Journal of Hydraulic Engineering

When a stone/armor layer on a sand bed is exposed to flow, the sand underneath will be agitated by the flow turbulence. When the flow velocity reaches a critical value, the sand will be sucked (winnowed out) from between the armor blocks. In a previous investigation, we studied suction removal of sediment in steady currents. The present study is an extension of our previous investigation to waves. The critical condition for the onset of suction is determined. It is found that the onset of suction is governed by three parameters: (1) the sediment mobility number (based on the sediment size); (2) the ratio of sediment size to stone size, $d∕D$ ; and (3) the Keulegan-Carpenter (KC) number, based on the armor block/stone size. The variation of the critical mobility number for suction as a function of $d∕D$ and KC is determined for the ranges of the parameters $0.001<d∕D⩽1$ and $1<\mathrm{KC}<50$ . The case of steady current is included as a reference case. The effect of waves superimposed on current, the effect of a multilayer stone cover, and the effect of regularly placed armor blocks are investigated. Suction of the base-bottom sediment will cause sinking of the armor layer and, therefore, general lowering of the bed. The time scale of the latter process and the downward displacement of armor blocks/stones are also investigated.

A theoretical model is developed to describe the process of fine sediment infiltration into immobile coarse sediment deposits. The governing equations are derived from mass conservation and the assumption that the amount of fine sediment deposition per unit vertical travel distance into the deposit is either constant or increases with increasing fine sediment fraction. Model results demonstrate that fine sediment accumulation decreases rapidly with depth into coarse substrate initially void of fine sediment, which is consistent with experimental observations that significant fine sediment infiltration occurs to only a shallow depth. Comparisons of the theory with flume data indicate that the model adequately reproduced the weighted-averaged fine sediment fraction values from experiments. An early model developed by Sakthivadivel and Einstein for fine sediment infiltration is in part based on the generally incorrect assumption that intragravel flow remains constant following fine sediment infiltration. Applying a correction to the Sakthivadivel and Einstein model based on alternate hypothesis that introgravel flow is driven by a constant head gives similar results as the proposed model.

This study investigates the applicability of five bed-load-transport formulas (the Meyer-Peter and Müller, Schoklitsch, Bagnold, Smart and Jaeggi, and Rickenmann equations) to predict bed-load transport rates of frequent, low-magnitude flood events (maximal bankfull discharge) for a mountainous, poorly sorted gravel-bed river characterized by a bimodal sediment-size distribution and spatially distributed patches. For model parametrization, special emphasis was placed on the spatial composition of the grain-size distribution (GSD) to evaluate the impact of preferential removal of sediments from patches with finer sediments on bed-load transport. Three parametrization approaches to the choice of an appropriate sediment size that considered the apparent bimodality of the GSD to varying degrees were tested. The modeling study demonstrated that the incorporation of spatial structure of GSD and its bimodal character has an important impact on model performance—a unimodal parametrization failed to reproduce measured bed-load rates for all tested bed-load formulas; a threshold parametrization approach that considered only finer sediments from the small patches as bed-load source material in combination with the Schoklitsch, Smart and Jaeggi, and Rickenmann equations yielded the best results, whereas the Meyer-Peter and Müller and the Bagnold equations failed to predict bed-load rates for all parametrization approaches. The modeling study thus showed that bed-load formulas are sensitive to the spatial structure of the GSD, which should not be treated as a continuum of sediment size fractions but rather as composition of finer sediment patches to enable an adequate reproduction of measured bed-load data from low-magnitude floods in gravel-bed rivers.

Standard bed-load sediment-transport formulas are extended using basic mechanical principles to include gravitational influence on large slopes of arbitrary orientation. The resulting sediment fluxes are then incorporated into a morphodynamics model in a general-purpose, three-dimensional, finite-volume, Reynolds-averaged Navier–Stokes (RANS) code. Major features are: (1) the downslope component of weight is combined with the fluid stress to form an effective bed stress (similar to the work of Wu in 2004); (2) the critical effective stress is reduced in proportion to the component of gravity normal to the slope; (3) a simple flux-based model for avalanching is implemented as a numerical means of preventing the local slope from exceeding the angle of repose; (4) an entirely vectorial formulation of bed-load transport is developed to account for arbitrary surface orientation; and (5) methods for reducing numerical instability in the morphodynamics equation are described. Sample computations are shown for scour and accretion in a channel bend and for the movement of sand mounds on erodible and nonerodible bases.

Local scour below a piggyback pipeline in steady currents is investigated numerically. A piggyback pipeline comprises two pipelines that are arranged in the so-called piggyback configuration with the small pipeline being located directly above the large pipeline. The Reynolds-averaged Navier–Stokes equations and the transport equation for suspended sediment concentration are solved using a finite element method. The bed scour profile is determined through solving sediment mass conservation equation. The numerical model is validated against experimental data available in literature on scour below a single pipeline. Computations are carried out for the diameter ratio [the small pipe diameter $\left(d\right)$ to the larger one $\left(D\right)$ ] of 0.2 and the gap ( $G$ , between the two pipelines) to the large diameter ratio $G∕D$ ranging from 0.0 to 0.5. It is found that the flow and the scour profiles are influenced significantly by the gap ratio.

Wind sheltering can have a strong effect in small, sheltered water bodies; wind-induced mixing in the surface layer of a small mine lake has been investigated using field measurements. Wind speed was recorded at three locations and data suggested sheltering by topography and surface roughness changes with both fetch and the land–water transition. Wind sheltering effects in the near-surface waters were assessed using turbulent microstructure profiler measurements, providing an estimate of the sheltering distance consistent with the literature on “backward-facing” steps. A numerical simulation of the annual density stratification cycle was then performed, using the model DYRESM. Simulations indicated that inclusion of a sheltering algorithm based on the results of the field campaign significantly improved the model’s performance in capturing the surface mixed layer deepening associated with strong wind events.

This paper presents and discusses a new static solver that implements the pseudotransient continuation method for the quasi-steady state analysis, or extended-period simulation of water distribution systems. The implementation is based on the concept of virtual tanks and has a clear physical meaning. The steady state solver described in this paper can analyze a pipe network under pressure deficient conditions and is free from some convergence problems that occur in the Newton-Raphson method-based solvers when analyzing a pipe network with control devices. The numerical examples considered in the paper demonstrate the convergence of the proposed method in cases where existing static solvers (e.g., that of the EPANET 2 hydraulic simulator) fail.

Analytical predictions of numerical errors in method of characteristics analyses using time-line interpolation in a rectangular grid are obtained for (1) both time-line and space-line interpolation and (2) both rectangular and diamond grids. Amplitude and frequency errors are investigated for each of these four cases using purpose-developed polynomial transfer matrices. Both semiinfinite and finite pipes are investigated. The time-line analysis permits reach back in time and the space-line analysis permits reach out in space. A common definition is adopted for the Courant number in the four cases and it is shown why stability can be achieved in reach-out analyses with Courant numbers greater than 1. In contrast with most work on error estimation, the predicted errors are obtained analytically, not numerically. This is made possible by restricting the analysis to special, but important, cases such as liquid-filled pipes in which the waves may be assumed to propagate at constant speed. Furthermore, the development is restricted to inviscid flows, thereby enabling interpolation errors to be assessed in the absence of complicating influences of discretization errors. In contrast with the latter, it is found that interpolation errors are more sensitive to the shape of numerical grids (i.e., Courant number and rectangular versus diamond grid) than to the size of the numerical time step.

A new methodology for the experimental analysis of the equilibrium scour depth at bridge piers is introduced and validated for clear-water conditions. The proposed experimental methodology determines the flow conditions for a given equilibrium scour instead of determining the equilibrium scour for given flow conditions, which is the usual practice. The basic hypothesis is that the shape of the scour hole is essentially related to the scour depth and sediment properties, but not to flow conditions. This hypothesis is checked experimentally. The proposed methodology may drastically reduce the time period required for experiments (from weeks to hours), and avoids the uncertainties due to the equilibrium scour being usually achieved asymptotically. Some preliminary results of the equilibrium scour obtained with the proposed methodology are compared to the expressions given in the literature, showing fair agreement.

The paper reports on an experimental investigation concerning two important issues: (1) local scour and (2) riprap stability at a 45° wing-wall abutment in a degrading river bed of noncohesive sediment. The abutment considered was short (that is abutment length/flow depth $<1$ ). From the experimental observations, no influence of abutment inclusion on bed degradation was evident, as bed profiles with and without abutment were quite identical apart from the immediate vicinity of the abutment. Total scour depth at an abutment is found to be the maximum abutment scour depth in addition to the reduction of bed elevation due to bed degradation. The maximum abutment scour depth can be estimated from the equation given by Kandasamy and Melville in their 1998 paper. For scouring time beyond $24\mathrm{h}$ , the local abutment scour depth remains independent of time. In a degrading bed, the bed forms cause edge failure of the riprap at an abutment when the dunes propagate over the riprap layer. Initially, the dune height is significant causing the maximum damage of riprap layer. As the flow velocity reduces, the resulting bed-shear stress diminishes with the degrading bed and gradually the formation of dunes ceases. An additional experiment reveals that the damaged riprap layer is significantly vulnerable against a subsequent flood accompanied by large dunes.

This paper analyzes the effect of flume test section length on sediment erodibility measurements. A modular flume was constructed and experiments were conducted with two test section lengths: $0.15$ and $1.10\mathrm{m}$ . The internal height and width of the flume were $0.11$ and $0.13\mathrm{m}$ , respectively. A fine $\left(7\mu \mathrm{m}\right)$ commercially available quartz sediment was used for the tests. The expectation was that the shorter flume test section would experience a significantly higher erosion rate (per unit surface area) due to its greater sensitivity to edge effects (i.e., scour) at the entrance and exit of the flume test section. However, the measured erosion rates at comparable bottom stresses were only 35% greater in the short test-section tests. These results were consistent with the lack of significant scour development at the entrance or exits of the test sections. Hence, flume test section length alone does not appear to significantly affect erodibility measurements provided edge effects (i.e., scour) are minor.

The purpose of this study is to evaluate the adequacy of the $100\text{-}\text{year}$ discharge along with the Froehlich bridge abutment scour equation adopted by the U.S. Federal Highway Administration (FHwA) in predicting abutment scour for bridge design purposes in South Carolina streams. The analysis utilized bridge properties, stream cross-sectional and hydraulic data, local flood frequency equations, a one-dimensional steady river flow computer model (WSPRO), and procedures recommended by the FHwA for predicting abutment scour. A method was developed to identify the single stream-discharge at each bridge that can cause the abutment scour that was observed at 73 bridge abutments. Analysis of the results revealed that for one-third of the abutments in the sandy soil region of South Carolina, the flow rates required to produce the observed scour depths had return periods greater than $100\text{years}$ . Although for bridges in the region dominated by clay soil, the return periods were significantly smaller than $100\text{years}$ .

Recent empirical and numerical evidence shows that the Basset force plays an important role in the description of acceleration of relatively small sediment particles moving close to solid boundaries. This force can make the numerical solution of the equations of motion computationally time and memory consuming. This technical note presents a two-stage methodology to deal with the difficulties associated with computing the Basset force. The Basset term is first approximated based on a semiderivative (fractional mathematics), and then the integration time is redefined in terms of appropriate flow and particle time scales, thus, avoiding unnecessary computations. Important savings in computational time are reported.

Coupling the Saint-Venant equations with the Exner equation a morphodynamic model is produced, which can be used to describe flow and bed evolution in natural rivers. The system of governing equations is hyperbolic and is expressed in nonconservative form. For this reason, fully primitive formulations of the model are often adopted for the solution, which however are known to incorrectly compute strength and celerity of shock waves (bores). In the present work a quasi-conservative formulation of the differential system is proposed, which aims at reducing these errors to a minimum. The performances of the model are assessed by comparison with primitive formulations applied to some schematic cases and with experimental observations obtained on a physical model of a river reach. Results are satisfactory and overcome predictions based on fully primitive formulations.

In the mid-Atlantic region of the United States, sediment loads from stream runoff generally change more rapidly in the rising limb than in the falling limb of a storm hydrograph. As a result, sediment load reaches its peak prior to flow peak, an observation known as clockwise hysteresis. This dynamic load–flow relationship is poorly reproduced by the existing multivariate linear regression models. This paper explores regressors that attempt to incorporate observed features in a statistical model and thus improve load estimates. These included inverse discharge and flow-change regressors. The load estimates using three regression models for eight rivers are compared, and recommended regression equations are proposed.

The energy loss of the vertical drop with subcritical flow in the upstream channel has been studied experimentally with a physical model of $0.20\mathrm{m}$ drop height. Experimental data were collected in a range where few data exist. Based on a similarity between a turbulent surface jet and the flow over the drop, a model is developed using the theories of the shear layer and fully developed surface jet to estimate the energy loss. The results were compared with previous and current experimental data and were found to agree well with the proposed model.