Variability of shallow overland flow velocity and soil aggregate transport observed with digital videography

Field experiments at Tiramoana station 30 km north of Christchurch, New Zealand using an erosion plot 16·5 m long, 0·6 m wide, and with a slope of 14–14·5° on rendzina soil aimed to measure the variability of flow velocity and of soil aggregates transport rate in shallow overland flow. Discharge/cross‐section area ratio was used to estimate mean velocity, and high‐speed digital video camera and image analysis provided information about flow and sediment transport variability. Six flow runs with 0·5–3·0 L s^?1 discharges were supercritical with Froude numbers close to or more than 1. Mean flow velocity followed Poiseuille law, float numbers were more than 1·5 and hydraulic resistance was an inverse proportional function of the Reynolds number, which is typical for laminar flows. Hence actual velocity varied through time significantly and the power spectrum was of ‘red‐noise’, which is typical for turbulent flow. Sediment transport rates had even higher variability, and soil aggregates transport was a compound Poisson process. Copyright © 2008 John Wiley & Sons, Ltd.     

Testing a theoretical resistance law for overland flow on a stony hillslope

Overland flow, sediments, and nutrients transported in runoff are important processes involved in soil erosion and water pollution. Modelling transport of sediments and chemicals requires accurate estimates of hydraulic resistance, which is one of the key variables characterizing runoff water depth and velocity. In this paper, a new theoretical power–velocity profile, originally deduced neglecting the impact effect of rainfall, was initially modified for taking into account the effect of rainfall intensity. Then a theoretical flow resistance law was obtained by integration of the new flow velocity distribution. This flow resistance law was tested using field measurements by Nearing for the condition of overland flow under simulated rainfall. Measurements of the Darcy–Weisbach friction factor, corresponding to flow Reynolds number ranging from 48 to 194, were obtained for simulated rainfall with two different rainfall intensity values (59 and 178 mm hr⁻¹). The database, including measurements of flow velocity, water depth, cross-sectional area, wetted perimeter, and bed slope, allowed for calibration of the relationship between the velocity profile parameter Γ, the slope steepness s, and the flow Froude number F, taking also into account the influence of rainfall intensity i. Results yielded the following conclusions: (a) The proposed theoretical flow resistance equation accurately estimated the Darcy–Weisbach friction factor for overland flow under simulated rainfall, (b) the flow resistance increased with rainfall intensity for laminar overland flow, and (c) the mean flow velocity was quasi-independent of the slope gradient.     

Roughness coefficients and velocity estimation in well-inundated sheet and rilled overland flow without strongly eroding bed forms

Even with the flow of water over a soil surface in which roughness elements are well inundated, and in less erosive situations where erosional bed forms are not pronounced, the magnitude of resistance coefficients in equations such as those of Darcy–Weisbach, Chezy or Manning vary with flow velocity (at least). Using both original laboratory and field data, and data from the literature, the paper examines this question of the apparent variation of resistance coefficients in relation to flow velocity, even in the absence of interaction between hydraulics and resulting erosional bed forms. Resistance equations are first assessed as to their ability to describe overland flow velocity when tested against these data sources. The result is that Manning's equation received stronger support than the Darcy–Weisbach or Chezy equations, though all equations were useful. The second question addressed is how best to estimate velocity of overland flow from measurements of slope and unit discharge, recognizing that the apparent flow velocity variation in resistance coefficients is probably a result of shortcomings in all of the listed resistance equations. A new methodology is illustrated which gives good agreement between estimated and measured flow velocity for both well-inundated sheet and rill flow. Comments are given on the predictive use of this methodology. Copyright © 1999 John Wiley & Sons, Ltd.     

Field studies of sediment transport by overland flow

Field studies on sandy soils of the Cottenham Series in mid-Bedfordshire show that the mean annual rate of sediment transport by overland flow on an 11° mid-slope is 98 g cm¹. The feasibility of using sediment transport equations to predict erosion by overland flow on a storm basis is examined by comparing the observed values of sediment yield with values predicted by four sediment transport equations and a regression equation which relates soil loss to runoff energy and rainfall energy. An expression combining Engelund's sediment transport capacity equation and the Manning equation for flow velocity, as modified by Savat for disturbed flow, best reflects field conditions. Although there is a significant correlation (r = 0.69; n 30) between the observed and predicted values using this expression, the coefficient of determination is too low for predictive purposes. Reasons for this are presented.     

Effects of rainfall,overland flow and their interactions on peatland interrill erosion processes

Interrill erosion processes on gentle slopes are affected by mechanisms of raindrop impact, overland flow and their interaction. However, limited experimental work has been conducted to understand how important each of the mechanisms are and how they interact, in particular for peat soil. Laboratory simulation experiments were conducted on peat blocks under two slopes (2.5° and 7.5°) and three treatments: Rainfall, where rainfall with an intensity of 12 mm h^?1 was simulated; Inflow, where upslope overland flow at a rate of 12 mm h^?1 was applied; and Rainfall + Inflow which combined both Rainfall and Inflow. Overland flow, sediment loss and overland flow velocity data were collected and splash cups were used to measure the mass of sediment detached by raindrops. Raindrop impact was found to reduce overland flow by 10 to 13%, due to increased infiltration, and reduce erosion by 47% on average for both slope gradients. Raindrop impact also reduced flow velocity (80–92%) and increased roughness (72–78%). The interaction between rainfall and flow was found to significantly reduce sediment concentrations (73–85%). Slope gradient had only a minor effect on overland flow and sediment yield. Significantly higher flow velocities and sediment yields were observed under the Rainfall + Inflow treatment compared to the Rainfall treatment. On average, upslope inflow was found to increase erosion by 36%. These results indicate that overland flow and erosion processes on peat hillslopes are affected by upslope inflow. There was no significant relationship between interrill erosion and overland flow, whereas stream power had a strong relationship with erosion. These findings help improve our understanding of the importance of interrill erosion processes on peat. Copyright © 2017 John Wiley & Sons, Ltd.     

Using a thermal tracer to estimate overland and rill flow velocities

Flow velocity is a basic hydraulic property of surface flows and its precise calculation is necessary for process based hydrological models, such as soil erosion and rill development models, as well as for modelling sediment and solute transport by runoff. This study presents a technique based on infrared thermography to visualize very shallow flows and allow a quantitative measurement of overland flow and rill flow velocities. Laboratory experiments were conducted to compare the traditional dye tracer technique with this new thermal tracer technique by injecting a combined tracer (heated dye) into shallow flowing surface water. The leading edge tracer velocities estimated by means of infrared video and by the usual real imaging video were compared. The results show that thermal tracers can be used to estimate both overland and rill flow velocities, since measurements are similar to those resulting from using dye tracers. The main advantage of using thermography was the higher visibility of the leading edge of the injected tracer compared with the real image videos. Copyright © 2013 John Wiley & Sons, Ltd.     

Sediment deposition and overland flow hydraulics in simulated vegetative filter strips under varying vegetation covers

Vegetative filter strips (VFSs) can effectively trap sediment in overland flow, but little information is available on its performance in controlling high‐concentration sediment and the runoff hydraulics in VFS. Flume experiments were conducted to investigate the sediment deposition, hydraulics of overland flow and their relationships in simulating VFS under a great range of sediment concentrations with four levels of vegetation cover (bare slope and 4%, 11% and 17%) and two flow rates (15 and 30 L min^?1). Sediment concentrations varied from 30 to 400 kg m^?3 and slope gradient was 9°. Both the deposited sediment load and deposition efficiency in VFS increased as the vegetation cover increased. Sediment concentration had a positive effect on the deposited load but no effect on deposition efficiency. A lower flow rate corresponded to greater deposition efficiency but had little effect on deposited load. Flow velocities decreased as vegetation cover increased. Sediment concentration had a negative effect on the mean velocity but no effect on surface velocity. Hydraulic resistance increased as the vegetation cover and sediment concentration increased. Sediment deposition efficiency had a much more pronounced relationship with overland flow hydraulics compared with deposited load, especially with the mean flow velocity, and there was a power relationship between them. Flow regime also affected the sediment deposition efficiency, and the efficiency was much higher under subcritical than supercritical flow. The results will be useful for the design of VFS and the control of sediment flowing into rivers in areas with serious soil erosion. Copyright © 2015 John Wiley & Sons, Ltd.     

Roughness effect on the correction factor of surface velocity for rill flows

Flow velocity is one of the most important hydrodynamic variables for both channelized (rill and gullies) and interrill erosive phenomena. The dye tracer technique to measure surface flow velocity V_s is based on the measurement of the travel time of a tracer needed to cover a known distance. The measured V_s must be corrected to obtain the mean flow velocity V using a factor α_v = V/V_s which is generally empirically deduced. The V_s measurement can be influenced by the method applied to time the travel of the dye-tracer and α_v can vary in different flow conditions. Experiments were performed by a fixed bed small flume simulating a rill channel for two roughness conditions (sieved soil, gravel). The comparison between a chronometer-based (CB) and video-based (VB) technique to measure V_s was carried out. For each slope-discharge combination, 20 measurements of V_s, characterized by a sample mean V_m, were carried out. For both techniques, the frequency distributions of V_s/V_m resulted independent of slope and discharge. For a given technique, all measurements resulted normally distributed, with a mean equal to one, and featured by a low variability. Therefore, V_m was considered representative of surface flow velocity. Regardless of roughness, the V_m values obtained by the two techniques were very close and characterized by a good measurement precision. The developed analysis on α_v highlighted that it is not correlated with Reynolds number for turbulent flow regime. Moreover, α_v is correlated neither with the Froude number nor with channel slope. However, the analysis of the empirical frequency distributions of the correction factor demonstrated a slope effect. For each technique (CB, VB)-roughness (soil, gravel) combination, a constant correction factor was statistically representative even if resulted in less accurate V estimations compared to those yielded by the slope-specific correction factor.     

Estimating flow resistance in steep slope rills

Recent research recognized that the slope of 18% can be used to distinguish between the ‘gentle slope’ case and that of ‘steep slope’ for the detected differences in hydraulic variables (flow depth, velocity, Reynolds number, Froude number) and those representatives of sediment transport (flow transport capacity, actual sediment load). In this paper, using previous measurements carried out in mobile bed rills and flume experiments characterized by steep slopes (i.e., slope greater than or equal to 18%), a theoretical rill flow resistance equation to estimate the Darcy-Weisbach friction factor is tested. The main aim is to deduce a relationship between the velocity profile parameter Γ, the channel slope, the Reynolds number, the Froude number and the textural classes using a data base characterized by a wide range of hydraulic conditions, plot or flume slope (18%–84%) and textural classes (clay ranging from 3% to 71%). The obtained relationship is also tested using 47 experimental runs carried out in the present investigation with mobile bed rills incised in a 18%—sloping plot with a clay loam soil and literature data. The analysis demonstrated that: (1) the soil texture affects the estimate of the Γ parameter and the theoretical flow resistance law (Equation 25), (2) the proposed Equation (25) fits well the independent measurements of the testing data base, (3) the estimate of the Darcy-Weisbach friction factor is affected by the soil particle detachability and transportability and (4) the Darcy-Weisbach friction factor is linearly related to the rill slope.     

Assessing the dye‐tracer correction factor for documenting the mean velocity of sheet flow over smooth and grassed surfaces

In the investigation of overland flow hydraulics, mean flow velocity (V) is frequently estimated using the measured surface flow velocity (Vs) multiplied by a correction factor, α. In total, 291 tests were performed in a flume with three beds [smooth glass (GL), sandpaper (SD), and plastic grass (GR)] to investigate α under submerged and non‐submerged flows, and Vs was observed using dye‐tracer method whilst V was calculated by the measured water depth and flow rate. For GL with 5.2% slope and 100 < Re < 5000 [Reynolds number (Re)], α ranged from 0.35 to 0.79, with an average of 0.54. For SD with slopes ranging from 2.6% to 25.9% and 300 < Re < 1200, α varied from 0.18 to 0.48 with an average of 0.32. Raindrop impacts decreased α for GL at 5.2% slope, but the effect diminished for SD as the slope increased. The α‐values less than the theoretical value of 0.67 in laminar flows may be attributed to the greater spatial variability in overland flow compared with channel flow. For GR with non‐submerged flows and Re < 4200, α varied inversely with sediment concentration (SC) at 5.2% slope but was only slightly related to SC at steep slopes of 15.6% and 25.9%. The α‐values were approximately 0.8 for turbulent flows and even greater than 1.0 under high flow discharges. This finding may relate to sheet flow disturbance and retarded surface velocity due to the protruding scattered grass stems. For each surface, α varied positively with Re; α was inversely related to slope for SD but positively related to slope for GR. There was a positive relation between h and α for GL and SD but a negative relation for GR, which highlights the importance of flow inundation status to α. The inundation ratio (h/Δ) is a promising indicator for predicting α; thus, further investigations using different submerged and non‐submerged surfaces are required to predict α effectively based on (h/Δ). Copyright © 2015 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.     

MATHEMATICAL MODEL OF OVERLAND FLOW AND MECHANISM OF SOIL CONSERVATION FOR FORESTED STEEP HILLSLOPE

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Determining friction coefficients for interrill flows: the significance of flow filaments and backwater effects

Friction coefficients in overland flows are customarily estimated from mean flow properties (depth, velocity, slope) that subsume spatial variations in flow arising from two major causes: microtopography and obstacles. This paper uses laboratory experiments in shallow flumes to examine the extent of non‐uniformity in flow conditions associated with each cause. Randomly placed emergent obstacles in a flume with a shallow axial channel generally yielded higher hydraulic roughness than the same pattern of obstacles on a planar flume, as well as greater variation in roughness as the obstacle locations were altered. In both flumes, hydraulic roughness fell with increasing Reynolds number for 10% obstacle cover, showed a flattening trend at 20% cover, and exhibited a convex‐downward trend at 30% obstacle cover. These results indicate the progressive onset of flow controls at narrow gaps in the obstacle field. In such flows, the use of mean flow properties conceals the existence of two main subdivisions of flow: flow filaments and backwater flows. In the experiments, flow filaments involved velocities more than twice the overall mean, whereas backwater flows were much slower than the mean. The existence of fast‐moving flow filaments may be significant in understanding soil transport in surface runoff, and backwater depths may modify splash detachment. Similarly, friction coefficients that fail to reflect these important non‐uniform flow components may not be optimal for hydraulic calculations or in erosion models. It is concluded that new approaches to observing and processing flow data may be required, in order to avoid the loss of important flow detail that is entailed in assuming uniform flow conditions. Copyright © 2003 John Wiley & Sons, Ltd.     

An experimental investigation of the effects of thawed soil depth on rill flow velocity

Water flow velocity is an important hydraulic variable in hydrological and soil erosion models, and is greatly affected by freezing and thawing of the surface soil layer in cold high-altitude regions. The accurate measurement of rill flow velocity when impacted by the thawing process is critical to simulate runoff and sediment transport processes. In this study, an electrolyte tracer modelling method was used to measure rill flow velocity along a meadow soil slope at different thaw depths under simulated rainfall. Rill flow velocity was measured using four thawed soil depths (0, 1, 2 and 10 cm), four slope gradients (5°, 10°, 15° and 20°) and four rainfall intensities (30, 60, 90 and 120 mm·h⁻¹). The results showed that the increase in thawed soil depth caused a decrease in rill flow velocity, whereby the rate of this decrease was also diminishing. Whilst the rill flow velocity was positively correlated with slope gradient and rainfall intensity, the response of rill flow velocity to these influencing factors varied with thawed soil depth. The mechanism by which thawed soil depth influenced rill flow velocity was attributed to the consumption of runoff energy, slope surface roughness, and the headcut effect. Rill flow velocity was modelled by thawed soil depth, slope gradient and rainfall intensity using an empirical function. This function predicted values that were in good agreement with the measured data. These results provide the foundation for a better understanding of the effect of thawed soil depth on slope hydrology, erosion and the parameterization scheme for hydrological and soil erosion models.     

The performance of grass filter strips in controlling high‐concentration suspended sediment from overland flow under rainfall/non‐rainfall conditions

There is little information on the performance of vegetative filter strips (VFS) in filtering high‐concentration sediment from subcritical overland flow. Flume experiments on simulated grass strips were conducted using combinations of three slope gradients (3°, 9° and 15°), five 1‐m‐wide slope positions (from upslope to downslope), two flow rates (60 and 20 L min^‐1 m^‐1) and sediment concentrations of 100–300 kg m^‐3 under simulated rainfall and non‐rainfall conditions. The results showed that sediment deposition efficiency increased with VFS width as a power function. Rainfall significantly reduced sediment deposited within VFS. Higher sediment concentration corresponded to a larger sediment deposition load but reduced deposition efficiency. Flow rate had a negative effect on deposition efficiency but no effect on deposition load. Sediments were more easily deposited at the upper slope position than downslope, and the upper slope position had a higher percentage of coarse sediments. The deposited sediment had significantly greater median diameters (D₅₀) than the inflow sediment. A greater proportion of coarse sediments larger than 25 µm in diameter were deposited, and particles smaller than 1 µm and of 10–25 µm had a better deposition performance than particles of 1–10 µm. Rainfall reduced the deposited sediment D₅₀ at a slope gradient of 3° and had no significant influence on it at 9° or 15°. A higher sediment concentration led to a smaller D₅₀ of the deposited sediment. Rainfall had no significant effect on overland flow velocity. Both the deposited sediment load and D₅₀ decreased with increasing flow velocity, and flow velocity was the most sensitive factor impacting sediment deposition. The results from this study should be useful to control sediment flowing into rivers in areas with serious soil erosion. Copyright © 2013 John Wiley & Sons, Ltd.     

Effects of patterned Artemisia capillaris on overland flow velocity under simulated rainfall

Vegetation cover is an important factor for erosion control. Laboratory‐simulated rainfall experiments were conducted to quantify the effectiveness of patchy distributed Artemisia capillaris in retarding overland flow velocity. Simulated storms (60, 90, 120, and 150 mm h^?1) were applied on a bare plot (CK) and four different plant patterns, a banded pattern perpendicular to the slope direction (BP), a single long strip parallel to slope direction (LP), small patches distributed like a checkerboard (SP1), and small patches distributed like a letter “X” (SP2). All treatments had three replicates. Each plot underwent two sets of experiments, intact plant plots and root plots (the above‐ground parts were removed, only roots were reserved), respectively. Results showed that flow velocity increased with rainfall intensity, and the lower slope velocity (V_l) was higher than the upper slope velocity (V_u). The removal of grass shoots increased flow velocity. Compared with bare soil plot, intact plants reduced mean flow velocity by 14%–60%, whereas the reduction declined to <40% for the root plots. BP and both SP treatments performed more effectively than LP in retarding flow velocity, whereas no significant differences were identified between BP and SP. The contributions of A. capillaris shoots and roots to the reductions in flow velocity under different rainfall intensities were different. The shoots made greater contribution of 53%–97% at 60 and 90 mm h^–1, and the roots contributed more (51%–81%) at 120 and 150 mm h^–1. Runoff and sediment rate had significant (p < 0.05) linear correlations with mean flow velocity. Copyright © 2012 John Wiley & Sons, Ltd.     

Hydraulic properties affected by litter and stem cover under overland flow

Vegetation stems and litter cover have different effects on sediment transport capacity under the same experimental conditions, which in essence, may be due to differences in their hydraulic properties, but the availability of comparative studies is limited. This study aimed to compare the hydraulic properties affected by litter and stem cover, compare differences in the drag forces exerted by litter and stems on overland flow, and develop new Manning's n and flow velocity equations for litter cover. Two series of flume experiments were conducted with the same slope gradients (8.8%, 17.6%, 26.8%) and flow discharge rates (0.5, 1.0 × 10⁻³ m³ s⁻¹). Artificial Gramineae stems with a 0%–30% cover level and Pinus tabulaeformis litter with a 0%–70% cover level were used in series 1 and series 2, respectively. The flow velocity and depth were measured. The results showed that the Froude number and flow velocity affected by stem cover were much lower than those affected by litter cover, while the opposite trend was observed in the relative magnitude of the Reynolds number, flow depth and shear stress. The form resistance caused by stems was 22–57 times greater than that caused by litter for the same cover level, which suggests that stem cover contributes more than litter cover to increasing the flow resistance and reducing the flow's ability for sediment detachment and transport. Two new equations for calculating Manning's n and flow velocity under the influence of litter cover were developed, with R² and NSE values of 0.96. The results of this study contribute to revealing the mechanisms of the differences of the effects of stem and litter cover on soil erosion.     

Effects of sediment load on hydraulics of overland flow on steep slopes

Eroded sediment may have significant effects on the hydraulics of overland flow, but few studies have been performed to quantify these effects on steep slopes. This study investigated the potential effects of sediment load on Reynolds number, Froude number, flow depth, mean velocity, Darcy–Weisbach friction coefficient, shear stress, stream power, and unit stream power of overland flow in a sand‐glued hydraulic flume under a wide range of hydraulic conditions and sediment loads. Slope gradients were varied from 8·7 to 34·2%, unit flow rates from 0·66 to 5·26×10^?3 m² s^?1, and sediment loads from 0 to 6·95 kg m^?1 s^?1. Both Reynolds number (Re) and Froude number (Fr) decreased as sediment load increased, implying a decrease in flow turbulence. This inverse relationship should be considered in modeling soil erosion processes. Flow depth increased as sediment load increased with a mean value of 1·227 mm, caused by an increase in volume of sediment‐laden flow (contribution 62·4%) and a decrease in mean flow velocity (contribution 37·6%). The mean flow velocity decreased by up to 0·071 m s^?1 as sediment load increased. The Darcy–Weisbach friction coefficient (f) increased with sediment load, showing that the total energy consumption increased with sediment load. The effects of sediment load on f depended on flow discharge: as flow discharge increased, the influence of sediment load on f decreased due to increased flow depth and reduced relative roughness. Flow shear stress and stream power increased with sediment load, on average, by 80·5% and 60·2%, respectively; however, unit stream power decreased by an average of 11·1% as sediment load increased. Further studies are needed to extend and apply the insights obtained under these controlled conditions to real‐world overland flow conditions. Copyright © 2010 John Wiley & Sons, Ltd.     

Macroscale surface roughness and frictional resistance in overland flow

The hydraulics of overland flow on rough granular surfaces can be modelled and evaluated using the inundation ratio rather than the flow Reynolds number, as the primary dimensionless group determining the flow behaviour. The inundation ratio describes the average degree of submergence of the surface roughness and is used to distinguish three flow regimes representing partially inundated, marginally inundated and well-inundated surfaces. A heuristic physical model for the flow hydraulics in each regime demonstrates that the three states of flow are characterized by very different functional dependencies of frictional resistance on the scaled depth of flow. At partial inundation, flow resistance is associated with the drag force derived from individual roughness and therefore increases with depth and percentage cover. At marginal inundation, the size of the roughness elements relative to the depth of flow controls the degree of vertical mixing in the flow so that frictional resistance tends to decrease very rapidly with increasing depth of flow. Well-inundated flows are described using rough turbulent flow hydraulics previously developed for open channel flows. These flows exhibit a much more gradual decrease in frictional resistance with increasing depth than that observed during marginal inundation. A data set compiled from previously published studies of overland flow hydraulics is used to assess the functional dependence of frictional resistance on inundation ratio over a wide range of flow conditions. The data confirm the non-monotonic dependence predicted by the model and support the differentiation of three flow regimes based on the inundation ratio. Although the percentage cover and the surface slope may be of importance in addition to the inundation ratio in the partially and marginally inundated regimes, the Reynolds number appears to be of significance only in describing well-inundated flows at low to moderate Reynolds numbers. As these latter conditions are quite rare in natural environments, the inundation ratio rather than the Reynolds number should be used as the primary dimensionless group when evaluating the hydraulics of overland flow on rough surfaces. © 1997 by John Wiley & Sons, Ltd.     

NONUNIFORMOPEN CHANNEL FLOW WITH UPWARD SEEPAGE THROUGH LOOSE BEDS

The Reynolds stress and bed shear stress are important parameters in fluvial hydraulics. Steady-nonuniform flow in open channels with streamwise sloping beds having upward seepage through loose beds is theoretically analyzed to estimate the Reynolds stress and bed shear stress. Equations of the Reynolds stress and bed shear stress are developed, assuming a modified logarithmic velocity distribution law due to upward seepage, and using the Reynolds and continuity equations of two-dimensional flow in open channels.