Volumetric displacement of flow depth by obstacles,and the determination of friction factors in shallow overland flows

Large roughness elements such as stones or plant stems (obstacles) influence the depth of overland flows in two ways. The first effect is a dynamic one, involving frictional retardation of the flow and associated reduction in flow speeds. The second influence is static, and arises from the upward volumetric displacement of flow depth because of the submerged volume of the obstacles. Depending upon the distribution of submerged obstacle volume with height above the soil surface, the proportion of the flow volume occupied (and so, the perturbation of flow depth arising from volumetric displacement) can vary irregularly or systematically with flow stage. Furthermore, the amount of volumetric displacement of flow depth would vary among surfaces carrying different cover fractions of identical obstacles. Consequently, estimates of the change in friction factors arising from the drag on flow traversing varying obstacle cover fractions are confounded with the parallel shift volumetric displacement. To understand the true frictional drag arising from obstacles, a correction must be made for the volumetric displacement. A method for making this correction is outlined. New laboratory experiments provide precise observations of depths and friction coefficients in laminar flows passing fields of regular obstacles. After making the proposed correction for volumetric displacement, increases of 40 to 75 per cent in the derived value of the Darcy–Weisbach friction factor, f, are found for an obstacle cover of 20 per cent. Many published studies of friction coefficients in shallow overland flows, such as those on stone‐covered dryland soils, involve larger obstacle cover fractions, and evidently involve the significant confounding effect of volumetric displacement. Copyright © 2002 John Wiley & Sons, Ltd.     

Mean and turbulent flow fields in a simulated ice‐covered channel with a gravel bed: some laboratory observations

Northern rivers experience freeze‐up over the winter, creating asymmetric under‐ice flows. Field and laboratory measurements of under‐ice flows typically exhibit flow asymmetry and its characteristics depend on the presence of roughness elements on the ice cover underside. In this study, flume experiments of flows under a simulated ice cover are presented. Open water conditions and simulated rough ice‐covered flows are discussed. Mean flow and turbulent flow statistics were obtained from an Acoustic Doppler Velocimeter (ADV) above a gravel‐bed surface. A central region of faster flow develops in the middle portion of the flow with the addition of a rough cover. The turbulent flow characteristics are unambiguously different when simulated ice covered conditions are used. Two distinct boundary layers (near the bed and in the vicinity of the ice cover, near the water surface) are clearly identified, each being characterized by high turbulent intensity levels. Detailed profile measurements of Reynolds stresses and turbulent kinetic energy indicate that the turbulence structure is strongly influenced by the presence of an ice cover and its roughness characteristics. In general, for y/d > 0·4 (where y is height above bed and d is local flow depth), the addition of cover and its roughening tends to generate higher turbulent kinetic energy values in comparison to open water flows and Reynolds stresses become increasingly negative due to increased turbulence levels in the vicinity of the rough ice cover. The high negative Reynolds stresses not only indicate high turbulence levels created by the rough ice cover but also coherent flow structures where quadrants one and three dominate. Copyright © 2012 John Wiley & Sons, Ltd.     

Sediment transport in high‐speed flows over a fixed bed: 1. Particle dynamics

Particle dynamics are investigated experimentally in supercritical high‐speed open channel flow over a fixed planar bed of low relative roughness height simulating flows in high‐gradient non‐alluvial mountain streams and hydraulic structures. Non‐dimensional equations were developed for transport mode, particle velocity, hop length and hop height accounting for a wide range of literature data encompassing sub‐ and supercritical flow conditions as well as planar and alluvial bed configurations. Particles were dominantly transported in saltation and particle trajectories on planar beds were rather flat and long compared with alluvial bed data due to (1) increased lift forces by spinning motion, (2) strongly downward directed secondary currents, and (3) a planar flume bed where variation in particle reflection and damping effects were minor. The analysis of particle saltation trajectories revealed that the rising and falling limbs were almost symmetrical contradicting alluvial bed data. Furthermore, no or negligible effect of particle size and shape on particle dynamics were found. Implications of experimental findings for mechanistic saltation‐abrasion models are briefly discussed. Copyright © 2017 John Wiley & Sons, Ltd.     

Numerical simulation of overbank processes in topographically complex floodplain environments

This article presents results from an investigation of the hydraulic characteristics of overbank flows on topographically‐complex natural river floodplains. A two‐dimensional hydraulic model that solves the depth‐averaged shallow water form of the Navier–Stokes equations is used to simulate an overbank flow event within a multiple channel reach of the River Culm, Devon, UK. Parameterization of channel and floodplain roughness by the model is evaluated using monitored records of main channel water level and point measurements of floodplain flow depth and unit discharge. Modelled inundation extents and sequences are assessed using maps of actual inundation patterns obtained using a Global Positioning System, observational evidence and ground photographs. Simulation results suggest a two‐phase model of flooding at the site, which seems likely to be representative of natural floodplains in general. Comparison of these results with previous research demonstrates the complexity of overbank flows on natural river floodplains and highlights the limitations of laboratory flumes as an analogue for these environments. Despite this complexity, frequency distributions of simulated depth, velocity and unit discharge data closely follow a simple gamma distribution model, and are described by a shape parameter (α) that exhibits clear systematic trends with changing discharge and floodplain roughness. Such statistical approaches have the potential to provide the basis for computationally efficient flood routing and overbank sedimentation models. Copyright © 2002 John Wiley & Sons, Ltd.     

INITIATION OF SEDIMENT MOTION IN LAMINAR OVERLAND FLOW

IINTRODUCTIONWhileriverflowsareusuallydeepandturbulent,overlandflowisextremelyshallowandcanbelaminar,transitionalandturbulent.Becauseoftheshallownessoftheflolw,overlandflowhydraulicsisgreatlyaffectedbysurfaceroughness,raindropimpact,andinthecaseoflaminarflow,flui(Iviscosity.Theinitiationofsedimentmovementinoverlandflowisthereforeexpectedtodifferfromthatinriverflows.InriverstUdies,bedshearStressgbhastraditionallybeenusedtocharacterizethecriticalflowconditionatwhichsedimentbeginstomove.At…     

Determining hydraulic resistance in gravel‐bed rivers from the dynamics of their water surfaces

Traditionally, approaches to account for the effect of the boundary roughness of a gravel‐bed river have used a grain‐size index of the bed surface as a surrogate for hydraulic resistance. The use of a single grain‐size does not take into account the spatial heterogeneity in the bed surface and how this heterogeneity imparts resistance on the flow, nor the way in which this relationship changes with variables such as flow stage. A new technique to remotely quantify hydraulic resistance is proposed. It is based on measuring the dynamics of a river's water surface and relating this to the actual hydraulic resistance created by a rough sediment boundary. The water surface dynamics are measured using a new acoustic technique, grazing angle sound propagation (GRASP). This proposed method to measure hydraulic resistance is based on a greater degree of physical reasoning, and this is discussed in the letter. By measuring acoustically the temporal dynamics of turbulent water surfaces over a water‐worked gravel bed in a laboratory flume, a dependency is demonstrated between the temporal variation in the reflected acoustic pressure and measured hydraulic resistance. It is shown that the standard deviation in acoustic pressure decreases with increasing hydraulic resistance. This is shown to apply for a range of relative submergences and bed slopes that are typical of gravel‐bed rivers. This remote sensing technique is both rapid and inexpensive, and has the potential to be applied to natural river channels and to other environmental turbulent flows, such as overland flows. A whole new class of low‐cost, remote and non‐intrusive instruments could be developed as a result and used in a wide range of hydraulic and hydrological applications. Copyright © 2006 John Wiley & Sons, Ltd.     

Modelling the effect of time‐dependent river dune evolution on bed roughness and stage

This paper presents an approach to incorporate time‐dependent dune evolution in the determination of bed roughness coefficients applied in hydraulic models. Dune roughness is calculated by using the process‐based dune evolution model of Paarlberg et al. ( 2009 ) and the empirical dune roughness predictor of Van Rijn ( 1984 ). The approach is illustrated by applying it to a river of simple geometry in the 1‐D hydraulic model SOBEK for two different flood wave shapes. Calculated dune heights clearly show a dependency on rate of change in discharge with time: dunes grow to larger heights for a flood wave with a smaller rate of change. Bed roughness coefficients computed using the new approach can be up to 10% higher than roughness coefficients based on calibration, with the largest differences at low flows. As a result of this larger bed roughness, computed water depths can be up to 15% larger at low flow. The new approach helps to reduce uncertainties in bed roughness coefficients of flow models, especially for river systems with strong variations in discharge with time. Copyright © 2010 John Wiley & Sons, Ltd.     

Experimental study on the influence of river flow confluences on the open channel stage–discharge relationship

ABSTRACT

Accurate assessment of stage–discharge relationships in open channel flows is important to the design and management of hydraulic structures and engineering. Flow junctions commonly occur at the confluence of natural rivers or streams. The effect of flow junctions on the stage–discharge relationship at mountain river confluences was found by measuring velocity fields and water levels in experimental models. The results show that the backwater and accumulation–separation at flow junctions affect the flow structures and patterns in the channel; also, flow confluences may induce complex flow characteristics of backwater and flow separation at river junctions, indicating potential submerged flooding disasters within the confluence zone. The impacts of flow junctions on the stage–discharge relationship are investigated for two physical confluence models built from river confluence prototype systems in southwest China. The results show that the presence of tributary river inflows tends to increase the water level of the main river. This is important for flood control, flood-risk evaluation and engineering (e.g. hydropower station construction) in mountain rivers. Finally, a comparative quantitative analysis based on flow motion equations is conducted to evaluate the stage–discharge relationship in both uniform and regular confluence systems. The results indicate that more accurate prediction can be made when taking into account the flow non-uniformity induced by flow separation, backwater and distorted bed in the junction region.     

Terrestrial laser scanning soil surfaces: a field methodology to examine soil surface roughness and overland flow hydraulics

Conventional roughness–resistance relationships developed for pipe and open‐channel flows cannot accurately describe shallow overland flows over natural rough surfaces. This paper develops a new field methodology combining terrestrial laser scanning (TLS) and overland flow simulation to provide a high‐resolution dataset of surface roughness and overland flow hydraulics as simulated on natural bare soil surfaces. This method permits a close examination of the factors controlling flow velocity and a re‐evaluation of the relationship between surface roughness and flow resistance. The aggregate effect of flow dynamics, infiltration and depression storage on retarding the passage of water over a surface is important where runoff‐generating areas are distant from well‐defined channels. Experiments to separate these effects show that this ‘effective resistance’ is dominated by surface roughness. Eight measurements of surface roughness are found to be related to flow resistance: standard deviation of elevations, inundation ratio, pit density (measured both perpendicular and parallel to the flow direction), slope, median depth, skewness of the depth distribution and frontal area. Hillslope position is found to affect the significant roughness measures. In contrast, infiltration rate has little effect on the velocity of water fronts advancing over the soil surfaces examined here and the effect of depression storage is limited. Overland flow resistance is depth dependent where complex microtopographic structures are progressively inundated. Copyright © 2010 John Wiley & Sons, Ltd.     

Improvement of surface run‐off in the hydrological model ParFlow by a scale‐consistent river parameterization

We propose an improvement of the overland‐flow parameterization in a distributed hydrological model, which uses a constant horizontal grid resolution and employs the kinematic wave approximation for both hillslope and river channel flow. The standard parameterization lacks any channel flow characteristics for rivers, which results in reduced river flow velocities for streams narrower than the horizontal grid resolution. Moreover, the surface areas, through which these wider model rivers may exchange water with the subsurface, are larger than the real river channels potentially leading to unrealistic vertical flows. We propose an approximation of the subscale channel flow by scaling Manning's roughness in the kinematic wave formulation via a relationship between river width and grid cell size, following a simplified version of the Barré de Saint‐Venant equations (Manning–Strickler equations). The too large exchange areas between model rivers and the subsurface are compensated by a grid resolution‐dependent scaling of the infiltration/exfiltration rate across river beds. We test both scaling approaches in the integrated hydrological model ParFlow. An empirical relation is used for estimating the true river width from the mean annual discharge. Our simulations show that the scaling of the roughness coefficient and the hydraulic conductivity effectively corrects overland flow velocities calculated on the coarse grid leading to a better representation of flood waves in the river channels.     

Turbulence characteristics of flows passing through a tetrahedron frame in a smooth open-channel

The turbulence characteristics of flows passing through a tetrahedron frame were investigated by using a 2-dimensional fiber-optic laser Doppler velocimeter (2-D FLDV). Experiments for uniform flows with different bed slopes under both submerged and un-submerged conditions were carried out in a re-circulating flume with glass side walls. The experimental bed was a smooth fixed bed. It was observed that with the tetrahedron frame the mean longitudinal velocity decrease in the retardation zone. However, both the longitudinal and the vertical turbulence intensities are larger than those for the undisturbed approach flow. The tetrahedron frame may reduce the probability of sediment entrainment by retarding the flow and reducing the boundary shear stress. In addition, it may induce sediment deposition in a sediment laden flow by changing the flow direction and increasing the energy dissipation.     

Velocities of shallow overland flow on semiarid hillslopes

A series of 188 rainfall plot simulations was conducted on grass, shrub, oak savanna, and juniper sites in Arizona and Nevada. A total of 897 flow velocity measurements were obtained on 3.6% to 39.6% slopes with values ranging from 0.007 m s^‐1 to 0.115 m s^‐1. The experimental data showed that shallow flow velocity on rangelands was related to discharge and ground litter cover and was largely independent of slope gradient or soil characteristics. A power model was proposed to express this relationship. These findings support the slope–velocity equilibrium hypothesis. Namely, eroding soil surfaces evolve such that steeper areas develop greater hydraulic roughness. As a result overland flow velocity becomes independent of the slope gradient over time. Our findings have implications for soil erosion modeling suggesting that hydraulic friction is a dynamic, slope and discharge dependent property. Copyright © 2018 John Wiley & Sons, Ltd.     

Numerical modelling of aeolian erosion over a surface with non‐uniformly distributed roughness elements

The present study is focused on the analysis of the mean wall friction velocity on a surface including roughness elements exposed to a turbulent boundary layer. These roughness elements represent non‐erodible particles over an erodible surface of an agglomeration of granular material on industrial sites. A first study has proposed a formulation that describes the evolution of the friction velocity as a function of geometrical parameters and cover rate with different uniform roughness distributions. The present simulations deal with non‐uniform distributions of particles with a random sampling of diameters, heights, positions and arrangements. The evolution (relative to geometrical parameters of the roughness elements) of the friction velocity for several non‐uniform distributions of roughness elements was analysed by the equation proposed in the literature and compared to the results obtained with the numerical simulations. This comparison showed very good agreement. Thus, the formulation developed for uniform particles was found also to be valid for a larger spectrum of particles noted on industrial sites. The present work aims also to investigate in detail the fluid mechanics over several roughness particles. Copyright © 2013 John Wiley & Sons, Ltd.     

Predicting sediment transport by interrill overland flow on rough surfaces

Modelling soil erosion requires an equation for predicting the sediment transport capacity by interrill overland flow on rough surfaces. The conventional practice of partitioning total shear stress into grain and form shear stress and predicting transport capacity using grain shear stress lacks rigour and is prone to underestimation. This study therefore explores the possibility that inasmuch as surface roughness affects flow hydraulic variables which, in turn, determine transport capacity, there may be one or more hydraulic variables which capture the effect of surface roughness on transport capacity suffciently well for good predictions of transport capacity to be achieved from data on these variables alone. To investigate this possibility, regression analyses were performed on data from 1506 flume experiments in which discharge, slope, water temperature, rainfall intensity, and roughness size, shape and concentration were varied. The analyses reveal that 89·8 per cent of the variance in transport capacity can be accounted for by excess flow power and flow depth. Including roughness size and concentration in the regression improves that explained variance by only 3·5 per cent. Evidently, flow depth, when used in combination with excess flow power, largely captures the effect of surface roughness on transport capacity. This finding promises to simplify greatly the task of developing a general sediment equation for interrill overland flow on rough surfaces. Copyright © 1998 John Wiley & Sons, Ltd.     

Hydrodynamic characteristics of rill flow on steep slopes

Rill erosion is a dominant sediment source on sloping lands. However, the amount of soil loss from rills on steep slopes is vastly more than that on gentle slopes because of differences in rill shape and hydraulic patterns. The aims of this paper are to determine the hydrodynamic characteristics of rills and the friction coefficients in steep slope conditions and to propose modifications of some hydraulic parameters used in soil loss prediction models. A series of inflow experiments was conducted on loess slopes. The results show that the geometric and hydraulic properties of rill on the steep loess slopes, which are characterized by the mean width of cross sections, mean velocity and mean depth of flow, are related to discharge and slope gradient in power functions. However, the related exponents to discharge are 0.26, 0.48 and 0.26, respectively, which are different from the exponents derived in previous studies, which were conducted on gentle slopes. The Manning roughness coefficient ranged from 0.035 to 0.071, with an average of 0.0536, and the Darcy–Weisbach friction coefficients varied from 0.4 to 1.9. The roughness coefficients are closely related to the Reynolds numbers and flow volumes; however, the correlations vary with slope gradient. The roughness coefficients are directly proportional to the Reynolds number and the flow volume on steep slopes, in contrast with the roughness coefficients found on gentle slopes, which decrease as the Reynolds number and flow volume increase. This difference is caused by the interactions among the hydraulics of the flow, the shape of the rills and the sediment concentrations on steep slopes. The results indicate that parameters used in models to predict rill erosion have to be modified according to slope gradient. Copyright © 2015 John Wiley & Sons, Ltd.     

CORRECTION FACTORS IN THE DETERMINATION OF MEAN VELOCITY OF OVERLAND FLOW

The velocity of overland flow has been conventionally measured using tracers, but it is difficult to measure the mean flow velocity directly because the centroid of the tracer plume is not easily identified. Consequently, previous investigators have measured the velocity of the leading edge of the plume and multiplied it by a correction factor α to obtain an estimate of mean velocity. An alternative method is to measure the velocity of the peak concentration in the tracer plume and multiply this velocity by another correction factor β to estimate mean velocity. To investigate the controls of α and β and develop predictive models for these correction factors, 40 experiments were performed in a flume with a mobile sand bed. Multiple regression analyses reveal that both α and β vary inversely with slope and directly with Reynolds number. The derived regression equations may be used to calculate the mean velocity of other shallow overland flows, at least within the range of slope and Reynolds number for which the equations were developed. In the experiments, slope ranged from 2.7;° to 10° and Reynolds number from 1900 to 12 600.     

Hydraulics of interrill overland flow on rough,bare soil surfaces

A set of laboratory experiments on bare, rough soil surfaces was carried out to study the relationship between soil surface roughness and its hydraulic resistance. Existing models relating roughness coefficients to a measure of surface roughness did not predict the hydraulic resistance well for these surfaces. Therefore, a new model is developed to predict the hydraulic resistance of the surface, based on detailed surface roughness data. Roughness profiles perpendicular to the flow are used to calculate the wet cross‐sectional area and hydraulic radius given a certain water level. The algorithm of Savat is then applied to calculate the hydraulic resistance. The value for the equivalent roughness, which is used in the algorithm of Savat, could be predicted from the roughness profiles. Here, the tortuosity of the submerged part of the surface was used, which means that the calculated roughness depends on flow depth. The roughness increased with discharge, due to the fact that rougher parts of the surface became submerged at higher discharges. Therefore, a single measure of surface roughness (e.g. random roughness) is not sufficient to predict the hydraulic resistance. The proposed model allows the extension of the flow over the surface with increasing discharge to be taken into account, as well as the roughness within the submerged part of the surface. Therefore, the model is able to predict flow velocities reasonably well from discharge and roughness data only. Copyright © 2000 John Wiley & Sons, Ltd.     

Relation of sediment transport capacity to stone cover and size in rain‐impacted interrill flow

This study examines how the sediment transport capacity of interrill overland flow varies with stone cover and stone size at two flow intensities. Six series of flume experiments were conducted on two slopes (2° and 10°) with stones of three sizes (28·0, 45·5 and 91·3 mm) serving as roughness elements. Bed sediment size, water discharge and simulated rainfall intensity were the same in all experiments. It was found (1) that transport capacity is positively related to stone size, with the relation becoming stronger as stone cover increases and flow intensity decreases; and (2) that transport capacity is negatively related to stone cover at the high flow intensity and curvilinearly related to stone cover at the low flow intensity. The curvilinear relations are concave‐upward with the lowest transport capacities occurring at stone covers between 0·40 and 0·60. The highest transport capacities are found at stone covers of 0 and 1, with the transport capacity being greater at the former stone cover than at the latter. Copyright © 2000 John Wiley & Sons, Ltd.     

Closure relations for mobile bed debris flows in a wide range of slopes and concentrations

Debris flows are flows of water and sediment driven by gravity that initiate in the upper part of a stream, where the slope is very steep, allowing high values of solid concentration (hyperconcentrated flows), and that stop in the lower part of the basin, which is characterized by much lower slopes and reduced speeds and concentrations. Modelling these flows requires mathematical and numerical tools capable of simulating the behavior of a fluid in a wide range of concentrations of the solid phase, spanning from hyperconcentrated flows to flows in the fluvial regime. According to a two-phase approach, the depth integrated equations of mass and momentum conservation for water and sediments, under the shallow water hypothesis, are employed to solve field problems related to debris flows. These equations require suitable closure relations that in this case should be valid in a very wide range of slopes. In the hypothesis of absence of cohesive material, we derived these closure relations properly combining the relative relations valid separately in the fluvial and in the hyperconcentrated regimes. In the intermediate regime, the shear stress is due to the combined effect of the deformation of the liquid phase (grain roughness turbulence) and of inter-particle collisions. Therefore, an approach based on the sum of the effects of the two causes has been proposed, combining the Darcy–Weisbach equation and the Bagnoldian grain-inertia theory.A similar treatment has been made for the transport capacity relations, combing the Bagnold expression of the collisional regime with a transport capacity monomial formula valid in the fluvial regime.The closure relations are expressed in non-dimensional form as a function of the Froude number, of the solid concentration, of the relative submergence, and of the slope.In order to test the closure relation, a set of experiments with mixtures of non-cohesive sediments and water have been carried out in a laboratory flume under steady uniform flow conditions, with different solid and liquid discharges and different grain size distributions. The closure equations are satisfactorily tested against experimental investigation.