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Local scour processes can be divided into initial, progressing, and equilibrium stages. Due to its short duration and high scour rate, the initial stage has not been well investigated to date. By applying laser-based technique and particle image velocimetry, this study conducted a series of measurements of scour hole profile and flow field at the beginning of scour hole development for the case of plane jet–induced scour. The results show that the scouring process in the initial stage is dominated by the wall shear, and thus can be classified as shear scour, whereas that in the progressing stage largely is affected by the turbulent vortex, and therefore can be referred to as vortex scour. The two modes of scour could be characterized by different mechanisms of sediment erosion. A bedload model is proposed to analyze the sediment transport for the shear scour, and the results agreed well with the experimental data. [ABSTRACT FROM AUTHOR]

The article "Closure to 'Mixed Velocity Scale for Predicting Bed-Material Sediment Discharges in Open Channel Flows'" by Nian-Sheng Cheng, Keqi Zheng, and Chengxiao Lu discusses the relationship between sediment discharge and bedform dimensions in open channel flows. The authors highlight the importance of understanding shear stress partitioning in predicting sediment discharge accurately. They suggest that while sediment discharge and bed morphology are interconnected, predicting sediment discharge may not necessarily require shear stress partitioning. This research provides valuable insights into the complexities of sediment transport in open channel flows. [Extracted from the article]

This note concerns variations of the friction factor in the two transitional regimes, one between laminar and turbulent flows and the other between fully smooth and fully rough turbulent flows. An interpolation approach is developed to derive a single explicit formula for computing the friction factor in all flow regimes. The results obtained for pipe flows give a better representation of Nikuradse's experimental data, in comparison with other implicit formulas available in the literature. Certain modifications are also made for applying the obtained friction formula to open-channel flows. DOI: 10.1061/(ASCE)0733-9429(2008) 134:9(1357) CE Database subject headings: Friction; Pipe flow; Open channel flow; Laminar flow: Turbulent flow; Reynolds number.

The critical condition for incipient sediment motion is formulated in this note based on the settling velocity. The formula obtained is simple, relating the ratio of critical shear velocity to settling velocity to the dimensionless sediment diameter. Comparisons are then made with other settling-velocity based formulas available in the literature. To facilitate the computation of the effective near-bed velocity at the threshold condition, a generalized law-of-the-wall function is proposed for predicting the velocity distribution under various boundary conditions. This study demonstrates that the settling velocity is equivalent to the critical near-bed velocity, which is experienced by a typical bed sediment particle under the threshold condition, but only for large sediment sizes such as sand and gravel. Comparison results show that Yang's formula is suitable for flows with small flow depth relative to sediment size while Le Roux's formula may overestimate the threshold condition for fine particles by up to 30%. DOI: 10.1061/(ASCE)0733-9429(2008)134:8(1136) CE Database subject headings: Velocity; Sediment transport; Comparative studies.

When investigating sediment transport in laboratory open-channel flows, it is often necessary to remove sidewall effects for computing effective bed shear stress. Previous sidewall correction methods are subject to some assumptions that have not been completely verified, and different values of the bed shear stress may be obtained depending on the approach used in making sidewall corrections. This study provides a quantitative assessment of the existing correction procedures by comparing them to a new sidewall correction model proposed in this study. The latter was derived based on the shear stress function and equivalent roughness size for both rigid and mobile bed conditions, which were obtained directly from experimental measurements. The comparisons show that the Einstein correction formula and the Vanoni and Brooks method generally predict relatively lower and higher bed shear stresses, respectively, while the Williams' empirical function leads to more scatter. This study also demonstrates that the widely used Vanoni and Brooks approach can be well approximated by a simple formula derived based on the Blasius resistance function. The sidewall effects, when removed in the different ways, would consequently affect the presentation of the bedload function. Experimental results of bedload transport, when plotted as the dimensionless transport rate against the dimensionless shear stress with the latter being corrected using the present model, exhibit less scatter than those associated with the previous procedures. CE Database subject headings: Shear stress; Open channel flow: Channel beds: Laboratory tests.

Laboratory experiments have recently confirmed that the streamwise particle velocity is largely less than that of the fluid in sediment-laden flows. This velocity lag is investigated analytically in the present study based on the drag force exerting on a particle in the presence of other neighbors. The normalized drag force or the hindrance coefficient is found generally dependent on the particle concentration, particle Reynolds number, and specific gravity. The velocity lag is then derived by relating the hindrance coefficient to the shear stress distribution for uniform sediment-laden open channel flows. The analysis shows that the profile of the velocity lag, when normalized by the shear velocity, is associated with the shear Reynolds number, dimensionless particle diameter, and specific gravity. For the dilute condition, the velocity lag distribution varies only with the shear Reynolds number, and the lag can be ignored if the shear Reynolds number is less than unity. The theoretical predictions are comparable to limited experimental results. CE Database subject headings: Suspended sediments; Velocity profile; Two phase flow; Open channels; Interactions.

An exponential formula that does not involve the concept of the critical shear stress is derived in this study for computing bedload transport rates. The formula represents well various experimental data sets ranging from the weak transport to high shear conditions. Comparisons of the present study are also made with many previous bedload formulas commonly cited in the literature. CE Database keywords: Bed load; Sediment transport; Transport rate; Shear stress.

A theoretical analysis of the initiation of sediment suspension is performed based on the concept of probability of suspension. The proposed condition for the initiation of sediment suspension from the top of the bed-load layer is comparable with most existing empirical relationships for large particle Reynolds numbers. The study shows that a constant Rouse parameter can be used as the critical condition for sediment suspension only for large dimensionless particle diameters. When the probability of suspension is taken to be an infinitesimal value (P = [10.sup.-7]), the derived relationship of the Shields parameter and the particle Reynolds number is in good agreement with the updated Shields diagram.

A modified logarithmic law is derived to describe the velocity distribution in open-channel flow with an upward seepage. The derived function agrees well with the experimental measurements conducted in a laboratory flume. The roughness function included in the modified logarithmic law is found to be dependent on the boundary Reynolds number and the ratio of the seepage velocity to the shear velocity. With the integration of the modified logarithmic law, the bed-shear stress subjected to upward seepage can be computed based on the depth-averaged velocity, water depth, boundary roughness, and seepage velocity. Using this method, variations of the bed-shear stress over the seepage zone are studied. The results show that the bed-shear stress decreases rapidly from the leading section of the seepage zone and then increases gradually toward the downstream end of the seepage zone.

A semi-empirical analysis on the time-averaged equilibrium live-bed scour at an abutment, placed perpendicular to the flow direction, is presented. The approach is based on the flow and sediment mass continuity equations, scour geometry, flow resistance, and a generalized bed-load transport relation in an alluvial channel. The proposed equation can be reduced to the equilibrium clear-water scour equation proposed earlier by the first writer (Lim). A total of 111 live-bed scour data from various sources were analyzed and compared with the developed equation. The agreement between the computed and measured data is acceptable.

The drag coefficient for dispersed particles settling in a fluid is related to the particle Reynolds number with the same function as that used for a single particle falling in a clear fluid, after taking into account the effects of concentration both on the effective density of particles and on the viscosity of fluid-sediment mixture. A new method is developed for evaluating the settling velocity of natural sediment particles dispersed in a fluid; it agrees well with the available experimental data. The differences among various empirical expressions are illustrated using the present relationship.

A new and simplified formula for predicting the settling velocity of natural sediment particles is developed. The formula proposes an explicit relationship between the particle Reynolds number and a dimensionless particle parameter. It is applicable to a wide range of Reynolds numbers from the Stokes flow to the turbulent regime. The proposed formula has the highest degree of prediction accuracy when compared with other published formulas. It also agrees well with the widely used diagrams and tables proposed by the U.S. Inter-Agency Committee in 1957.

Turbulence generated by a vertically oscillating grid in a water tank was investigated using the digital particle image velocimetry technique. The statistical turbulence characteristics computed based on the experimental data agree well with the two main findings reported in the literature: (1) The turbulence decays following the power law; and (2) the integral length scale increases linearly with the distance from the grid. In addition, the flow structure near the grid was observed in detail with the advantage of the planar measurements. It was found that the velocity fluctuations in the region near the grid vary depending on the grid geometry. The fluctuations immediately over the bar position are significantly different from those over the grid openings. Turbulence with the highest intensity occurs above the intersection of the square bars that constitute the grid. The results imply that shear flow clearly exists near the grid and homogeneity of the turbulence can only be achieved at a distance from the grid greater than about three mesh sizes. In addition, it was found that at least 400 vector maps should be taken to ensure the accuracy of the measured velocity fluctuations.

Presents contradicting and opposing views on a study about a simplified explicit formula for the terminal velocity of a natural sediment particle in an otherwise quiescent fluid. Diameter of natural sediment particle; Shape factor of natural sediment formula; Accuracy of the proposed formula.