Journal of Hydraulic Engineering

A coincident frequency analysis using the total probability theorem was performed for an 80‐mile (129‐km) reach of the Illinois River to evaluate existing stage‐frequency relationships and revisions caused by a proposed higher levee system. Frequency and duration relationships were derived to establish the upstream and downstream boundaries. A water surface profile model was applied to calculate stage at 210 points in the reach for given starting backwater and discharge conditions. The analytical process was calibrated to stage data in the reach through iterative adjustments in the boundary duration curves. Comparisons of the adopted results to previous analyses using simplified techniques showed a significant reduction in levee design profile and potential cost savings of $1,600,000 in levee construction.

A new method for calculating the mean value of the local hydrodynamic pressure acting upon a hinged gate and a mathematical model of pressure pulsation are developed. The mean hydrodynamic pressure at an optional point on the surface of a hinged gate is obtained by using the Bernoulli equation and model test data. The problem of the pulsation phenomenon of hydrodynamic pressure is solved by considering the random character of the process and by making measurements of pressure fluctuation. Numerical analysis of the results obtained make it possible to determine the autocorrelation function and the power spectral density function and, in consequence, to draw conclusions concerning the character of and reasons for the pulsation phenomenon of the pressure. As a result of the investigations, a normalized power density spectrum equation, which characterized the frequency of the pressure pulsation, is derived.

A series of numerical experiments is performed to determine the flow and channel characteristics that are most conducive to kinematic wave steepening and associated kinematic shock phenomena. Relevant flow and channel characteristics are identified at the outset, and a program of 80 computer runs is completed, varying the inflow hydrograph peak Froude number, time‐to‐peak, and base‐to‐peak flow ratio, and the channel cross‐sectional shape. It is found that all have a definite effect on kinematic shock development. The size of the wave is perhaps mostly responsible for the occurrence or nonoccurrence of the shock.

It is often necessary to estimate the mean velocity in ungaged mountain rivers, but the flow resistance equations available for this purpose require further testing and development. Such rivers are characterized by coarse bed materials, steep slopes, and low depths. For these conditions, boulders protrude well into or completely through the flow, and bed roughness is said to be large‐scale. Recently, three equations specifically intended for large‐scale roughness have been developed to address this problem. Data from a mountain river were used to test the equations. All were prone to errors of the order of 30%. The errors were systematic, all the equations tending to overestimate mean velocity compared to observed values. An investigation of the possible sources of error suggested that sampling error in the knowledge of bed material size was a major source of uncertainty in the predicted velocities, but that this and discharge errors could not wholly account for the observed discrepancies. Boulder shape is not represented in the equations, but this was discounted as an important parameter on the basis of a flume study. It was concluded that further research is required to produce a reliable, process based, flow resistance equation for mountain rivers.

Examination of the flow resistance of high‐gradient gravel and boulder‐bed rivers, using data collected in British mountain rivers with slopes of 0.4–4%, shows that there are differences in resistance variation between mountain and lowland rivers and that between‐site variations do not necessarily reflect at‐a‐site variations. Comparison of data with the familiar resistance equation relating the Darcy‐Weisbach friction factor to the logarithm of relative submergence shows that the equation tends to overestimate the resistance in uniform flow. The equation also tends to underestimate the rate of change of resistance at a site (as discharge varies) at high gradients. The influences of nonuniform channel profile, sediment size distribution, channel slope and sediment transport are reviewed, but the data do not allow any quantification of these effects. Instead an empirical approach based on the available data is presented, allowing the friction factor to be calculated from the relative submergence with an error of up to $\pm 25\%$ to $\pm 35\%\text{.}$ A summary of the field data is included.

A mathematical model for water and sediment routing through curved alluvial channels is developed and applied in a case study. This model, which is for alluvial streams with nonerodible banks, may be employed to simulate stream bed changes during a given flow, thereby providing the necessary information for the design of dikes, levees, or other bank protection. This model incorporates the major effects of transverse circulation, inherent in curved channels, on the flow and sediment processes. In the simulation of the evolution in stream bed profile, the effect of transverse flow is tied in with the aggradation and degradation development. River flow through curved channels is characterized by the changing curvature, to which variations of flow pattern and bed topography are closely related. Simulation of these changing features is based upon the fluid dynamics governing the growth and decay of transverse circulation along the channel.

An analytical solution for the thickness of the transition zone between fresh and seawater in aquifers on ocean islands is presented. The interface is treated as a mixing layer similar to a laminar boundary layer between fluids moving at different velocities. The method requires assumptions of homogeneous isotropic dispersion, uniform hydraulic conductivity and steady flow; all water withdrawal is assumed to occur at the water table. The slope of the sharp interface is used in the solution for the mixing layer and the sharp interface is determined using Dupuit‐Forchheimer assumptions of horizontal flow. The method presented efficiently estimates the transition zone thickness, thus providing information not available from sharp interface models. The method is illustrated by application to the freshwater lens on an island of the Tarawa Atoll in the Pacific Ocean, and is used to show the effects of different pumping arrangements on the width of the mixing layer.

Cyclic variations in bed load discharge at a point, which are an inherent part of the process of bed load movement, complicate calibration of bed load samplers and preclude the use of average rates to define sampling efficiencies. Calibration curves, rather than efficiencies, are derived by two independent methods using data collected with prototype versions of the Helley‐Smith sampler in a large calibration facility capable of continuously measuring transport rates across a 9 ft (2.7 m) width. Results from both methods agree. Composite calibration curves, based on matching probability distribution functions of samples and measured rates from different hydraulic conditions (runs), are obtained for six different versions of the sampler. Sampled rates corrected by the calibration curves agree with measured rates for individual runs.

A laboratory investigation was conducted to study the mean flow characteristics of radial turbulent flow. The fluid—air in this case—is supplied from a pipe at the center and spreads out radially between two parallel plates separated by a small distance. The distribution of pressure and shear stress on the front plate and the velocity at different radial distances from the center has been studied. The velocity distribution has been analyzed in a manner similar to that for radial wall jets—with appropriate velocity and length scales to get similarity profiles. The information obtained enables one to predict the velocity if the discharge and geometric characteristics of the flow configuration are known.

Results of laboratory experiments concerning the development of scour around a cylindrical pier placed in a bed of cohesionless sediment overlain by an armoring layer of coarser sediment are presented. Both the armoring layer and the bed beneath it were composed of uniform‐sized sediment. It was found that, under these conditions, the depth of scour at a pier may exceed that which occurs at a pier in a nonarmored bed. Local scour due to the local flow structure around a pier may either develop through the armor layer and into the finer, more erodible, sediment, or it may trigger a more extensive localized scour of the bed sediment exposed to the flow by the erosion of the armor layer. Design formulas to estimate the maximum equilibrium depths of scour are proposed.