Hyporheic Exchange with Gravel Beds: Basic Hydrodynamic Interactions and Bedform-Induced Advective Flows

Stream-subsurface exchange processes are important because of their role in controlling the transport of contaminants and ecologically relevant substances in streams. Laboratory flume experiments were conducted to examine solute exchange with gravel streambeds. Two morphologies were studied: flat beds and beds covered by dune-shaped bedforms. High rates of exchange were observed with flat beds under a wide range of stream flow conditions, indicating that there was considerable turbulent coupling of stream and pore water flows. The presence of bedforms produced additional exchange under all flow conditions. The exchange with bedforms could be represented well by considering solute flux caused by bedform-induced advective pumping. Pumping exchange was enhanced by inertial effects, including non-Darcy flow and turbulent diffusion. For the flat bed case, dye injections showed that exchange also occurred by a combination of advective pore water flow and turbulent diffusion near the stream–subsurface interface. The relative effects of advective and diffusive transport processes could not be separated due to the complex nature of the induced flows in the gravel bed. However, exchange was found to scale with the square of the stream Reynolds number in all cases. Comparison of these results with those obtained with coarser and finer sediments demonstrated that the exchange rate is also proportional to the square of the characteristic bed sediment size. These scaling relationships can be used to improve interpretation of solute transport observed in natural rivers.     

Sediment Pickup on Streamwise Sloping Beds

This paper presents an experimental investigation on noncohesive sediment pickup under a unidirectional steady-uniform stream flow on streamwise steeply sloping (down slope and adverse) sedimentary beds. The characteristic parameters affecting the sediment pickup, identified based on the physical reasoning and dimensional analysis of the sediment particle movement under stream flow, are the transport-stage parameter, particle parameter, and geometric standard deviation of sediment particles. A large number of experiments (426 runs) were carried out in two long rectangular ducts (closed-conduit flow) with nine types of sediments (six uniform and three nonuniform sediments), having a variation of bed slope from ?15° (adverse slope) to 25° (down slope). In an open channel flow (laboratory flume study), the uniform flow is a difficult, if not impossible, proposition for a steeply sloping channel and is impossible to obtain in an adversely sloping channel. To avoid this problem, the tests were conducted with a closed-conduit flow. Measurements included flow discharge and sediment pickup rate. The bed shear stress for a particular run was computed considering side wall correction. The experimental data were used to determine the equation of sediment pickup function through a regression analysis. The equation is adequate to estimate sediment pickup not only on horizontal and mild slopes but also on steep and adverse slopes.     

Effect of Sand Supply on Transport Rates in a Gravel-Bed Channel

In a series of flume experiments using constant discharge, flow depth, and gravel feed rate, sand feed rates were varied from 0.16 to 6.1 times that of gravel. The bed slope decreased with increasing sand supply, indicating that the gravel could be transported at the same rate, along with increasing amounts of sand, at smaller shear stresses. Prediction of river response to an increase in sediment supply requires prediction of mutual changes in bed composition and transport, and therefore a transport model defined in terms of the grain size of the bed surface. A recent model provides satisfactory prediction of the experimental observations and indicates the general response of gravel beds to increased sand supply. An increase in sand supply may increase the sand content of the river bed and the mobility of gravel fractions, which can lead to bed degradation and preferential evacuation of these sediments from the river.     

Preventing Sediment Deposition in Inverted Sewer Siphons

Laboratory experiments were carried out to determine minimum self-cleansing velocities for preventing deposition of sediment in upward sloping and vertical pipes of inverted siphons. Tests were made using sediment sizes of 0.78 and 4.3 mm in a pipe of 150 mm diameter for eight angles of inclination between 0 and 90°. The criterion for self-cleansing conditions was defined as the minimum velocity needed to prevent the formation of deposits on the invert of the pipe. For a given sediment concentration the self-cleansing velocity was found to be a maximum at pipe slopes between about 22.5 and 45°. Analysis of the forces acting on sediment particles in inclined pipes led to the development of a formula for predicting self-cleansing velocities taking account of pipe size, sediment size, sediment concentration, and pipe slope.     

Numerical Model of Sediment Pulses and Sediment-Supply Disturbances in Mountain Rivers

Sediment pulses in rivers can result from many mechanisms including landslides entering from side slopes and debris flows entering from tributaries. Artificial sediment pulses can be caused by the removal of a dam. This paper presents a numerical model for the simulation of gravel bedload transport and sediment pulse evolution in mountain rivers. A combination of the backwater and quasi-normal flow formulations is used to calculate flow parameters. Gravel bedload transport is calculated with the surface-based bedload equation of Parker in 1990. The Exner equation of sediment continuity is used to express the mass balance at different grain size groups and lithologies, as well as the abrasion of gravel. The river is assumed to have no geological controls such as bedrock outcrops and immobile boulder pavements. The results of nine numerical experiments designed to study various key parameters relevant to the evolution of sediment pulses are reported here. Results of the numerical runs indicate that the evolution of sediment pulses in mountain rivers is dominated by dispersion rather than translation. Here dispersion is an expression for the observation that a sediment pulse aggrades both upstream and downstream of its apex whereas its amplitude decreases in time. The results also indicate that grain abrasion is an important and yet often neglected mechanism in removing the excess sediment associated with pulse inputs from some mountain rivers.     

Unified View of Sediment Transport by Currents and Waves. II: Suspended Transport

The problem of suspended sediment transport in river and coastal flows is addressed. High-quality field data of river and coastal flows have been selected and clustered into four particle size classes (60–100, 100–200, 200–400, and 400–600?μm). The suspended sand transport is found to be strongly dependent on particle size and on current velocity. The suspended sand transport in the coastal zone is found to be strongly dependent on the relative wave height (Hs/h), particularly for current velocities in the range 0.2–0.5?m/s. The time-averaged (over the wave period) advection–diffusion equation is applied to compute the time-averaged sand concentration profile for combined current and wave conditions. Flocculation, hindered settling, and stratification effects are included by fairly simple expressions. The bed-shear stress is based on a new bed roughness predictor. The reference concentration function has been recalibrated using laboratory and field data for combined steady and oscillatory flow. The computed transport rates show reasonably good agreement (within a factor of 2) with measured values for velocities in the range of 0.6–1.8?m/s and sediments in the range of 60–600?μm. The proposed method underpredicts in the low-velocity range (<0.6?m/s). A new simplified transport formula is presented, which can be used to obtain a quick estimate of suspended transport. The modeling of wash load transport in river flow based on the energy concept of Bagnold shows that an extremely large amount of very fine sediment (clay and very fine silt) can be transported by the flow.     

Numerical Modeling of Abutment Scour with the Focus on the Incipient Motion on Sloping Beds

A three-dimensional computational fluid dynamics model is applied to predict local scour around an abutment in a rectangular laboratory flume. When modeling local scour, steep bed slopes up to the angle of repose occur. To predict the depth and the shape of the local scour correctly, the reduction of the critical shear stress due to the sloping bed must be taken into account. The focus of this study is to investigate different formulas for the threshold of noncohesive sediment motion on sloping beds. Some formulas only take the transversal angle (perpendicular to the flow direction) into account, but others also consider the longitudinal angle (streamwise direction). The numerical model solves the transient Reynolds-averaged Navier-Stokes equations in all three dimensions to compute the water flow. Sediment continuity in combination with an empirical formula is used to capture the bed load transport and the resulting bed changes. When the sloping bed exceeds the angle of repose, the bed slope is corrected with a sand-slide algorithm. The results from the numerical simulations are compared with data from physical experiments. The reduction of the bed shear stress on the sloping bed improves the results of the numerical simulation distinctly. The best results are obtained with the formulas that use both the transversal and the longitudinal angle for the reduction of the critical bed shear stress.     

Sediment Transport in River Models with Overbank Flows

Some laboratory sediment-transport experiments are described in which a compound channel with a mobile-bed composed of uniform sand with a d50 of 0.88?mm was subjected to overbank flows. The main river channel was monitored to determine the effect of floodplain roughness on conveyance capacity, bed-form geometry, resistance, bed-load transport, and dune migration rate. The floodplain roughness was varied to simulate a wide range of conditions, commensurate with conditions that can occur in a natural river. For a given discharge, the main river channel bed was found to adjust itself to a quasi-equilibrium condition governed by the lateral momentum transfer between the floodplain and main channel flows and the local alluvial resistance relationship appropriate for the proportion of total flow in the main river channel. The sediment transport rate was found to reflect all these influences. The data are summarized in equation form for comparison with other experimental studies and for checking numerical river simulation models.     

Turbulence and Secondary Flow over Sediment Stripes in Weakly Bimodal Bed Material

Longitudinal stripes are a common bed form in heterogeneous alluvial sediments and consist of periodic, spanwise variations in bed texture and elevation that are aligned parallel to the mean flow direction. This paper quantifies mean and turbulent flow structures over self-formed sediment stripes in a weakly bimodal sand and gravel mixture. Turbulence anisotropy generates two secondary circulation cells across the channel half-width, which produce a cross-stream perturbation in boundary shear stress. The interaction between this flow structure and the selective transport of bed material generates spanwise sediment sorting that is symmetrical about the centerline. Finer sediments are entrained from regions of high shear stress, transported laterally by the secondary flow, and deposited in regions of lower shear stress. Lateral changes in bed texture further enhance the near-bed secondary flow, which provides a positive feedback mechanism for stripe growth. In bimodal sediments, at shear stresses just above the entrainment threshold, stripes may replace lower-stage plane beds. At higher shear stresses the coarser sediment becomes more mobile and the stripes are replaced by flow transverse bed forms.     

Pollution of Gravel Spawning Grounds by Deposition of Suspended Sediment

Observations have shown that accumulation of fine sediment in the pores of spawning open-work gravel have a detrimental effect on stream biota. The rate of deposition is intimately linked to the concentration of suspended fines near the gravel bed. If interstitial voids in coarse sediment deposits are filled or covered with sand or inorganic fine materials, their habitat value is greatly reduced. In this paper, a simple method is proposed to predict analytically the concentration profile and transport of fine suspended sediment when a steady, uniform suspension flows from a sediment-covered bed to an open-work gravel bed. Comparisons of the analytical model predictions with previous laboratory observations show reasonable agreement. The proposed solution can be used to estimate “clarification distances” for streams carrying fine sediments over open-work gravel beds.     

Shields’ Entrainment Criterion in Bridge Hydraulics

Two related problems of sediment hydraulics are addressed: (1) Inception of sediment transport for nearly uniform flow of both uniform and nonuniform sediment beds for two different sediment densities and grain sizes ranging from sand to gravel, and (2) generalized inception conditions if elements are inserted in a plane sediment bed. The Shields’ criterion is formulated with basic quantities involving gravity, viscosity, and densities of the two-phase flow. The results of the analysis relate to the viscous, the transition, and the fully turbulent regimes. The transition regime is verified with extended laboratory experiments. Then, these conditions are used as a basis for formulating a general stability criterion for loose bed hydraulics, and compared to detailed experiments involving pier and square elements located either at the channel side or at its axis. In addition, a generalized densimetric particle Froude number is introduced that accounts for both uniform sediments and mixtures. The engineering application of the present results is straightforward, given that basic parameters of hydraulics, sediment, and fluid are involved.     

Bed-Load Transport Equation for Sheet Flow

When open-channel flows become sufficiently powerful, the mode of bed-load transport changes from saltation to sheet flow. Where there is no suspended sediment, sheet flow consists of a layer of colliding grains whose basal concentration approaches that of the stationary bed. These collisions give rise to a dispersive stress that acts normal to the bed and supports the bed load. An equation for predicting the rate of bed-load transport in sheet flow is developed from an analysis of 55 flume and closed conduit experiments. The equation is ib = ω where ib = immersed bed-load transport rate; and ω = flow power. That ib = ω implies that eb = tan?α = ub/u, where eb = Bagnold’s bed-load transport efficiency; ub = mean grain velocity in the sheet-flow layer; and tan?α = dynamic internal friction coefficient. Given that tan?α ≈ 0.6 for natural sand, ub ≈ 0.6u, and eb ≈ 0.6. This finding is confirmed by an independent analysis of the experimental data. The value of 0.60 for eb is much larger than the value of 0.12 calculated by Bagnold, indicating that sheet flow is a much more efficient mode of bed-load transport than previously thought.     

Influence of Coherent Flow Structures on the Dynamics of Suspended Sediment Transport in Open-Channel Flow

The influence of suspended sediments on coherent flow structures has been studied by simultaneously measuring the longitudinal and vertical components of the instantaneous velocity vector and the instantaneous suspended particle concentration with an acoustic particle flux profiler. The measurements were carried out in clear water and in particle-laden open-channel flows. In both cases, they clearly show the predominance of ejection and sweep phases that are part of a burst cycle. The analysis further demonstrates the importance of the ejection and sweep phases in sediment resuspension and transport. Ejections pick up the sediment at the bed and carry it up through the water column close to the surface. It is shown that ejections and sweeps are in near equality in the near-bottom layer, whereas ejections clearly dominate in the remaining water column. The implications of these results for sediment transport dynamics are discussed.     

Closed-Conduit Bed-Form Initiation and Development

Nonintrusive measurement of closed-conduit erodible-bed development was undertaken for 12 experiments of ranges of flow strengths and sediment (solids) sizes. Analogous to open-channel flows, wavelets on the sediment bed of a closed-conduit are instigated by discontinuities in the bed, with wavelet lengths λ for laminar and turbulent open-channel and closed-conduit flows given by λ = 175d0.75, where λ and sediment size d are in millimeters. For closed-conduit flows, ripples, and dunes grow from these wavelets (at rates increasing with increasing flow strength, and utilizing the mechanisms of bed-form coalescence and throughpassing) to limiting lengths, heights, steepnesses, and bed friction factors that are approximately maintained or possibly decrease thereafter. Limitation of free-surface deformation results in increased rates of bed-wave development for closed-conduit flows in comparison to open-channel flows. Measured results indicate that equilibrium closed-conduit ripple and dune magnitudes can be predicted using relations derived for equivalent open-channel flows. The present findings are of particular relevance for understanding and modeling engineering activities ranging from dredging to transport of solids in stormwater and sewer systems, bed-form transport of solids in closed conduits influencing (potentially markedly) conduit conveyance, rate of solids transport, and system head losses for such flows.     

Near-Bed Sediment Concentration Distribution and Basic Probability of Sediment Movement

Sediment concentration distribution and the basic probability of sediment movement near the channel bed are two of the most important and fundamental issues in the study of sediments. Based on statistical analysis and considering the transport mechanisms, the rules of sediment concentration distribution near a channel bed are studied. Analytical expressions for the near-bed sediment concentration distribution and mean sediment concentration are derived, and the expression for the mean sediment concentration near the bed is verified by measured data, which were obtained from previous experiments. With the help of statistical theory, the expressions of basic probabilities, i.e., rolling, saltating, and suspending probabilities, for sediment movement near the bed are also derived. The expression for starting probability is verified by the measured data. The verification shows that the results from the proposed expression agree well with the measured data. This research has both theoretical and practical significance for further investigation concerning rules of bed load and suspended sediment transport.     

Validation of Existing Bed Load Transport Formulas Using In-Sewer Sediment

Granular sediment in pipe inverts has been reported in a number of sewer systems in Europe. Given the range of flow conditions and particle characteristics of inorganic sewer sediments the mode of transport may normally be considered as bed load. Current commercial software for modeling the erosion and transport of sediments in sewer pipes still utilizes well-known, or modified versions of transport equations that were derived for transport of noncohesive sediment in alluvial streams. In this paper the performances of the equations of Ackers and White (originally developed for the transport of river sediments) and of May (derived from laboratory pipe experiments) are examined against two separate data sets. One set is from laboratory erosion experiments on sewer sediment obtained in Paris. A second data set has bed load transport rate measurements recorded in a sewer inlet pipe. The formulas were selected because of their widespread use in the prediction of in-sewer sediment transport both in commercial software and in the latest United Kingdom design guidance for new sewers. The results indicated that both the relationships performed poorly, even in such well-controlled conditions. These formulas have significant difficulties in predicting the erosion thresholds and fractional transport rates for non-uniformly sized in-sewer sediments. An empirical formula to adjust the threshold of motion for individual grain size fractions was developed which significantly improved predictions. Although such techniques have been used in gravel bed rivers, the threshold adjustment function for in-sewer deposits was significantly different from these previously published for fluvial gravels, indicating that a direct transfer of fluvial relationships to sewers may be inappropriate without further research.     

Energy Dissipation and Air Entrainment in Stepped Storm Waterway: Experimental Study

For the last three decades, research focused on steep stepped chutes. Few studies considered flat-slope stepped geometries such as stepped storm waterways or culverts. In this study, experiments were conducted in a large, flat stepped chute (θ=3.4°) based upon a Froude similitude. Three basic flow regimes were observed: nappe flow without hydraulic jump, transition flow, and skimming flow. Detailed air–water flow measurements were conducted. The results allow a complete characterization of the air concentration and bubble count rate distributions, as well as an accurate estimate of the rate of energy dissipation. The flow resistance, expressed in terms of a modified friction slope, was found to be about 2.5 times greater than in smooth-chute flow. A comparison between smooth- and stepped-invert flows shows that greater aeration and larger residence times take place in the latter geometry. The result confirms the air–water mass transfer potential of stepped cascades, even for flat slopes (θ<5°).