Journal of Hydraulic Engineering

A continuous velocity distribution is derived for the laminar, transition, and logarithmic regions of the near‐bed portions of boundary layers for smooth and rough surfaces and drag‐reducing fluids. The solution is based on the equations of motion for uniform flow and a parabolic distribution of eddy viscosity over the turbulent portion of the boundary layer. Effects of increased roughness are accounted for by a shift of the distribution of eddy viscosity toward the flow boundary. The resulting velocity distribution agrees with published data and has an advantage over the classical logarithmic distribution for flow over rough surfaces in that the lower velocity limit is zero at the assigned origin for distance measurements near the boundary. The distribution function approaches the logarithmic expression in the outer regions of the boundary layer and has an advantage that the predicted slope of the velocity distribution is zero at the top of the boundary layer. Although the parabolic distribution of eddy diffusivity does not account for velocity distributions with wake components, other distributions of eddy diffusivity to account for these effects are suggested.

A mathematical simulation model of the spatial and temporal rainfall process was developed. The model is used as input to distributed rainfallrunoff models in order to obtain streamflow series at multiple locations in large river basins. Frequency analysis under different basin development and control alternatives can then be performed. A case study in the Cumberland River Basin (Kentucky and Tennessee) is presented. The basin is $46\text{,}397{\mathrm{km}}^2\left(17\text{,}914{\mathrm{mile}}^2\right)$ and thus exhibits large rainfall variability in space. The rainfall model was calibrated with 28 yr of hourly and daily rainfall data in 274 stations in and around the basin. By using generated rainfall as input to a previously calibrated distributed rainfall‐runoff model, discharge frequency curves were obtained at 14 locations. The curves corresponded to both the system with eight operational flood control reservoirs and the natural system without regulation.

The energy exchange in streams carrying suspended material is analyzed using an efficiency concept. The efficiency is defined as the ratio between the gain in potential energy of the suspended material and the turbulent dissipation. It is shown that the efficiency is not constant, but depends linearly on Shields' parameter. The linear relation is used to develop a simple formula, which describes the suspended load as a function of well‐known parameters. With the results from open streams an auto‐suspension criterion is developed for turbidity currents. This criterion describes the situation when a submerged current carrying suspended material neither deposits nor erodes material.

Experimental data on surface buoyant jets in steady and reversing crossflows is presented. The experiments were conducted in a 130 ft (40 m) by 81 ft (25 m) by 1.5 ft (0.45 m) deep basin, which was large enough to ensure negligible boundary effects while allowing controlled ambient, conditions. The test results are presented nondimensionally and referenced to controlling length scales. The steady crossflow results are trajectories and longitudinal temperatures, which show the effects of the discharge buoyancy and initial flowrate. Comparing these results with those of other experimental studies leads to the suspicion that boundary effects may be present in some of the latter. The reversing crossflow tests furnish surface temperature patterns and plume depths for a range of conditions. These results can be used to evaluate mathematical models. In addition, the effects of tidal reversals on the offshore extent and depth of the plume are examined. Dispersion tests reveal that buoyancy played an important role in plume spreading. This factor is important as buoyant spreading is frequently omitted in two dimensional farfield mathematical models of thermal plumes.

A tensor model for the dispersion coefficient for saturated flow in anisotropic, homogeneous porous media is proposed. The tensor components are evaluated from experiments with an anisotropic, homogeneous porous medium, constructed from thin, alternating layers of two types of sand, having different mean particle sizes. Tests were conducted for flow parallel, perpendicular, and inclined at 60° to the direction of the layers. The hydraulic conductivity and the longitudinal dispersion coefficient were found to be second‐rank tensors with equal and constant eccentricities and with major and minor principal axes oriented along and perpendicular to the direction of the sand layers, respectively. The lateral dispersion coefficient was found to be a second‐rank tensor whose principal axes were orthogonal to those of the hydraulic conductivity tensor and whose eccentricity increased with increasing seepage velocity. Two values of the off‐principal diagonal dispersivities were found to be nearly equal in magnitude but opposite in sign. Experimental results support the dispersion coefficient tensor model proposed in the investigation.

Rotary tidal currents or site constraints can result in an outfall diffuser being alined with the current in shallow water. Experiments using a small model laboratory diffuser flume and a much larger scale model in an estuarine channel were used to establish the significant processes causing initial dilution of effluent discharged from a multiport diffuser alined parallel to the ambient current. From considerations of momentum conservation and mixing, and the results of the flume experiments, an expression for the initial dilution in shallow water was obtained and the conditions defining shallow water were established. The results of the field experiments carried out in an estuarine channel were in agreement with the laboratory results and verified the derived expression. A relationship between the initial dilution and the angle between the diffuser and the current was developed from the field studies.

The mechanisms of seawater circulation in tunnelled ocean sewage outfalls are investigated. The magnitude of the circulation is determined in terms of the sewage flow and geometric parameters of the outfall. An expression is derived for the sewage flow required to arrest the circulation. The theory is well supported by laboratory experiments. Means by which the risk of seawater intrusion may be minimized are discussed.

Hydraulic jumps at abrupt bottom drops in rectangular, prismatic channels are either A-jumps (downstream controlled), B-jumps (upstream controlled), or undular jumps (transition between the two). B-jumps are investigated in detail by accounting for the effective pressure distribution at the vertical drop. Traditional description, which assumes strictly hydrostatic pressure distribution at the drop, is modified to yield smaller downstream flow depths for given inflow Froude number, drop height, and inflow depth, a trend suggested by comparing the present formulation with observations. All results are given in terms of design quantities, which enables simple estimation of the major flow characteristics.

In the study of flow in curved open channels, it is observed that a gradual transition from a flat to a superelevated water surface occurs when the curvature of the channel is abruptly changed. The length of this transition depends on the curvature, channel width and Froude number. An approximate analysis, based on the depth-averaged flow equations with friction neglected, is used to evaluate the water surface configuration and provide a simple expression for the transition length. Comparison of the predicted water surface configuration with a few preliminary experiments is also made, and the agreement is seen to be reasonable.

It is shown that minimization of standing waves in supercritical flow in a contraction is equivalent to simultaneous satisfaction of the momentum equation parallel to and perpendicular to the wave front, the continuity equation across the wave front, and continuity through the contraction. Solution of these four governing equations is presented in a graphical form which eliminates the necessity of trial and error in the design procedure. Finally, choking criteria are defined to assist the designer in maintaining supercritical flow through the transition.