing methods, except for those based on the De Saint-Venant equations, it may be considered to be the one that most closely complies with the physics of open-channel hydraulics. However, common implementations of the diffusive wave approach (linear diffusion, variable parameter diffusion) involve additional approximations that diminish its physical significance and accuracy. A new formulation for the nonlinear diffusive wave is presented that better respects conservation principles through close consistency with the fundamental flow equations. The accuracy and reliability of the proposed model are shown on test cases consisting both of a hypothetical, regular channel, and of an actual river reach. Simulated discharges are compared to those obtained by a full De Saint-Venant model and by ordinary diffusion methods, as well as to observed hydrographs in the real-world test case. This model, based on hydraulic theory, can be safely applied to a wide range of flow conditions, while complying with the practical constraints of flow routing applications, including the usual nonavailability of adequate channel geometry data.

No entirely satisfactory method of estimating discharge capacity in compound channels and rivers has been developed. However, a large body of experimental data has now been acquired covering small-scale and large-scale laboratory compound channels as well as full-sized rivers. Two key ratios, namely total to bank-full discharge and main channel to floodplain discharge, have been shown by theoretical analysis to be significant and the available data have been analyzed to illustrate their behavior for smooth and homogeneously roughened compound shapes at various scales. The ratio of total compound section to bank-full discharge has been shown to be independent of bed slope and scale and to be a function of cross-sectional geometry only. The ratio of main channel to floodplain discharge is independent of bed slope and scale, but is influenced by lateral floodplain bed slope. The coefficients and exponents in equations relating the ratios to depth have been evaluated. It has been suggested that the use of these ratios may provide a comparatively simple method of discharge estimation in compact homogeneously roughened compound channels, and may be extended to other cases when more data are available.

Natural rivers and streams are observed to maintain stable banks while transporting sediment over a central bed region. The development of a numerical model that accounts for this essential feature of natural rivers and streams is discussed in this paper. The model considers the concept of momentum diffusion, and assumes a channel comprising a flat-bed region and two curving bank regions. The resulting boundary stress distribution is such that boundary particles in the flat-bed region are subjected to stresses great enough to put them in motion, while particles in the bank regions are only in a state of incipient motion. It is the combination of this channel geometry and the phenomenon of momentum diffusion that allows for the successful simulation of the “stable bank, mobile bed” condition experienced by rivers. While this paper emphasizes the theoretical and numerical aspects of the problem, a companion paper deals with the application and verification of the model. It presents design equations and graphs that can be directly used to obtain channel dimensions, and tests the model against field and laboratory data.

A one-dimensional mathematical model is presented for quantification of fine-grained sediment movement in small canals. The model is based on the time-dependent, advection-dispersion equation. The model simulates the effects of deposition and erosion through appropriate sink and source terms. The rate of deposition is treated by a linear relation, and the rate of erosion is represented by an exponential function. Selective settling and consolidation effects are incorporated through the depositional and erosional terms. The governing equation is solved by a finite integral transformation that reduces the original PDE into a Sturm-Liouville ODE. Closed-form solutions are given in terms of eigenseries for various boundary and initial conditions. Depending on the situation, the eigenfunctions and eigenvalues are obtained either analytically or estimated by using the Kramers-Wentzel-Brillouin (KWB) approximation. Comparison of the simulated results with experimental data has shown good agreement.

Supercritical flow in chute bends is considered both theoretically and experimentally. The conventional approach is found to apply to small relative curvature only. The knowledge is extended to large bend numbers, and a design procedure is presented. Supercritical bend flow in the smooth horizontal and rectangular channel is considered. It is found that the maximum standing wave heights are influenced by the bend number, that is, the approach Froude number times the square root of the average relative curvature. Current models are demonstrated to apply for relatively small bend numbers. For modest and large bend numbers, however, the flow pattern is modified. Besides the extreme wave lengths, the generalized surface profiles along either bend wall, the typical velocity fields, and the separation mechanism are experimentally studied. Also, a model for separated bend flow is developed. Photographs are presented that illustrate the uneven distribution of separated bend flow in regard to the cross-sectional area. This study allows a simple and straightforward design of chute bends.

A numerical method of solution of the inviscid flow under planar gates is developed and evaluated. The results of the calculations show good agreement with previous inviscid flow solutions and with experimental results for the water surface profile, velocity, and pressure distributions throughout the flow domain. The discrepancies between the experimental and numerical inviscid flow values of the coefficient of contraction are analyzed. After detailed examination of alternative explanations for the discrepancies, it is suggested that the most plausible explanation is the energy loss due to the vortex system attached to the upstream region of the gate.

One of the basic impediments to a clear understanding of a variety of fundamental problems in the context of sediment transport has been the lack of a well-grounded formulation of bed sediment entrainment. This is dealt with herein, physically based on the mechanism that bed sediment particles are actually entrained by the bursting process inherent in wall turbulent flows. A simple theoretical model for sediment entrainment from flat, loose bed is established using the averaged bursting period scaled on inner variables and the spatial scales of turbulent bursts. Sediment entrainment is shown to depend strongly on bed-shear velocity. The theoretical entrainment flux is compared to available laboratory data sets covering both hydraulically smooth and transitional bed situations. Generally good agreement is obtained, representing the best performance of the present model in relation to existing entrainment functions. It appears to characterize a rather encouraging aspect for a new approach to sediment transport, given the enhanced understanding of turbulent bursting.

Based on the flow-continuity equation, scour geometry, and a generalized form of the power-law formula for flow resistance in an alluvial channel, a semiempirical analysis of equilibrium local clear-water scour at an abutment is presented. The method is based on the premise that the flow obstruction and subsequent increases in bed shear stress due to projection of the abutment into the flow are responsible for the scouring action around the structure. The proposed scour-depth equation is derived for an abutment placed perpendicular to the flow direction and involves only the approach flow quantities, the median sediment size, and the projecting length of the abutment. A total of 252 data on clear-water maximum scour depth, from the present study and other sources, were analyzed and compared with the developed relationship. The formula is extended to include the effects of abutment shapes and nonuniform sediment mixtures. For mixtures an effective sediment size, d_50a, that corresponds to the critical armor layer in the scour hole is used. In general, comparisons of computed and measured maximum equilibrium scour depths indicate that the predictions are satisfactory and the approach is reasonable.

The model performance of an engineering system is affected by many variables subject to uncertainty. Point estimate (PE) methods are practical tools to assess the uncertainty features of a model involving multivariate stochastic parameters. Two PE methods have been developed for engineering applications. One is Rosenblueth's PE method, which preserves the first three moments of random variables and the other is Harr's PE method, which reduces the computations of Rosenblueth's method but only as appropriate for application to random variables with normal distributions. In this study, two algorithms are proposed to encompass the advantages of the two PE methods: computational practicality and the handling of mixture distributions. Through a numerical experiment, the proposed methods yielded more accurate estimations than those of Rosenblueth's method with about the same amount of computation as Harr's method. The two proposed methods were also applied to estimate statistical moments of a pier scouring model output to demonstrate their performance in an engineering application.