Journal of Hydraulic Engineering

Meander flow and meander‐planform development are described. The basis is a steady, two‐dimensional model of flow and bed topography in an alluvial channel with variable curvature. The model is developed from the equations for conservation of mass (water and sediment) and momentum, and from a stability criterion for sediment particles on the stream bed. By order of magnitude considerations and linearization, these equations are reduced to those of a damped, oscillating system. The meander development is described by forcing a traveling, small‐amplitude channel alignment wave on the system, and determining the growth characteristics of the wave. The growth rate of the amplitude is determined by relating the alignment wave and the change in channel alignment through a bankerosion model. Formulas are thereby developed for calculation of: (1) Velocity and depth distribution in meandering channels; and (2) rate and direction of channel migration. Laboratory and field data are used to verify the formulas.

An analytical model for the description of flow and bed topography in, and planform development of meanders is tested with data from rivers in India, Pakistan, and the United States. The model is steady, two‐dimensional and linear, and it describes the channel flow as a damped, oscillating system with curvature as forcing function. The description of planform development is obtained by forcing a small, traveling perturbation on the system and determining the migration features of the perturbation. The model describes planform development in terms of lateral and downstream migration rates, and flow and bed topography in terms of transverse gradients of depth and depth‐averaged velocity. Formulas for estimates of dominant meander wavelength and phase shift are also tested. The agreement with data is good. Guidelines for use of the model are described, using data from a hypothetical river.

Experimental data on dam break flows obtained on a test facility are presented in this paper. The test facility comprises a 3.65 m by 2.3 m upstream reservoir and a 0.3 by 0.3 m rectangular downstream channel. This channel has two straight segments that are connected by a 180° bend. Capacitance probes are used to record water levels in the upstream reservoir. A new procedure using electronic digitization of video images is used to record water levels in the downstream channel. This procedure does not disturb flow and gives accurate results. Comparison of the unsteady water levels computed by using the Lax scheme with the measured water levels is satisfactory. The conservation form of the St. Venant equations predicts the height and celerity of the wave better than the nonconservation form. An approximate procedure is presented to compute the lateral gradient of water surface in a curved channel. Comparison with the measured results shows satisfactory agreement.

TO analyze unsteady flow in a curved channel, three‐dimensional equations describing the conservation of mass and momentum are transformed from a Cartesian coordinate system to a channel‐fitted coordinate system. This transformation allows the use of a simple reflection boundary to simulate the walls of a curved channel. Equations in channel‐fitted coordinates are then integrated over the depth to obtain a set of depth‐averaged two‐dimensional equations that are then solved using the MacCormack explicit finite‐difference scheme. The results of the mathematical model are compared for verification to experimental data obtained on a laboratory test facility. The agreement between the computed and measured water levels is satisfactory. However, the computed wave speed is slower than the measured wave speed when the flow is near critical conditions. Reflection technique works well, except in regions close to the entrance of a bend.

A generalized mechanistic model is presented for the hydraulic transport of mixed‐regime slurries in pipelines. Mixed‐regime slurries are defined as those two phase (solids‐liquid) mixtures containing a wide range of particle sizes, the distribution of which generally lies between pseudo‐homogeneous slow‐settling slurries and heterogeneous rapid‐settling slurries. The mechanistic model presented herein consists of three components—a vehicle portion, a suspended portion, and a bed‐load portion. Each component of the particle size distribution is analyzed to determine its contribution to the fraction of vehicle load, suspended load, and bed load. The vehicle and suspended load components are combined to determine the wall shear above the bed load interface. This wall shear is converted to a force and added to the bed load resisting force to determine the total friction head loss gradient along the pipe. The incipient sliding bed condition is found by equating the bed load resisting force to the driving force on the bed load. The mechanistic model is compared to experimental results from laboratory pipelines. Each component of the particle size distribution is analyzed to determine its contribution to the fraction of vehicle load, suspended load, and bed load.

The mechanistic model presented in the first paper of this series is compared to existing correlations in the literature, for mixed regime flow. Threethousand data points were used, of which about half were obtained from the University of Cape Town Hydrotransport Research test facility and the other half of the data points from other institutions. The experimental test facility and experimental procedure used at the University of Cape Town is described in detail. This experimental procedure, which is computer data acquisition based, ensures accurate, reliable results.

A new computational methodology for fully coupled simulation of unsteady water and sediment movement in mobile‐bed alluvial rivers has been developed and tested. The one‐dimensional approach treats bedload transport of nonuniform sediment mixtures with sorting and armoring effects considered. Spatial lag effects in nonequilibrium bedload transport are taken into account through innovative use of the recently developed notion of a loading law. The new system of equations for water and sediment movement is solved in a fully coupled, implicit manner using the Preissmann finite difference scheme implemented to allow for either upstream‐ or downstream‐induced mobile‐bed perturbations. Formal analysis of the coupled system sheds new light on boundary‐condition requirements for the multiple‐size‐class problem. The fully coupled implicit solution has proven to be robust and stable, and it respects the underlying volumetric conservation laws remarkably well, as demonstrated in continuity analyses of computed bed evolution for systematic test runs. Implementation of the new code is demonstrated through application to a schematic river reach resembling a portion of the lower Rhone River in France.

Velocity measurements, using a laser‐doppler anemometer, are carried out in a fully developed, rectangular, subcritical open channel flow on smooth and rough beds. The average roughness heights of the “rough” surfaces, used in the experiments, are 1 mm, 4 mm, 8 mm, and 12 mm. A model is presented for determining the reference level of the velocity distribution on “rough” surfaces. The shear velocities are determined from velocity profiles measured close to the bed. The calculated shear velocities show an increasing tendency as the wall roughness increases. In the fully turbulent inner region on a “smooth” wall, the coefficients in the logarithmic law‐of‐the‐wall distribution take values of 2.44 and 5.5; the former corresponds to 0.41 for the von Kármán constant. The velocity‐defect expression of Coles has a profile parameter of 0.1, rather than 0.55. For “rough” channels, the representation of the overall data in terms of law‐of‐the‐wall distribution seems reasonable; however, the velocity‐defect distribution is not satisfactory.

For a variety of design purposes there is increasing interest in estimating probabilities of rare floods, with magnitudes up to the probable maximum flood. One estimation approach, which we term “stochastic storm transposition,” is a generalization of the concept of storm transposition, which is the basis for estimating probable maximum precipitation. We explore the concept of stochastic storm transposition, and demonstrate the application of two alternative formulations of this concept to a catchment in the midwestern United States. It is clear from these applications that before the concept can be applied routinely its theoretical basis must be strengthened and several potentially large sources of uncertainty must be explored.

Sediment transport relationships have been calibrated under a certain range of experimental conditions described here by three dimensionless parameters. For given stream-flow conditions, an applicability index is defined as the number of dimensionless parameters falling within the range of experimental values. An example involving four sediment transport equations applied to limited flow conditions illustrates the usefulness of the index. Good agreement between these four calculated rates of sediment transport is obtained when the index is high. At low values of the index, however, the discrepancies between the four equations can exceed several orders of magnitude. The Toffaleti method predicts very low transport rates for coarse sands. At larger flow depth, the equations of Toffaleti and of Ackers and White are sensitive to sediment size.

A severe restriction to dilution discharge measurements is that they are to be applied to steady-flow conditions only. Using a computational model, dilution discharge measurements by constant-rate injection are simulated during unsteady-flow conditions caused by a Gaussian flood wave propagating down a prismatic channel with rectangular cross section. The accuracy of the discharge measurement is deduced from the computational results. The main source causing discrepancies between the actual and measured discharges is the difference in propagation velocities of the tracer cloud and the flood wave. Correction procedures are recommended, since maximum inaccuracies can easily be larger by an order of magnitude than inaccuracies during steady flow conditions.