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1.
Detailed hydraulic measurements were made in nine step‐pool, five cascade and one plane‐bed reach in Fraser Experimental Forest, Colorado to better understand at‐a‐station hydraulic geometry (AHG) relations in these channel types. Average values for AHG exponents, m (0·49), f (0·39), and b (0·16), were well within the range found by other researchers working in steep gradient channels. A principal component analysis (PCA) was used to compare the combined variations in all three exponents against five potential control variables: wood, D84, grain‐size distribution (σ), coefficient of variation of pool volume, average roughness‐area (projected wetted area) and bed gradient. The gradient and average roughness‐area were found to be significantly related to the PCA axis scores, indicating that both driving and resisting forces influence the rates of change of velocity, depth and width with discharge. Further analysis of the exponents showed that reaches with m > b + f are most likely dominated by grain resistance and reaches below this value (m < b + f) are dominated by form resistance. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

2.
Recent research has started to focus on how prolonged periods of sub‐threshold flows may be capable of imparting structural changes that contribute to increased bed stability. To date, this effect (termed ‘stress history’) has been found to be significant in acting to increase a bed's critical shear stress at entrainment threshold. However, it is supported by only limited, qualitative and often speculative information on the mechanisms of this stabilization process in grade‐specific studies. As such, this paper uses high resolution laser scanning to quantitatively ascertain the granular mechanics underpinning the relationship between stress history and entrainment threshold for beds of a range of grain size distributions. Employing a bed slope of 1/200, three grain size distributions with median grain sizes (D50) of 4·8 mm [uniform (σg = (D84/D16)0.5 = 1·13; bimodal (σg = 2·08); and, unimodal (σg = 1·63)] were exposed to antecedent stress histories of 60 and 960 minutes duration. Antecedent shear stress magnitude was set at 50% of the critical shear stress for the D50 when no stress history period was employed. Two laser displacement scans of the bed surface (approximate area 100 mm × 117 mm) were taken, one prior to the antecedent period and one after this period, so that changes to surface topography could be quantified (resolution of x = 0·10 mm, y = 0·13 mm and z = 0·24 mm). Rearrangement of bed surface structure is described using statistical analysis and two‐dimensional (2D) semi‐variograms to analyse scaling behaviour. Results reveal vertical settlement, changes to bed roughness and particle repositioning. However, the bed grain size distribution influences the relative importance of each mechanism in determining stress history induced bed stability; this is the focus of discussion in this paper. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

3.
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   

4.
Hans A. Einstein initiated a probabilistic approach to modelling sediment transport in rivers. His formulae were based on theory and were stimulated by laboratory investigations. The theory assumes that bed load movement occurs in individual steps of rolling, sliding or saltation and rest periods. So far very few attempts have been made to measure stochastic elements in nature. For the first time this paper presents results of radio‐tracing the travel path of individual particles in a large braided gravel bed river: the Waimakariri River of New Zealand. As proposed by Einstein, it was found that rest periods can be modelled by an exponential distribution, but particle step lengths are better represented by a gamma distribution. Einstein assumed an average travel distance of 100 grain‐diameters for any bed load particle between consecutive points of deposition, but larger values of 6·7 m or 150 grain‐diameters and 6·1 m or 120 grain‐diameters were measured for two test particle sizes. Together with other available large scale field data, a dependence of the mean step length on particle diameter relative to the D50 of the bed surface was found. During small floods the time used for movement represents only 2·7% of the total time from erosion to deposition. The increase in percentage of time being used for transport means that it then has to be regarded in stochastic transport models. Tracing the flow path of bed load particles between erosion and deposition sites is a step towards explaining the interactions between sediment transport and river morphology. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

5.
The acceleration of saltating grains by overland flow causes momentum to be transferred from the flow to the grains, thereby increasing flow resistance and bed roughness. To assess the impact of saltating sediment on overland flow hydraulics, velocity profiles in transitional and turbulent flows on a fixed sand-covered bed were measured using hot-film anemometry. Five discharges were studied. At each discharge, three flows were measured: one free of sediment, one with a relatively low sediment load, and one with a relatively high sediment load. In these flows from 83 to 90 per cent of the sediment was travelling by saltation. As a result, in the sediment-laden flows the near-bed velocities were smaller and the velocity profiles steeper than those in the equivalent sediment-free flows. Sediment loads ranged up to 87·0 per cent of transport capacity and accounted for as much as 20·8 per cent of flow resistance (measured by the friction factor) and 89·7 per cent of bed roughness (measured by the ratio of the roughness length to median grain diameter). It is concluded that saltating sediment has a considerable impact on overland flow hydraulics, at least on fixed granular beds. Saltation is likely to have a relatively smaller effect on overland flow on natural hillslopes and agricultural fields where form and wave resistance dominate. Still, saltation is generally of greater significance in overland flow than in river flow, and for this reason its effect on overland flow hydraulics is deserving of further study. © 1998 John Wiley & Sons, Ltd.  相似文献   

6.
Cheniers from Mont‐Saint‐Michel bay (France) are coarse shelly sand ridges migrating on the mudflat up to the salt marshes where they accumulate and merge in a littoral barrier. In this macrotidal setting and low wave forcing, the cheniers are rarely submerged. However, they are found to move up to several metres during coincidence of spring tide and wave activity. Their processes of migration, morphology and internal structure (composition of the beddings, grain size, sorting and grain arrangement) are thought to be closely related to the hydrodynamic behaviour of the coarse and shelly sediment. This paper focuses on the hydrodynamic behaviour of bioclastic sand sampled from the cheniers: settling velocities of the shell fragments were measured using a 2 m long sedimentation tube. Thresholds of motion under unidirectional current, velocity and turbulence vertical profiles were characterized in a small recirculating flume using Laser Doppler Anemometry (LDA). The flat‐shaped bioclastic particles feature low settling velocities and reveal a good resistance to the re‐suspension effect of the flow when imbricated in a sediment bed. The shear stress in the bottom boundary layer has been measured in the viscous and log sub‐layers. Nikuradse roughness heights (ks) for shell debris beds of different sizes have been quantified. It is found that ks ≈ 2·56d50. This value is close to the ones used for classic rounded sand grains despite their major differences of shape. The dual behaviour of the shell fragments (low settling velocity, good resistance to unidirectional flow) should be considered as a key to understanding how this coarse material is transported across the tidal flat, and finally accumulated as cheniers. Further flume experiments including wave activity and tidal fluctuations are necessary to better quantify these complex processes. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

7.
Estimates of the wind shear stress exerted on Earth's surface using the fully rough form of the law‐of‐the‐wall are a function of the aerodynamic roughness length, z0. Accurate prediction of aeolian sediment transport rates, therefore, often requires accurate estimates of z0. The value of z0 is determined by the surface roughness and the saltation intensity, both of which can be highly dynamic. Here we report field measurements of z0 values derived from velocity profiles measured over an evolving topography (i.e. sand ripples). The topography was measured by terrestrial laser scanning and the saltation intensity was measured using a disdrometer. By measuring the topographic evolution and saltation intensity simultaneously and using available formulae to estimate the topographic contribution to z0, we isolated the contribution of saltation intensity to z0 and document that this component dominates over the topographic component for all but the lowest shear velocities. Our measurements indicate that the increase in z0 during periods of saltation is approximately one to two orders of magnitude greater than the increase attributed to microtopography (i.e. evolving sand ripples). Our results also reveal differences in transport as a function of grain size. Each grain‐size fraction exhibited a different dependence on shear velocity, with the saltation intensity of fine particles (diameters ranging from 0.125 to 0.25 mm) saturating and eventually decreasing at high shear velocities, which we interpret to be the result of a limitation in the supply of fine particles from the bed at high shear velocities due to bed armoring. Our findings improve knowledge of the controls on the aerodynamic roughness length and the grain‐size dependence of aeolian sediment transport. The results should contribute to the development of improved sediment transport and dust emission models. © 2018 John Wiley & Sons, Ltd.  相似文献   

8.
A series of laboratory flume experiments under conditions of sediment starvation (zero sediment feeding) and recirculation were conducted in order to identify the temporal evolution and surface properties of static and mobile armour layers. The experiments were carried out in an 8 m long flume using a bimodal grain‐size mixture (D50 = 6·2 mm) and a range of shear stresses ranging from 4·0 to 8·6 N m–2. The results confirm that a static armour layer is coarser than a mobile one, and that the grain size of a mobile armour layer is rather insensitive to changes in the imposed flow strength. An analysis of laser scan bed surveys revealed the highly structured and imbricated nature of the static armour layer. Under these conditions the vertical roughness length scale of the bed diminished and it became topographically less complex at higher forming discharges. The topography of mobile armour layers created by rising discharges differed. They exhibited a greater roughness length scale and were less organized, despite the fact that the grain size of the surface material maintained an approximately constant value during recirculation. Also, the mobile armour tended to create larger cluster structures than static armour layers when formed by higher discharges. These differences were mainly due to the transport of the coarser fraction of bed sediments, which diminished to zero over the static armour because of being hidden within the bed, whereas in the mobile armour the coarser particles protruded into the flow and were actively transported, increasing the vertical roughness length scale. Overall, the results show that an examination of the grain size characteristics of armour layers cannot be used to infer sediment mobility and bed roughness. Detailed elevation models of exposed surfaces of gravel‐bed rivers are required to provide critical insight on the sediment availability and sedimentation processes. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

9.
The need to estimate velocity and discharge indirectly in gravel-bedded rivers is a commonly-encountered problem. Semilogarithmic friction equations are used to estimate mean velocity using a friction factor obtained from depth and grain size information. Although such equations have a semi-theoretical basis, in natural gravel-bed channels, an empirical constant (6.8 or 3.5) has to be introduced to scale-up the characteristic grain size (D50 or D84) to represent the effective roughness length. In this paper, two contrasting approaches are used to suggest that the multiplier of characteristic grain size is attributable to the effect of small-scale form resistance, reflecting the occurrence of microtopographic bedforms in gravel-bedded environments. First, spatial elevation dependence in short, detailed bed profiles from a single gravel-bedded river is investigated using semivariogram and zero-crossing analyses. This leads to objective identification of two discrete scales of bed roughness, associated with grain and microtopographic roughness elements. Second, the autocorrelation structure of the three-dimensional near-bed velocity field is examined to identify regularities associated with eddy shedding and energy losses from larger grains and microtopographic bedforms. Apart from improving the capacity to determine friction factors for velocity and discharge estimation, the findings have implications in general for the initial motion of gravelly bed material.  相似文献   

10.
In a small experimental catchment of the Dolomites (Rio Cordon, 5 km2) field observations have been carried out on the movement of various sized bed material particles. Displacement length of 860 marked pebbles, cobbles and boulders (0·032 < D < 0·512 m) has been measured along the river bed during individual snowmelt and flood events in the periods 1993–1994 and 1996–1998. Floods were grouped into two categories. The first includes ‘ordinary’ events, which are characterized by peak discharges with a return period of 1–5 years and by an hourly bedload rate not exceeding 20 m3 h?1. The second refers to ‘exceptional’ events with a return period of 50–60 years. A flood of this latter type occurred on 14 September 1994, with a peak discharge of 10·4 m3 s?1 and average hourly bedload rate of 324 m3 h?1. The variation according to grain size of total displacement length Li depends on the degree of mobilization of the individual fractions of the bed surface: Li is independent of Di for smaller, fully mobile grain sizes and decreases rapidly with Di for larger fractions in a state of partial transport. Sustained selective transport without a supply of sediment from upstream leads to the development of a stable coarse armoured surface through progressive winnowing of finer material from the bed surface. With supply unlimited conditions for transport, both the occurrence of extreme events and the duration of a sequences of ‘ordinary’ floods play an important role in the degree of mobilization of the individual fractions of the bed. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

11.
Flume experiments were conducted using four different gravel beds (D50 + 12–39 mm) and a range of marked particles (10–65 mm). The shear stresses were evaluated from friction velocities, when initial movement of marked particles occurred. Two kinds of equations were produced: first for the threshold of initial movement, and second for generalized movement. Equations of the type 0c + a(Di/D50)b, as proposed by Andrews (1983) are applicable even if the material is relatively well sorted. However, the values of a and b are lower (respectively 0·050 and -0·70) for initial movement. Generalized movement requires a higher shear stress (a + 0·068 and b + -0·80). D90 of the bed material and y0 (the bed roughness parameter) were also used as reference values in place of D50. They produced lower values than in natural streams, mainly owing to the fact that the material used in the flume is better sorted: clusters are less well developed and the bed roughness is lower.  相似文献   

12.
In several empirical and modelling studies on river hydraulics, dispersion was negatively correlated to surface roughness. In this study, it was aimed to investigate the influence of surface roughness on longitudinal dispersion under controlled conditions. In artificial flow channels with a length of 104 m, tracer experiments with variations in channel bed material were performed. By use of measured tracer breakthrough curves, average flow velocity, mean longitudinal dispersion, and mean longitudinal dispersivity were calculated. Longitudinal dispersion coefficients ranged from 0·018 m2 s?1 in channels with smooth bed surface up to 0·209 m2 s?1 in channels with coarse gravel as bed material. Longitudinal dispersion was linearly related to mean flow velocity. Accordingly, longitudinal dispersivities ranged between 0·152 ± 0·017 m in channels with smooth bed surface and 0·584 ± 0·015 m in identical channels with a coarse gravel substrate. Grain size and surface roughness of the channel bed were found to correlate positively to longitudinal dispersion. This finding contradicts several existing relations between surface roughness and dispersion. Future studies should include further variation in surface roughness to derive a better‐founded empirical equation forecasting longitudinal dispersion from surface roughness. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

13.
The rigin and fate of six phthalate esters (dimethyl phthalate (DMP), diethyl phthalate (DEP), di‐n‐butyl phthalate (DnBP), butyl benzyl phthalate (BBP), di (2‐ethylhexyl) phthalate (DEHP) and di‐n‐octyl phthalate (DnOP)), were investigated during 2005 and 2006 in the densely populated Seine river estuary. Four compounds, DMP, DEP, DnBP and DEHP were detected at all the stations with DEHP (160–314 ng L?1), followed by DEP (71–181 ng L?1) and next DnBP (67–319 ng L?1), except at la Bouille, where DnBP was the second most important compound. BBP and DnOP concentrations remained low and were not found at all the stations. Considering all six phthalates, Caudebec‐en‐Caux (beginning of the salinity gradient) was the least polluted station (464 ng L?1), whereas Honfleur (771 ng L?1) and La Bouille (716 ng L?1) displayed the highest contamination levels, probably related to important industrial plants. From Caudebec‐en‐Caux to Honfleur (maximum turbidity), variation of DEHP concentration was related to that of suspended matter. In addition, the salinity rise in that area might have facilitated DEHP sorption upon particles. A significant correlation between flow magnitude and DEHP concentration was found (P < 0·01, n = 12), supporting the influence of the hydrological cycle upon contamination. Runoff contribution (56·9 kg d?1) to river contamination was confirmed by the annual evolution of phthalate concentrations in the Seine river at Poses. Concentrations of DEHP in the tributaries were in the same range as those of the Seine River (100–350 ng L?1), except for two in densely populated and industrialized areas: Robec (800 ng L?1) and Cailly (970 ng L?1). The treatment plant discharge fluxes were in the same range as those of tributaries (30·4–250 g d?1). During high flow periods, the influence of tributaries and of treatment plants seemed to play a minor part in the contamination level of the Seine river estuary. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

14.
After its formation, a rill may remain in the field for months, often receiving lower flow rates than the formative discharge. The objective of this work was to evaluate the rill flow transport capacity of soil aggregates at discharges unable to erode the rill, and to analyse the influence of the rill macro‐roughness on this transport process. A non‐erodible rill was built in which roughness was reproduced in detail. In order to assess only the rill macro‐roughness, a flat channel with a similar micro‐roughness to that in the rill replica was built. Rill and channel experiments were carried out at a slope of 8 and at six discharges (8·3 × 10?5 to 5·2 × 10?4 m3 s?1) in the rill, and eight discharges (1·6 × 10?5 to 5·2 × 10?4 m3 s?1) in the channel. Non‐erodible aggregates of three sizes (1–2, 3–5 and 5–10 mm) were released at the inlet of the rill/channel. The number of aggregates received at the outlet was registered. The number and position of the remaining aggregates along the rill/channel were also determined. The rill flow was a major sediment transport mechanism only during the formation of the rill, as during that period the power of the flow was great enough to overcome the influence of the macro‐roughness of the rill bed. At lower discharges the transport capacity in the previously formed rill was significantly less than that in the flat channel under similar slope and discharge. This was determined to be due to local slowing of flow velocities at the exit of rill pools. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

15.
Coarse bed load was sampled in a gravel/cobble bed stream during two major floods in the snowmelt runoff season. The channel is characterized by high rates of bank erosion and, therefore, high rates of sediment supply and bed load flux. Peak discharge reached four times bank‐full, and bed load was sampled at flows 0·7–1·7 times bank‐full. A large aperture bed load sampler (1 m by 0·45 m) captured the largest particles in motion, and specifically targeted the coarse bed load size distribution by using a relatively large mesh (32 mm or D25 of streambed surface size distribution). Bed load flux was highly variable, with a peak value of 0·85 kg/s/m for the coarse fraction above 38 mm. Bed load size distribution and maximum particle size was related to flow strength. Entrainment was size selective for particles D70 and larger (88–155 mm), while particles in the range D30–D70 (35–88 mm) ceased to move at essentially the same flow. Bed load flux was size selective in that coarse fractions of the streambed surface were under‐represented in or absent from the bed load. Painted tracer particles revealed that the streambed surface in the riffles could remain stable even during high rates of bed load transport. These observations suggest that a large proportion of bed load sediments was sourced from outside the riffles. Repeat surveys confirmed major scour and fill in pools (up to 0·75 m), and bank erosion (>2 m), which together contributed large volumes of sediment to the bed load. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

16.
The fractal dimension of an individual floc is a measure of the complexity of its external shape. Fractal dimensions can also be used to characterize floc populations, in which case the fractal dimension indicates how the shape of the smaller flocs relates to that of the larger flocs. The objective of this study is to compare the fractal dimensions of floc populations with those of individual flocs, and to evaluate how well both indicate contributions of sediment sources and reflect the nature and extent of flocculation in streams. Suspended solids were collected prior to and during snowmelt at upstream and downstream sites in two southern Ontario streams with contrasting riparian zones. An image analysis system was used to determine area, longest axis and perimeter of flocs. The area–perimeter relationship was used to calculate the fractal dimension, D, that characterizes the floc population. For each sample, the fractal dimension, Di , of the 28 to 30 largest individual flocs was determined from the perimeter–step‐length relationship. Prior to snowmelt, the mean value of Di ranged from 1·19 (Cedar Creek, downstream) to 1·22 (Strawberry Creek, upstream and downstream). A comparison of the means using t‐tests indicates that most samples on this day had comparable mean values of Di . During snowmelt, there was no significant change in the mean value of Di at the Cedar Creek sites. In contrast, for Strawberry Creek the mean value of Di at both sites increased significantly, from 1·22 prior to snowmelt to 1·34 during snowmelt. This increase reflects the contribution of sediment‐laden overland flow to the sediment load. At three of the sampling sites, the increase in fractal dimensions was accompanied by a decreases in effective particle size, which can be explained by an increase in bed shear stress. A comparison of fractal dimensions of individual flocs in a sample with the fractal dimensions of the floc populations indicates that both fractal dimensions provide similar information about the temporal changes in sediment source contributions, about the contrasting effectiveness of the riparian buffer zones in the two basins, and about the hydraulic conditions in the streams. Nevertheless, determining the individual fractal dimensions of a set of large flocs in a sample is very time consuming. Using fractal dimensions of floc populations is therefore the preferred method to characterize suspended matter. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

17.
The effect of large roughness elements on sand transport efficiency was evaluated on a coastal sand sheet by measuring sand flux with two types of sand traps [Big Spring Number Eight (BSNE) and the Cox Sand Catcher (CSC)] at 30 positions through a 100 m‐long × 50 m‐wide roughness array comprised of 210 elements each with the dimensions 1·17 m long × 0·4 m high × 0·6 m wide. The 210 elements were used to create a roughness density (λ) of 0·022 (λ = n bh/S, where n is the number of elements, b the element breadth, h the element height, and S is the area of the surface that contains all the elements) in an area of 5000 m2. The mean normalized saltation flux (NSF) values (NSF = outgoing sand flux/incoming sand flux) at the furthest downwind distance for the two trap types were 0·44 and 0·41, respectively. This is in excellent agreement with an empirical model prediction of 0·5. The reduction in saltation flux is similar to an earlier separate study for an equivalent λ composed of elements of similar height (0·36 m), even though the roughness element forms were different (rectangular in this study as opposed to circular) as were the horizontal porosity of the arrays (49% versus 16%). This corroborates earlier results that roughness element height is a critical parameter that enhances reduction in sand transport by wind for similar λ configurations. The available data suggest the form of the relationship between transport reduction efficiency and height is likely a power relationship with two limiting conditions: (1) for elements ≤ 0·1 m high the effect is minimized, and (2) as element height matches and then exceeds the maximum height of the saltation layer (≥ 1 m), the effect will stabilize near a maximum of NSF ≈ 0·32. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

18.
This study investigates trends in bed surface and substrate grain sizes in relation to reach‐scale hydraulics using data from more than 100 gravel‐bed stream reaches in Colorado and Utah. Collocated measurements of surface and substrate sediment, bankfull channel geometry and channel slope are used to examine relations between reach‐average shear stress and bed sediment grain size. Slopes at the study sites range from 0·0003 to 0·07; bankfull depths range from 0·2 to 5 m and bankfull widths range from 2 to 200 m. The data show that there is much less variation in the median grain size of the substrate, D50s, than there is in the median grain size of the surface, D50; the ratio of D50 to D50s thus decreases from about four in headwater reaches with high shear stress to less than two in downstream reaches with low shear stress. Similar trends are observed in an independent data set obtained from measurements in gravel‐bed streams in Idaho. A conceptual quantitative model is developed on the basis of these observations to track differences in bed load transport through an idealized stream system. The results of the transport model suggest that downstream trends in total bed load flux may vary appreciably, depending on the assumed relation between surface and substrate grain sizes. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

19.
The morphology of suspended sediment particles reflects the origin of the suspended load and any modifying processes that may have occurred during transport and storage in the aquatic system. The objective of this study was to evaluate the use of four fractal dimensions to quantify visually observed changes in the morphology of fluvial suspended sediment particles during baseflow conditions. Samples were collected during summer low flow in a small stream on the Canadian Prairies. Particle morphology data were obtained with a transmitted light microscope, a CCD camera and an image analysis system. The morphology of the particle population was characterized using four fractal dimensions (D, DK, D1 and D2). D was derived from the area–perimeter relationship and showed an increase from 1·26±0·02 on 30 June, to 1·34±0·02 on 4 July, to 1·42±0·01 on 7 July. Visually, the increase in D represented the formation of large particles with intricate shapes and increased perimeters. DK was determined from the area–rank relationship and varied from 1·86±0·01 on 30 June, to 1·90±0·00 on 4 July, to 1·74±0·00 on 7 July. The decrease in DK between 4 July and 7 July would indicate a greater concentration of the particle area over a small number of large particles. Although the decrease in DK is consistent with observed changes in the particle size distributions, DK should be used with the considerable caution because DK varied more than one standard error between replicates. D1 and D2 were determined from the length–perimeter and length–area relationships, respectively. D1 proved to be of little value for quantifying changes in particle morphology as it showed little change with time, despite considerable visual changes. D2 however, was useful, despite some variation between replicates. Over the sampling period, D2 for the composite data sets showed a steady decrease from 1·74±0·02 on 30 June, to 1·68±0·02 on 4 July, to 1·60±0·01 on 7 July. This change in D2 indicates that, through time, the larger particles became longer and thinner relative to the smaller ones. This study shows that temporal changes in D, DK and D2 were consistent with, and allow quantification of, observed changes in particle morphology. D1 did not reflect observed morphological changes, and is therefore of little value for this type of study. The changes in particle morphology coincided with an increase in primary production in the form of algae. © 1997 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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