Journal of Hydraulic Engineering

Velocity measurements, using a two‐dimensional laser Doppler velocimeter (LDV), were made in turbulent channel flows of water, at a Reynolds number of 60,000, over a flat stationary sediment bed with covers of different roughness characteristics. The measurements confirmed the noncoincidence of the planes of maximum velocity and zero Reynolds stress. Significant diffusion of momentum and kinetic energy took place from the rough to the smooth surface. As the roughness of the cover was increased, the vertical transfer of vertical velocity fluctuations near the bed decreased, resulting in a decrease in the sediment‐suspension mechanism. The proper length scale in the outer region was the height of the plane of zero total stress from the corresponding surface. When the distance from each surface was normalized with this length scale, the measured mean streamwise velocity defects agreed with the log law, and the measured streamwise and vertical velocity fluctuations agreed with the exponential variations formulated in 1986 by Nezu and Rodi.

An empirical relation for the bed concentration of suspended sediment $c_b$ defined at a few grain diameters above the bed is developed. Its derivation is based on the experimental data sets of Guy et al. in 1966. The values of the near‐bed concentration were obtained by first isolating the suspended load transport from the observed rates of total load transport by use of a bed‐load formula. The suspended load was then equated to Einstein's formulation, which allowed the determination of $c_b$. The influence of large concentrations of suspended sediment and of the reference level for $c_b$ on the calculated values of bed concentration has been analyzed. The proposed relation compares satisfactorily to values of near‐bed concentration obtained from independent data sets. The procedure used to derive $c_b$ provides a simple method for the calculation of the total transport rate of noncohesive sediment.

Time‐varying sediment concentration exiting a plunge pool is analyzed by considering the effect of free‐overfall jet diffusion on sediment detachment and scour. The analysis results in dimensionless relationships between scour volume, sediment concentration, maximum scour depth, and time. Sediment concentration is at a maximum near the initiation of scour, when the eroding bed is at the tip of the impinging jet's potential core. Thereafter, sediment concentration decreases as a function of time and scour‐hole geometry, expressed as maximum scour depth. Dimensionless geometric relationships show that the scour volume per unit width can be expressed as twice the square of the maximum scour depth at the corresponding time for the cohesive and noncohesive soils tested. Analytical relationships between sediment concentration and time are verified by laboratory experiments of scour below a free overfall on two sand‐bed materials (one coarse and one fine) and on one cohesive soil, each replicated several times. The agreement between measured and predicted values is best for the noncohesive sands.

The unsteady flow regime and the temperature mixing in temperature‐stratified settling tanks associated with a warm influent are investigated by application of a numerical model with two different turbulence models. The model consists of a series of conservation equations for fluid mass, momentum, and temperature, with one version using the algebraic stress model and the other version using the conventional $k‐\epsilon$ model. The simulation results are compared with existing experimental data for the temperature distribution. The velocity measurements were made under the same laboratory conditions that were used for the temperature surveys. The experimental results are presented and compared with those predicted by the numerical model.

A simple design relationship is derived for the filter ratio of a stable geometrically open filter in a bed protection, the filter ratio here being defined as the ratio between the diameters of two layers, one on top of the other. The relationship is based on the assumption that the largest hydraulic loading in a bed protection is related to the hydraulic loading on the top layer. The stability of the top layer and the underlying layer under hydraulic loading is estimated using a Shields type relationship. The hydraulic gradient in the filter is derived from the time‐average hydraulic gradient, taking into account pressure fluctuations which determine the gradient fluctuations. The equation derived is compared with the results of published experimental work. This shows that the smaller the material needed for a stable bed protection, the higher the permissible filter ratio. Application of this result may lead to one or two filter layers less than required with a geometrically tight designed bed protection.

Backward‐characteristics schemes for solution of the mass transport equation are inherently nonconservative when the advective velocity is variable, and they have difficulties at boundaries where mass flux conditions are imposed. Also, they generally produce over‐ and undershoots of the solution or are not accurate enough if a sharp front exists. To circumvent these shortcomings, higher‐order‐characteristics schemes based on a minimax criterion are developed. The finite‐difference expressions of these schemes are then modified to follow a flux‐transport form, and a flux limiter is added to the schemes. The resulting schemes are accurate in simulating mass transport in saturated‐unsaturated flow in which sharp fronts exist, the velocity is variable, and the flux boundary condition is imposed.