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1.
A computational study is presented on the hydraulics of a natural pool–rif?e sequence composed of mixed cobbles, pebbles and sand in the River Lune, northern England. A depth‐averaged two‐dimensional numerical model is employed, calibrated with observed data at the ?eld site. From the computational outputs, the occurrence of longitudinally double peak zones of bed shear stress and velocity is found. In particular, at low discharge there exists a primary peak zone of bed shear stress and velocity at the rif?e tail in line with the local maximum energy slope, in addition to a secondary peak at the pool head. As discharge increases, the primary peak at the rif?e tail at low ?ow moves toward the upstream side of the rif?e along with the maximum energy slope, showing progressive equalization to the surrounding hydraulic pro?les. Concurrently, the secondary peak, due to channel constriction, appears to stand at the pool head, with its value increasing with discharge and approaching or exceeding the primary peak over the rif?e. The existence of ?ow reversal is demonstrated for this speci?c case, which is attributable to channel constriction at the pool head. A dynamic equilibrium model is presented to reconstruct the pool–rif?e morphology. A series of numerical modelling exercises demonstrates that the pool–rif?e morphology is more likely produced by shallow ?ows concentrated with coarse sediments than deep ?ows laden with low concentrations of ?ne sediments. It is concluded that channel constriction can, but may not necessarily, lead to competence reversal, depending on channel geometry, ?ow discharge and sediment properties. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

2.
Due to a lack of data on settling velocities (ws) and grain size distributions (GSDs) in ?oodplain environments, sedimentation models often use calibrated rather than measured parameters. Since the characteristics of suspended matter differ from those of deposited sediment, it is impossible to derive the ws and GSD from the latter. Therefore, one needs to measure in situ suspended sediment concentrations (SSCs), settling velocities, effective grain sizes and sedimentation ?uxes. For this purpose we used the LISST‐ST, a laser particle sizer combined with a settling tube. In 2002 (twice) and 2004, we located the LISST‐ST with an optical backscatter sensor and sediment traps in two ?oodplains in The Netherlands: one along the unembanked IJssel River, another along the embanked Waal River. Measurements revealed that the SSC in the ?oodplains varied in relation to the SSC in the river channel. Smaller ?ocs dominated the SSC, while larger ?ocs dominated the potential sedimentation ?uxes. The in situ GSD in the IJssel ?oodplain was signi?cantly coarser than in the Waal ?oodplain, while the dispersed median grain sizes were equal for both ?oodplains. Therefore, the dispersed median grain size was two to ?ve times smaller than the effective one. The in situ grain size exhibited a signi?cant positive relationship with ws, although the ws for the largest ?ocs showed high variability. Consequently, the variability in sedimentation ?uxes was also large. In the actual sedimentation ?uxes, and hence in sedimentation models, in situ grain sizes up to about 20 µm can be neglected. In ?oodplain sedimentation models the relation between settling velocity and in situ grain size can be used instead of Stokes's law, which is only valid for dispersed grain sizes. These models should also use adequate data on ?ow conditions as input, since these strongly in?uence the suspended sediment characteristics. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

3.
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4.
During bed‐load transport by overland ?ow, momentum is transferred from the ?ow to the bed via grain collisions, resulting in a decrease in ?ow velocity and an increase in ?ow resistance, herein termed bed‐load transport resistance. In overland ?ow on mobile plane beds, total ?ow resistance f consists of grain resistance fg and bed‐load transport resistance fbt. In order to identify and evaluate the relative importance of the factors controlling fbt, 38 ?ume experiments were performed on slopes of 2·7 and 5·5° using sediment with median diameters of 0·74 and 1·16 mm. All ?ows were supercritical and turbulent. This study is an extension of a recent study by Gao and Abrahams (Earth Surface Processes and Landforms 2004, vol. 29, pp. 423–435). These authors found that fbt is controlled by three factors: sediment concentration C, dimensionless sediment diameter D*, and relative submergence h/D, where h is ?ow depth, D is median sediment diameter. However, a new dimensional analysis identi?es two additional factors: Froude number F and slope S. Multiple regression analyses reveal (1) that these ?ve factors together explain 97 per cent of the variance of fbt, and (2) that S controls fbt entirely through C. The variable C is therefore redundant, and a new functional equation relating fbt to D*, h/D, S and F is developed. This equation may be used to predict fbt. An advantage of this equation is that it may be used to predict fbt without measuring bed‐load transport rate. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

5.
During bedload movement by saltation, streamwise momentum is transferred from the ?ow to the saltating grains. When the grains collide with other grains on the bed or in the ?ow, streamwise momentum is reduced, and there is a decrease in streamwise ?ow velocity and an increase in ?ow resistance, herein termed bedload transport resistance fbt. Based on experiments in two ?umes with ?xed and mobile plane beds and previously published data, an equation is developed that may be used to predict fbt for both capacity and non‐capacity ?ows. The variables in this equation are identi?ed by dimensional analysis and the coef?cients are determined by non‐linear regression. This equation applies to rough turbulent open‐channel ?ows, where the relative submergence is between 1 and 20 and the entire sediment load moves by saltation. An investigation of the relative magnitudes of fbt and grain resistance fc suggests that where dimensionless shear stress θ is less than 1 and saltation is the dominant mode of bedload transport, fbt/fc increases with θ but never exceeds 1. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

6.
Tracers, such as ?uorescein dye, are widely employed to measure overland ?ow speeds by time‐of‐travel along measured ?ow paths. Among several disadvantages of this method are the involvement of human reaction time when using stop‐watches, and the relatively long travel path that is consequently needed for reliable timing. Long ?ow paths mean that local variability along the ?ow path cannot be detected. This paper describes a new optical tachometer that overcomes these limitations, as well as offering other advantages. It is based on the use of a small ?oating re?ector target that is carried on the surface tension ?lm, and which passes between two re?ective sensors mounted above the ?ow. The new device allows virtual ‘spot’ measurements of surface ?ow speed over a path as short as 1 cm, and eliminates the in?uence of human reaction time. The new device is battery powered and portable, and provides an improved alternative to dye timing in many ?eld and laboratory applications. Its use will allow the collection of more re?ned data than have hitherto been easily achievable. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

7.
This paper reports results from two scaled centrifuge modelling experiments, designed to simulate thaw‐related geli?uction. A planar 12° prototype slope was modelled in each experiment, using the same natural ?ne sandy silt soil. However two different scales were used. In Experiment 1, the model scale was 1/10, tested in the centrifuge at 10 gravities (g) and in Experiment 2, the scale was 1/30, tested at 30 g. Centrifuge scaling laws indicate that the time scaling factor for thaw consolidation between model and prototype is N2, where N is the number of gravities under which the model was tested. However, the equivalent time scaling for viscous ?ow is 1/1. If geli?uction is a viscosity‐controlled ?ow process, scaling con?icts will therefore arise during centrifuge modelling of thawing slopes, and rates of displacement will not scale accurately to the prototype. If, however, no such scaling con?icts are observed, we may conclude that geli?uction is not controlled by viscosity, but rather by elasto‐plastic soil deformation in which frictional shear strength depends on effective stress, itself a function of the thaw consolidation process. Models were saturated, consolidated and frozen from the surface downwards on the laboratory ?oor. The frozen models were then placed in the geotechnical centrifuge and thawed from the surface down. Each model was subjected to four freeze–thaw cycles. Soil temperatures and pore water pressures were monitored, and frost heave, thaw settlement and downslope displacements measured. Pore water pressures, displacement rates and displacement pro?les re?ecting accumulated shear strain, were all similar at the two model scales and volumetric soil transport per freeze–thaw cycle, when scaled to prototype, were virtually identical. Displacement rates and pro?les were also similar to those observed in earlier full‐scale laboratory ?oor experiments. It is concluded therefore that the modelled geli?uction was not a time‐dependent viscosity‐controlled ?ow phenomenon, but rather elasto‐plastic in nature. A ?rst approximation ‘?ow’ law is proposed, based on the ‘Cam Clay’ constitutive model for soils. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

8.
Central Kentucky is characterized by a mixture of karst and ?uvial features, typically manifested as mosaic of karst‐rich/channel‐poor (KRCP) and channel‐rich/karst‐poor (CRKP) environments. At the regional scale the location and distribution of KRCP and CRKP areas are not always systematically related to structural, lithological, topographic, or other controls. This study examines the relationship of KRCP and CRKP zones along the Kentucky River gorge area, where rapid incision in the last 1·5 million years has lowered local base levels and modi?ed slopes on the edge of the inner bluegrass plateau. At the scale of detailed ?eld mapping on foot within a 4 km2 area, the development of karst and ?uvial features is controlled by highly localized structural and topographic constraints, and can be related to slope changes associated with retreat of the Kentucky River gorge escarpment. A conceptual model of karst/?uvial transitions is presented, which suggests that minor, localized variations are suf?cient to trigger a karst–?uvial or ?uvial–karst switch when critical slope thresholds are crossed. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

9.
The estimation of debris‐?ow magnitude is an essential step in the assessment of debris‐?ow hazard. Although different methods have been developed for the assessment of debris‐?ow magnitude, this is still a dif?cult task because of the complexity of ?ow processes and the lack of data to test estimation procedures in many mountainous regions. Data on debris‐?ow magnitude from 127 basins in the Eastern Italian Alps have been collected from scienti?c and technical journals, technical reports, historical documents gathered from local archives, and ?eld surveys. These data were used to develop and test different predictive approaches, encompassing regression equations, geomorphological surveys and probabilistic analysis of time series. Regression techniques were used to correlate debris‐?ow magnitude to morphometric parameters and geological characteristics of the basins. Values of the channel debris yield rate (contribution per unit length of channel), proposed in the literature, were compared with data from the study area for identifying reference values for channel stretches of different morphological characteristics. Although limited to the few basins in which suf?cient data were available, the probabilistic analysis of time series of debris‐?ow magnitude provides indications about the relations between magnitude and frequency of debris ?ows. Some observations about the capability and drawbacks of considered methods are presented and the combined use of different approaches for the estimation of debris‐?ow magnitude is suggested. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

10.
Much of the published literature relating to reach‐scale total ?ow resistance concentrates on alluvial rivers and little mention is made of the more extreme resistance found in bedrock‐in?uenced river systems. This paper presents the results of a detailed investigation of total ?ow resistance variation for ?ve channel types on the Sabie River, South Africa (cohesive mixed anastomosed, uncohesive mixed anastomosed, mixed pool–rapid, alluvial braided and alluvial single thread) over a range of discharges. Manning's ‘n’ and Darcy‐Weisbach f resistance coef?cients are calculated using Barnes' methodology (H. H. Barnes, US Geological Survey Water Supply Paper 1849, 1967). These data are analysed at the scales of channel type and morphologic unit and the resultant resistance values are compared with the literature. Generally the low‐?ow friction values estimated for the bedrock‐in?uenced channel types are higher than any reported. Flow resistance quanti?cation of the alluvial channel type study sites on the Sabie River produced values slightly higher than earlier studies of similar morphologies. In situations where signi?cant areas of irregular bedrock are exposed (cohesive mixed anastomosed and mixed pool–rapid channel types) the high ?ow resistance coef?cients at low discharges probably re?ect energy dissipation due to hydraulic jumps and internal distortions; however, these values fall as discharge increases to values comparable to those recorded for step–pool rivers. It is suggested that the slightly elevated resistance coef?cients recorded in the alluvial channel types are the result of the vegetation roughness component, operating when the macro‐channel bar features are inundated. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

11.
Soil surface microtopography produces non‐uniform surface run‐off, in which narrow threads of relatively deep and fast ?ow move within broader, shallower, slower‐moving regions. This kind of ?ow is probably widespread, given that microtopography is itself common. Methods used to record the properties of surface run‐off include grid‐ or transect‐based depth observations, with a single mean ?ow speed derived by calculation from V = Q/WD, and the use of dye timing to estimate velocity, with an effective mean depth calculated from D = Q/WV. Because these methods allow only single, ?ow‐?eld mean values to be derived for V or D, neither is well suited to non‐uniform ?ows. The use of depth data to derive a ?ow‐?eld mean V furthermore implicitly applies area weighting to the depth data; likewise, the use of dye speeds for V inherently overestimates mean V because dye dominantly follows the faster ?ow threads. The associated errors in derived parameters such as friction coef?cients are not readily quanti?ed and appear not to have been addressed previously. New ?eld experiments made on untilled soil surfaces in arid western NSW, Australia, explore these circumstances and the implications for deriving meaningful measures of ?ow properties, including friction coef?cients. On surfaces deliberately chosen for their very subtle microtopography, average thread velocities are shown to be commonly 2·5 times greater than the ?ow‐?eld mean, and locally 6–7 times greater. On the other hand, non‐thread ?ow speeds lie below the ?ow‐?eld mean, on average reaching only 84 per cent of this value, and often considerably less. Flow‐?eld means conceal the existence of regions of the ?ow ?eld whose properties are statistically distinct. Results con?rm that a reliance on ?ow‐?eld average depths yields estimates of friction coef?cients that are biased toward the shallower, high‐roughness parts of the ?ow, while if dye speeds are relied upon the results are biased toward the deeper, smoother threads of ?ow. A new approach to the evaluation of friction coef?cients in non‐uniform ?ows is advanced, involving the determination of separate coef?cients for threads and non‐thread zones of the ?ow ?eld. In contrast, ?ow‐?eld friction coef?cients as they are customarily derived in run‐off plot experiments subsume these distinct coef?cients in proportions that are generally unknown. The value of such coef?cients is therefore questionable. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

12.
Bed shear stress is a fundamental variable in river studies to link ?ow conditions to sediment transport. It is, however, dif?cult to estimate this variable accurately, particularly in complex ?ow ?elds. This study compares shear stress estimated from the log pro?le, drag, Reynolds and turbulent kinetic energy (TKE) approaches in a laboratory ?ume in a simple boundary layer, over plexiglas and over sand, and in a complex ?ow ?eld around de?ectors. Results show that in a simple boundary layer, the log pro?le estimate is always the highest. Over plexiglas, the TKE estimate was the second largest with a value 30 per cent less than the log estimate. However, over sand, the TKE estimate did not show the expected increase in shear stress. In a simple boundary layer, the Reynolds shear stress seems the most appropriate method, particularly the extrapolated value at the bed obtained from a turbulent pro?le. In a complex ?ow ?eld around de?ectors, the TKE method provided the best estimate of shear stress as it is not affected by local streamline variations and it takes into account the increased streamwise turbulent ?uctuations close to the de?ectors. It is suggested that when single‐point measurements are used to estimate shear stress, the instrument should be positioned close to 0·1 of the ?ow depth, which corresponds to the peak value height in pro?les of Reynolds and TKE shear stress. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

13.
The Butgenbach dam on the Warche River was built in 1932 in order to maintain a suf?cient supply of water to the Robertville reservoir situated 7 km downstream, for the production of hydroelectricity. During winter months, releases are made almost every day from the Butgenbach dam. From a hydrological point of view, this has resulted in signi?cantly reducing the number of discharges that are higher than bankfull. Despite the reduction in peak discharge, there is a signi?cant increase in the number of ef?cient discharges (0·6 bankfull). The impacts of these hydrological modi?cations on the bed morphology and sedimentology below the Butgenbach dam have been studied and the following geomorphological modi?cations have been identi?ed: a doubling of the width of the channel in 45 years, a reduction in the number of rif?es and pools, an increase in the number of gravel bars and islets and an increase in bedrock outcrops in the channel. Moreover, the ?nest bed particles are mobilized by the almost daily releases, inducing a signi?cant increase in bed‐material size sorting. The reduction of sinuosity and the disappearance of bed differentiation and rif?e/pool sequences have produced a diminution of bed roughness and an increase of the competence of the river. Thus relatively small ?oods can remove the armoured layer. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

14.
Barchans, isolated crescent‐shaped bedforms, are believed to be formed under almost unidirectional wind or water ?ows and limited sand supply. The formation of barchan morphologies under the action of purely oscillatory wave motion has not yet been fully investigated. The present study attempted to form barchan topography in a wave ?ume and to compare this with barchans in the ?eld. Barchan morphologies of ripple size, called the barchan ripples, were generated from a ?at bed by the action of waves. The horn width, the distance between horn tips, of the barchan ripples increased linearly with an increase in the total length, the overall length projected on the centre line of the barchan, with a coef?cient common to barchan dunes in deserts. The ratio of horn length to horn width of the barchan ripples was smaller than that of barchan dunes, but similar to that of subaqueous barchans in the ?eld. The longer the wave period was, the larger the ratio of the body length to horn width became. Most subaqueous barchans formed under waves (in the laboratory) and unidirectional ?ows (in the ?eld) had blunter horns than subaerial barchans. The shape of the barchan ripples changed with wave period. The outer rim became rounder with increasing wave period. The relationship between the base area and the height of barchan morphologies seems to be linear, with a constant coef?cient for the scale from ripples to dunes. The barchan ripples showed a linear relationship between the height and the horn width, similar to that for barchan dunes. The migration speed of the barchan ripples was proportional to the cube of the ?ow velocity and was inversely proportional to height. The same relation with a different value of the coef?cient was obtained for barchan dunes. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

15.
Velocity measurements carried out by an acoustic doppler velocimeter (ADV) in a rectangular laboratory ?ume having a gravel bed are presented. The velocity pro?les are measured in six verticals of the channel cross‐section having an increasing distance (from 4 to 38·5 cm) from the ?ume wall. The experimental runs are carried out for ?ve different bed arrangements, characterized by different concentrations of coarser elements, and for the two conditions of small‐ and large‐scale roughness. For both hydraulic conditions, the velocity measurements are ?rst used to test the applicability of the Dean pro?le and of the logarithmic pro?le corrected by a divergence function proposed in this paper. Then, for each value of the depth sediment ratio h/d84, the non‐dimensional friction factor parameter is calculated by integration of the measured velocity distributions in the different verticals of the cross‐section. Finally a semi‐logarithmic ?ow resistance equation is empirically deduced. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

16.
On 12 August 1997, the lower part of Diadem Glacier in the southern Coast Mountains of British Columbia fell into Queen Bess Lake and produced a train of large waves. The waves overtopped the broad end moraine at the east end of the lake and ?ooded the valley of the west fork of Nostetuko River. The displacement waves also incised the out?ow channel across the moraine. Stratigraphic and sedimentologic evidence supports the conclusion that the ?ood had two phases, one related to wave overtopping and a second to breach formation. Empirical equations were used to calculate the peak discharge of the ?ood at various points along the west fork of the Nostetuko valley and to describe the attenuation of the ?ood wave. The velocity of the ?ood was also calculated to determine the time it took for the ?ood to reach the main fork of Nostetuko River. The highest peak discharges were achieved in the upper reach of the valley during the displacement phase of the ?ood. Peak discharge declined rapidly just below the moraine dam, with little change thereafter for approximately 7 km. Empirical formulae and boulder measurements indicate a rise in peak discharge in the lower part of the west fork valley. We suggest that ?ow in the upper part of the valley records the passage of two separate ?ood peaks and that the rise in discharge in the lower part of the valley is due to amalgamation of the wave and breach peaks. Hydraulic ponding in con?ned reaches of the valley extended the duration of the ?ood. In addition, erosion of vegetation and sediment in the channel and valley sides may also have exerted an in?uence on the duration and nature of ?ooding. Sediments were deposited both upstream and downstream of channel constrictions and on a large fan extending out into the trunk Nostetuko River valley. This study extends our understanding of the variety and complexity of outburst ?oods from naturally dammed lakes. It also shows that simple empirical and other models for estimating peak discharges of outburst ?oods are likely to yield erroneous results. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

17.
We explore the link between channel‐bed texture and river basin concavity in equilibrium catchments using a numerical landscape evolution model. Theory from homogeneous sediment transport predicts that river basin concavity directly increases with bed sediment size. If the effective grain size on a river bed governs its concavity, then natural phenomena such as grain‐size sorting and channel armouring should be linked to concavity. We examine this hypothesis by allowing the bed sediment texture to evolve in a transport‐limited regime using a two grain‐size mixture of sand and gravel. Downstream ?ning through selective particle erosion is produced in equilibrium. As the channel‐bed texture adjusts downstream so does the local slope. Our model predicts that it is not the texture of the original sediment mixture that governs basin concavity. Rather, concavity is linked to the texture of the sorted surface layer. Two different textural regimes are produced in the experiments: a transitional regime where the mobility of sand and gravel changes with channel‐bed texture, and a sand‐dominated region where the mobility of sand and gravel is constant. The concavity of these regions varies depending on the median gravel‐ or sand‐grain size, erosion rate, and precipitation rate. The results highlight the importance of adjustments in both surface texture and slope in natural rivers in response to changes in ?uvial and sediment inputs throughout a drainage network. This adjustment can only be captured numerically using multiple grain sizes or empirical downstream ?ning rules. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

18.
Morphometric variables associated with 41 debris‐?ow and 18 ?uvial fans and their basins in the Southern Alps of New Zealand are examined. The results show statistically signi?cant differences in the area, maximum elevation, relief and ruggedness (Melton's R) of the basin and the area, gradient, and apex and toe elevations of the fan between debris‐?ow and ?uvial sites. Concavity of the fan longitudinal pro?le also differs between the two fan types, although this could not be tested statistically. Most of these morphometric differences re?ect differences in processes and environmental controls on them. Discriminant analysis indicates that basin area and fan gradient best differentiate the two fan types by process. Moderately strong correlations exist, on both debris‐?ow and ?uvial fans, between basin area or Melton's R and fan area. Correlations between basin area or Melton's R and fan gradient are generally weaker. The results of this study also indicate that on debris‐?ow‐prone fans the fan gradient and basin Melton's R have lower thresholds which overlap little with upper thresholds associated with basins where only stream?ow reaches the fan. These thresholds may therefore have value in preliminary morphometric assessments of debris‐?ow hazard on fans in the Southern Alps. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

19.
Geomorphology interacts with surface‐ and ground‐water hydrology across multiple spatial scales. Nonetheless, hydrologic and hydrogeologic models are most commonly implemented at a single spatial scale. Using an existing hydrogeologic computer model, we implemented a simple hierarchical approach to modeling surface‐ and ground‐water hydrology in a complex geomorphic setting. We parameterized the model to simulate ground‐ and surface‐water ?ow patterns through a hierarchical, three‐dimensional, quantitative representation of an anabranched montane alluvial ?ood plain (the Nyack Flood Plain, Middle Fork Flathead River, Montana, USA). Comparison of model results to ?eld data showed that the model provided reasonable representations of spatial patterns of aquifer recharge and discharge, temporal patterns of ?ood‐water storage on the ?ood plain, and rates of ground‐water movement from the main river channel into a large lateral spring channel on the ?ood plain, and water table elevation in the alluvial aquifer. These results suggest that a hierarchical approach to modeling ground‐ and surface‐water hydrology can reproduce realistic patterns of surface‐ and ground‐water ?ux on alluvial ?ood plains, and therefore should provide an excellent ‘quantitative laboratory’ for studying complex interactions between geomorphology and hydrology at and across multiple spatial scales. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

20.
A previously published mixing length (ML) model for evaluating the Darcy–Weisbach friction factor for a large‐scale roughness condition (depth to sediment height ratio ranging from 1 to 4) is brie?y reviewed and modi?ed (MML). Then the MML model and a modi?ed drag (MD) model are experimentally tested using laboratory measurements carried out for gravel‐bed channels and large‐scale roughness condition. This analysis showed that the MML gives accurate estimates of the Darcy–Weisbach coef?cient and for Froude number values greater than 0·5 the MML model coincides with the ML one. Testing of the MD model shows limited accuracy in estimating ?ow resistance. Finally, the MML and MD models are compared with the performance of a quasi‐theoretical (QT) model deduced applying the P‐theorem of the dimensional analysis and the incomplete self‐similarity condition for the depth/sediment ratio and the Froude number. Using the experimental gravel‐bed data to calibrate the QT model, a constant value of the exponent of the Froude number is determined while two relationships are proposed for estimating the scale factor and the exponent of the depth/sediment ratio. This indirect estimate procedure of the coef?cients (b0, b1 and b2) of the QT model can produce a negligible overestimation or underestimation of the friction factor. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

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