Journal of Hydraulic Engineering

Experiments to study the dilution and formation of wastefields resulting from discharge into a linearly density‐stratified steady current of arbitrary speed and direction are reported in three papers. The experiments were conducted using a model multi‐port diffuser for a range of parameters typical of ocean wastewater outfalls. In this paper, results are given from which the established wastefield characteristics for the “line plume” source conditions can be predicted. In general, the wastefield rise height and thickness decrease as the current speed increases. Dilution increases with current speed for all current directions, with diffusers perpendicular to the current resulting in higher dilutions than when parallel. Concentration profiles for perpendicular currents show little horizontal structure as the individual plumes rapidly merge. The results for dilution show no dependency on port spacing or source momentum flux over the parameter range tested, and the dominant source parameter is the buoyancy flux per unit length. The results confirm the value of the “line plume” approximation for predicting dilutions for deepwater ocean outfalls over a fairly wide parameter range.

Some of the basic features of submerged wastefield formation in stratified currents are reported in this paper. Dilution increased with distance from the diffuser in the initial mixing region until it attained a maximum value, which is the initial dilution, after which it remained constant. By assuming a model of buoyancy‐induced turbulence collapse, expressions for the observed dependency on current speed in the forced entrainment regime of initial dilution, rise height, and mixing region length were obtained. An expression for lateral spreading in parallel currents was derived which was found to be of the same form as for unstratified currents, except that the rate of spreading in stratified currents is much slower. An expression for the rate of spreading in perpendicular currents was derived by applying results from mixed‐region collapse. An applications example shows that the initial mixing region can extend for several hundred meters downstream from the discharge. Because of gravitational spreading, a line diffuser will produce a wastefield width comparable to the diffuser length for most oceanic conditions, suggesting that Y or similarly complex diffuser configurations are not necessary to produce a widely dispersed wastefield.

The effects of port spacing and jet momentum flux on the characteristics of submerged wastefields produced by multi‐port ocean outfalls in linearly stratified currents were investigated experimentally. Within the parameter range studied the primary effect of these variables is on the rise height and thickness of the wastefield, and dilution is closely approximated by line plume results. Increased momentum flux causes a reduction in rise height at low current speeds while leaving the total entrainment path length of the jets, and hence dilution, fairly constant. The effects of increased momentum flux decrease as the current speed increases. Increased port spacing still resulted in merging of individual plumes even when fairly widely spaced, particularly in flowing currents, so point plume results were of limited applicability in predicting wastefield properties. Results are presented in graphical and tabular form from which rise heights and thicknesses can be estimated for discharges which do not approximate line plumes. An example of the procedure is given, and some implications for diffuser design are discussed.

Experimental results concerning the axial concentration (or dilution) distribution of a round vertical turbulent buoyant jet of fresh water, discharged in a calm ambient saline solution and obstructed by a thin concentric disc of diameter D, placed horizontally at a distance H from the jet exit section of diameter d are presented and discussed. The functional relationship of axial concentration in the region beyond the disc is well established quantitatively and the important parameters affecting the concentration distribution are determined. A comparison of the present results with those of the unobstructed jet prove the effectiveness of the arrangement studied in increasing dilutions after the disc.

Empirical quantiles constitute a simple alternative for estimating flow values for which there is a specified nonexceedance probability. The standard error of empirical quantile estimators is a measure of the variability to be expected about the numerical estimates obtained from flow records. It is shown in this work that the standard error of empirical flow quantiles is a function of: (1) The specified probability level associated with a particular quantile; (2) the sample size used in the estimation; and (3) the probability density function governing the realization of flow variates. An example using a series of annual runoff from 1904–1986 in the American River at Folsom Reservoir, California, shows that empirical flow quantiles are efficient, i.e., have standard errors of estimates not exceeding 10% of the actual quantile value when the return periods involved are less than 100 years and the flow record is moderately large. Results from Monte Carlo simulations indicate that the approximate expression for standard error of the empirical quantile derived in this work is accurate to within $\pm 10\%$ of population values.

A bed load transport model based on the mechanics of sediment moving by saltation yields predicted values of bed load flux as a function of boundary shear stress, grain diameter and density. The parameters required to calculate bed load transport (particle velocity, bed load sediment concentration, and the height of the bed load layer) can all be determined from our model, which computes sequences of trajectories of individual saltating grains as well as the concentration of moving grains that the flow can support. The latter is related to the momentum the accelerating grains extract from the flow. Predicted curves of bed load transport vs. boundary shear stress agree well with transport data collected by Gilbert, Meyer‐Peter et al., and the Waterways Experimental Station; measured shear stress was corrected for pressure drag when bed forms were present. Comparison of predicted bed load transport with common bed load equations reveals considerable similarity among the relationships. The best agreement with the data is produced by relationships in which the transport rate vanishes as the shear stress approaches the critical Shields' number, as in our model and Yalin's equation.

Experiments on transport by water of synthetic lightweight sediments of specific gravities, $1.0<s<2.5\text{,}$ and uniform grain size, $D=3.5\mathrm{mm}\text{,}$ are described. The results confirm the dimensional reasoning that the volumetric specific sediment transport rate, $q_s\text{,}$ is proportional to a simple power relation of the quotient, shear velocity/grain fall velocity $(V*/w)\text{.}$ The sediment transport rate, $q_s\text{,}$ is found to be proportional to the sixth power of the shear velocity, $V*\text{,}$ and inversely proportional to the fifth power of the grain fall velocity, w. An empirical formula based on the dimensional reasoning and the results above is found to be equivalent to the Einstein‐Brown bed load formula. A comparison of the experimental data with the predictions of several common bed load formulas shows the behavior of these formulas with lightweight sediments. The Einstein‐Brown formula and a modified version of Smart's formula provide good predictions.