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A diffusive process is said to be anomalous if in any given direction the average square of the separation a particle experiences from its origin grows nonlinearly with time. Any diffusive process is anomalous if viewed on a short enough time scale, but interestingly, many diffusive processes remain anomalous over longer times. As a canonical example we study one such process here, diffusion in a laterally-confined nano-film as a function of the strain induced critical point. For this example we motivate and illustrate how a simple but novel process, Brownian motion run with a nonlinear clock (Bm-nlc), statistically mimics trajectories generated via Newton’s force law. The model is easily generalized to more complicated random processes and has application in many fields, including but not limited to, random conductivity field or terrain generation, Richardson turbulence in the atmosphere, and time dependent dispersion in hydrology.  相似文献   

3.
Laboratory experiments were performed with rain of uniform drop size (2·7 mm, 5·1 mm) impacting flows over non‐cohesive beds of uniform sized sand (0·11–0·9 mm) and coal (0·2–0·9 mm) particles with flow velocities (20 mm s?1, 40 mm s?1) that were insufficient for the flow to entrain the particles without the aid of raindrop impact. Measurement of particle travel distance under rain made up of 2·7 mm drops confirmed a theoretical relationship between settling velocity and the distance particles travel after being disturbed by drop impact. Although, in theory, a relationship between settling velocity and particle travel distance exists, settling velocity by itself was unable to account for the effect of changes in both particle size and density on sediment discharge from beds of uniform non‐cohesive material. Particle density was also a factor. Further study of how particle characteristics influence sediment discharge will aid modelling of the impact of the soil in process‐based models of erosion by rain‐impacted flow. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

4.
Laboratory flume experiments were carried out to evaluate the effect of particle density on bedload transport of sand‐sized particles and the effect of a suspended load of clay particles (kaolinite) on bedload transport of sand‐sized particles in rill flow conditions. Three materials in the range 400–600 µm were selected to simulate bedload transport of primary particles and aggregates: sand (2650 kg/m3), crushed brick (2450 kg/m3) and anthracite (1300–1700 kg/m3). In the two first experiments, two different methods were applied to determine bedload transport capacity of coarse particles for various conditions of flow discharge (from 2 to 15 L/min) and slope (2.2, 3 and 4%). In the third experiment, clear water was replaced with kaolinite–water mixture and bedload transport capacity of crushed brick particles was determined for a 4% slope and different concentrations of kaolinite (0, 7, 41 and 84 g/L). The results showed that bedload transport increased significantly with the decrease in particle density but the effect of particle density on transport rates was much less important than flow discharge. Velocity measurements of clear flow, flow mixed with coarse particles and coarse particles confirmed the existence of a differentiation between suspended load and bedload. In these experimental conditions, suspended load of kaolinite did not affect bedload rates of crushed brick particles. Three transport capacity formulae were tested against observed bedload rates. A calibration of the Foster formula revealed that the shear stress exponent should be greater than 1.5. The Low and the Govers unit stream power (USP) equations were then evaluated. The Low equation was preferred for the prediction of bedload rates of primary particles but it was not recommended in the case of aggregates of low density because of the limited experimental conditions applied to derive this equation. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

5.
The movement of sediment through mountain river networks remains difficult to predict, as processes beyond streamflow and particle size are responsible for the entrainment and transport of bedload sediment. In deglaciated catchments, additional complexity arises from glacial impacts on landscape organization. Research to date indicates that the quantity of sediment stored in the channel is an important component of sediment transport in systems which alternate between supply and transport limited states, but limited long-term field data exist which can capture storage-transfer dynamics over a timescale encompassing episodic supply typical of mountain streams. We use a 45-year dataset with annual and decadal-scale data on sediment storage, channel morphology, and wood loading to investigate the spatial and temporal organization of storage in Carnation Creek, a previously glaciated 11 km2 catchment on Vancouver Island, British Columbia. Sediment is supplied episodically to the channel, including additions from debris flows in the early 1980s just upstream of the studied channel region. Analyzing the spatial and temporal organization of sediment storage along 3.0 km of channel mainstem reveals a characteristic storage wavelength similar to the annual bedload particle travel distance. Over time, two scales of variation in storage are observed: small-scale fluctuation of 3–10 years corresponding to local erosional and depositional processes, and larger scale response over 25–35 years related to supply of sediment from hillslopes. Complex relationships between storage and sediment transfer (i.e., annual change in storage) are identified, with decadal-scale hysteresis present in storage-transfer relations in sites influenced by hillslope sediment and logjams. We propose a conceptual model linking landscape organization to temporal variability in storage and to storage–export cycles. Collectively, our results reaffirm the importance of storage to sediment transport and channel morphology, and highlight the complexity of storage–transport interactions. © 2019 John Wiley & Sons, Ltd.  相似文献   

6.
Tracer studies are a commonly used tool to develop and test Einstein-type stochastic bedload transport models. The movements of these tracers are controlled by many factors including grain characteristics, hydrologic forcing, and channel morphology. Although the influence of these sediment storage zones related to morphological features (e.g., bars, pools, riffles) have long been observed to “trap” bedload particles in transport, this influence has not been adequately quantified. In this paper we explore the influence of channel morphology on particle travel distances through the development of a Bayesian survival process model. This model simulates particle path length distributions using a location-specific “trapping probability” parameter (pi ), which is estimated using the starting and ending locations of bedload tracers. We test this model using a field tracer study from Halfmoon Creek, Colorado. We find that (1) the model is able to adequately recreate the observed multi-modal path length distributions, (2) particles tend to accumulate in trapping zones, especially during large floods, and (3) particles entrained near a trapping zone will travel a shorter distance than one that is further away. Particle starting positions can affect path lengths by as much as a factor of two, which we confirm by modelling “starting-location-specific” path length probability distributions. This study highlights the importance of considering both tracer locations and channel topography in examinations of field tracer studies. © 2020 John Wiley & Sons, Ltd.  相似文献   

7.
It is important to evaluate bedload discharge and temporal changes of the bed surface, and bed deformation can be estimated during floods if the bedload discharge is properly evaluated in an arbitrary cross‐section. With the exception of grain size and its distribution within the bedload, bedload discharge has been measured using both direct and indirect methods. Bedload slot is a direct method but cannot be used to measure bedload during a flood because of volume limitations. Indirect methods require correlation between the signals and sediment volume measured using another method. In the present study, a small, automatically recording bedload sensor with an iron plate and a pair of load cells is developed in order to evaluate not only large particles but also sand particles as bedload. Bedload mass is calculated by integrating with respect to both the velocity of sediment particles and the averaged particle weight as measured by a pair of load cells, and, as an example, the velocity is estimated by the cross‐correlation function of weights measured by load cells. The applicability of the proposed sensor is discussed based on the results of flume tests in the laboratory (2014) and the observation flume of the Hodaka Sedimentation Observatory of Kyoto University in Japan (2015). The system was installed in the observation flume in November of 2012, and flume data were obtained using natural sediment particles. In particular, it was difficult to estimate the velocity of averaged bedload particles, and it was better to apply a cross‐correlation function in the laboratory tests. However, it appears that the previous estimation can estimate these velocities in the observation flume using a connecting tube and submerged load‐cell systems. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

8.
It has generally been assumed that diffusive sediment transport on soil‐mantled hillslopes is linearly dependent on hillslope gradient. Fieldwork was done near Santa Barbara, California, to develop a sediment transport equation for bioturbation by the pocket gopher (Thomomys bottae) and to determine whether it supports linear diffusion. The route taken by the sediment is divided into two parts, a subsurface path followed by a surface path. The first is the transport of soil through the burrow to the burrow opening. The second is the discharge of sediment from the burrow opening onto the hillslope surface. The total volumetric sediment flux, as a function of hillslope gradient, is found to be: qs (cm3 cm−1 a−1) = 176(dz/dx)3 − 189(dz/dx)2 + 68(dz/dx) + 34(dz/dx)0·4. This result does not support the use of linear diffusion for hillslopes where gopher bioturbation is the dominant mode of sediment transport. A one‐dimensional hillslope evolution program was used to evolve hillslope profiles according to non‐linear and linear diffusion and to compare them to a typical hillslope. The non‐linear case more closely resembles the actual profile with a convex cap at the divide leading into a straight midslope section. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

9.
Using the 160‐m‐long flume at Tsukuba University we undertook an experiment to provide a first estimate of the virtual velocity of sand in the size range 0.5–2.0 mm. For the flow velocity used in our experiment this sediment‐size range would conventionally be regarded as suspended sediment. The virtual velocity was found to be 37–41% of the flow velocity. Paradoxically, virtual velocity decreases as particle size decreases. Such a lower virtual velocity of finer sediment is not inconceivable. First, trapping of the sediment appears to be a function of bed roughness, and there is a probable relationship between bed roughness and trapping efficiency for particles of different sizes. Second, finer particles are more likely to find sheltered positions on a rough bed and thus experience lower mobility, relative to the more exposed coarser grains, as observed for bedload transport. Third, the virtual velocity of particles undergoing bedload transport has been found, in some instances, to be lower for finer clasts. We combine our data with previous studies of virtual velocity of bedload to develop, for the first time, a hypothesis for a holistic analysis of sediment movement in rivers. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

10.
Field data are essential in evaluating the adequacy of predictive equations for sediment transport. Each dataset based on the sediment transport rates and other relevant information gives an increased understanding and improved quantification of different factors influencing the sediment transport regime in the specific environment. Data collected for 33 sites on 31 mountain streams and rivers in Central Idaho have enabled the analysis of sediment transport characteristics in streams and rivers with different geological, topographic, morphological, hydrological, hydraulic, and sedimentological characteristics. All of these streams and rivers have armored, poorly sorted bed material with the median particle size of surface layer coarser than the subsurface layer. The fact that the largest particles in the bedload samples did not exceed the median particle size of the bed surface material indicates that the armor layer is stable for the observed flow discharges (generally bankfull or less, and in some cases two times higher than bankfull discharge). The bedload transport is size‐selective. The transport rates are generally low, since sediment supply is less than the ability of flow to move the sediment for one range of flow discharges, or, the hydraulic ability of the stream is insufficient for entrainment of the coarse bed material. Detailed analyses of bedload transport rates, bedload and bed material characteristics were performed for each site. The obtained results and conclusions are used to identify different influences on bedload transport rates in analyzed gravel‐bed rivers. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

11.
The composition, grain‐size, and flux of stream sediment evolve downstream in response to variations in basin‐scale sediment delivery, channel network structure, and diminution during transport. Here, we document downstream changes in lithology and grain size within two adjacent ~300 km2 catchments in the northern Rocky Mountains, USA, which drain differing mixtures of soft and resistant rock types, and where measured sediment yields differ two‐fold. We use a simple erosion–abrasion mass balance model to predict the downstream evolution of sediment flux and composition using a Monte Carlo approach constrained by measured sediment flux. Results show that the downstream evolution of the bed sediment composition is predictably related to changes in underlying geology, influencing the proportion of sediment carried as bedload or suspended load. In the Big Wood basin, particle abrasion reduces the proportion of fine‐grained sedimentary and volcanic rocks, depressing bedload in favor of suspended load. Reduced bedload transport leads to stronger bed armoring, and coarse granitic rocks are concentrated in the stream bed. By contrast, in the North Fork Big Lost basin, bedload yields are three times higher, the stream bed is less armored, and bed sediment becomes dominated by durable quartzitic sandstones. For both basins, the geology‐based mass balance model can reproduce within ~5% root‐mean‐square error the composition of the bed substrate using realistic erosion and abrasion parameters. As bed sediment evolves downstream, bedload fluxes increase and decrease as a function of the abrasion parameter and the frequency and size of tributary junctions, while suspended load increases steadily. Variable erosion and abrasion rates produce conditions of variable bed‐material transport rates that are sensitive to the distribution of lithologies and channel network structure, and, provided sufficient diversity in bedrock geology, measurements of bed sediment composition allow for an assessment of sediment source areas and yield using a simple modeling approach. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

12.
Depth profiles of particle streamwise velocity, concentration and bedload sediment transport rate were measured in a turbulent and supercritical water flow. One‐size 6 mm diameter spherical glass beads were transported at equilibrium in a two‐dimensional 10% steep channel with a mobile bed. Flows were filmed from the side by a high‐speed camera. Particle tracking algorithms made it possible to determine the position, velocity and trajectory of a very large number of particles. Approximately half of the sediment transport rate was composed by rolling grains, and the other half by saltation. This revealed a complex structure, with several concentration and flux peaks due to rolling, and one peak due to saltation. With an increase of the sediment transport rate, the depth structure remained the same at the water/granular interface, with peak value increases but with no shift in elevations. The saltation region expanded towards higher elevations with an increase of the particle velocity commensurate to the water velocity. The proportion of the sediment transport rate in saltation did not vary significantly. The particle streamwise velocity profiles exhibited three segments: an exponential decay in the bed, a linear increase where rolling and saltation co‐existed, and above this, a logarithmic‐like shape due to saltating particles. These results are comparable to profiles measured and modelled in dry granular free surface flows and in more intense bedload such as sheet flows. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

13.
A two‐dimensional simulation model of travel distances of individual particles in a gravel‐bed river is presented. The model is based on a number of rules, which include particle size, entrainment, trajectory, distance of movement and entrapment. Particle interactions are controlled by resistance fields defined about each obstacle and critical elevation defined in the model. Resistance fields, particle dropping and critical elevation rules control particle interactions. The interaction rules cause the particles to develop pebble clusters, stone cells and transverse structures (transverse ribs). The simulated travel distances of individual particles are consistent with reported field results. Individual particle travel distances were simulated using two different models; one without interactions between the individual particles and the stationary bed and one with interactions. The case without interactions demonstrates the random nature of sediment transport, and narrow ranges of travel distances. Wider ranges of travel distances, similar to those for natural situations, were obtained for the cases with interactions. The more intense the interaction between the mobile stones and the stationary ones, the wider the range of distances of travel for a given particle size. Modelling the mean travel distance yielded a result similar to that published previously, which was based on empirical data. Well developed bed‐surface structures were obtained for relatively poorly sorted sediment with intense interactions between particles. Transverse structures developed when relatively large particles were allowed to move. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

14.
Sediment transport during flood events often reveals hysteretic patterns because flow discharge can peak before (counterclockwise hysteresis) or after (clockwise hysteresis) the peak of bedload. Hysteresis in sediment transport has been used in the literature to infer the degree of sediment availability. Counterclockwise and clockwise hysteresis have been in fact interpreted as limited and unlimited sediment supply conditions, respectively. Hysteresis has been mainly explored for the case of suspended sediment transport, but it was rarely reported for bedload transport in mountain streams. This work focuses on the temporal variability of bedload transport in an alpine catchment (Saldur basin, 18.6 km2, Italian Alps) where bedload transport was monitored by means of an acoustic pipe sensor which detects the acoustic vibrations induced by particles hitting a 0.5m‐long steel pipe. Runoff dynamics are dominated by snowmelt in late spring/early summer, mostly by glacier melt in late summer/early autumn, and by a combination of the snow and glacier melt in mid‐summer. The results indicate that hysteretic patterns during daily discharge fluctuations are predominantly clockwise during the snowmelt period, likely due to the ready availability of unpacked sediments within the channel or through bank erosion in the lower part of the basin. On the contrary, counterclockwise hysteresis tend to be more frequent during late glacier melting period, possibly due to the time lag needed for sediment provided by the glacial and peri‐glacial area to be transported to the monitoring section. However, intense rainfall events occurring during the glacier melt period generated predominantly clockwise hysteresis, thus indicating the activation of different sediment sources. These results indicate that runoff generation processes play a crucial role on sediment supply and temporal availability in mountain streams. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

15.
Several methods were employed in the Ardennian rivers (Belgium) to determine the depth of the active layer mobilized during floods and to evaluate the bedload discharge associated with these events. The use of scour chains has shown that the depth of the active layer is systematically less than the b‐axis of the average particle size (D50) of the elements which compose the surface layer of the riffles. This indicates that only a partial transport exists during low magnitude floods. The bedload discharge has been evaluated by combining data obtained using the scour chains technique and the distance covered by tracers. Quantities of sediment transported during frequent floods are relatively low (0·02 t km–2) due to the armour layer which protects the subsurface material. These low values are also related to the fact that the distance calculated for mobilized bedload only applies to tracers fitted with PIT (passive integrated transponder)‐tags (diameter > 20 mm), whereas part of the bedload discharge is composed of sand and fine gravel transported over greater distances than the pebbles. The break‐up of the armour layer was observed only once, for a decennial discharge. During this event, the bedload discharge increased considerably (2 t km–2). The use of sediment traps, data from dredging and a Helley–Smith sampler confirm the low bedload transport in Ardennian rivers in comparison to the bedload transport in other geomorphological contexts. This difference is explained by the presence of an armoured layer but also by the imbricated structures of flat bed elements which increase the resistance to the flow. Finally, the use of the old iron industry wastes allowed to quantify the thickness of the bed reworked over the past centuries. In the Lembrée River, the river‐bed contains slag elements up to a depth of about 50 cm, indicating that exceptional floods may rework the bed to a considerable depth. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

16.
It is widely recognized nowadays that there are at least two different phases of bedload sediment transport in gravel‐bed rivers. However, the transition between these phases is still poorly or subjectively defined, especially at bends in rivers, where cross‐stream sediment transport can strongly influence changes in the texture of the transported sediment. In this paper, we use piecewise models to identify objectively, at two points in the cross‐section of a river bend, the discharge at which the transition between bedload transport phases occurs. Piecewise models were applied to a new bedload data set collected during a wide range of discharges while analysing the associated changes in sediment texture. Results allowed the identification of two well‐differentiated phases of sediment transport (phase I and phase II), with a breakpoint located around bankfull discharge. Associated with each phase there was a change in bedload texture. In phase I there was non‐dominance in the transport of fine or coarse fractions at a particular sampling point; but in phase II bedload texture was strongly linked to the position of the sampling point across the channel. In this phase, fine particles tended to be transported to the inner bank, while coarse sizes were transferred throughout the middle parts of the channel. Moreover, bedload texture at the inner sampling point became bimodal while the transport of pebble‐sized particles was increasing in the central parts of the river channel. It is suggested that this general pattern may be related both to secondary currents, which transfer finer particles from the outer to the inner bank, and to the progressive dismantling of the riverbed surface layer. Copyright © 2018 John Wiley & Sons, Ltd.  相似文献   

17.
In the Erlenbach stream, a pre‐alpine steep channel in Switzerland, sediment transport has been monitored for more than 25 years. Near the confluence with the main valley river, stream flow is monitored and sediment is collected in a retention basin with a capacity of about 2000 m3. The basin is surveyed at regular intervals and after large flood events. In addition, sediment transport has been continuously monitored with piezoelectric bedload impact and geophone sensors since 1986. In 2008–2009, the measuring system in the Erlenbach stream was enhanced by installing an automatic system to obtain bedload samples. Movable metal baskets are mounted on a rail at the downstream wall of the large check dam above the retention basin, and they can be moved automatically into the flow to take bedload transport samples. The wire mesh of the baskets has a spacing of 10 mm to sample all sediment particles coarser than this size (which is about the limiting grain size detected by the geophones). The upgraded measuring system permits to obtain bedload samples over short sampling periods and to measure the grain size distribution of the transported material and its variation over time and with discharge. The analysis of calibration relationships for the geophone measuring system confirms findings from very similar measurements which were performed until 1999 with piezoelectric bedload impact sensors; there is a linear relationship between impulse counts and bedload mass passing over the sensors. Findings from flume experiments are used to discuss the most important factors which affect the calibration of the geophone signal. The bedload transport rates as measured by the moving baskets are among the highest measured in natural streams, with values of the order of several kilograms per meter per second. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

18.
The Rouse formula and its variants have been widely used to calculate the steady-state vertical concentration distribution for suspended sediment in steady sediment-laden flows, where the diffusive flux is assumed to be Fickian. Turbulent flow, however, exhibits fractal properties, leading to non-Fickian diffusive flux for sediment particles. To characterize non-Fickian dynamics of suspended sediment, the current study proposes a Hausdorff fractal derivative based advection-dispersion equation(H...  相似文献   

19.
We report bedload data and acoustic impulse measurements due to particle impact from the Pitzbach in Austria. Impulse counts can be viewed as a measure of the energy delivered to the bed by moving particles. Impulse counts show a large scatter even for the same discharge and bedload supply. This scatter is due to varying grain size distribution, grain shape, mode of transport of the sediment particles and spatial and temporal distribution of the sediment load. The mean impulse count at given hydraulic conditions may increase or decrease with increasing sediment supply, suggesting that both tools and cover effects are active on the channel bed. Dependent on the local balance between sediment supply and transport capacity, either effect may be dominant at different locations along the cross‐section at the same time. Furthermore, the same bed location may respond to increasing sediment supply as tools‐dominated at some discharges and cover‐dominated at other discharges. Our observations may have implications for modelling of bedrock erosion in landscape evolution models and of bedrock channel morphology. Erosion models that do not incorporate both tools and cover effects are not sufficient to describe observations. Furthermore, a local erosion law cannot in general be used to describe erosion averaged over the channel cross‐section. The changing balance between sediment supply and transport capacity with increasing discharge highlights that a single representative discharge is not sufficient to capture the full erosion dynamics. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

20.
Modeling of suspended sediment particle movement in surface water can be achieved by stochastic particle tracking model approaches.In this paper,different mathematical forms of particle tracking models are introduced to describe particle movement under various flow conditions,i.e.,the stochastic diffusion process,stochastic jump process,and stochastic jump diffusion process.While the stochastic diffusion process can be used to represent the stochastic movement of suspended particles in turbulent flows,the stochastic jump and the stochastic jump diffusion processes can be used to describe suspended particle movement in the occurrences of a sequence of extreme flows.An extreme flow herein is defined as a hydrologic flow event or a hydrodynamic flow phenomenon with a low probability of occurrence and a high impact on its ambient flow environment.In this paper,the suspended sediment particle is assumed to immediately follow the extreme flows in the jump process(i.e.the time lag between the flow particle and the sediment particle in extreme flows is considered negligible).In the proposed particle tracking models,a random term mainly caused by fluid eddy motions is modeled as a Wiener process,while the random occurrences of a sequence of extreme flows can be modeled as a Poisson process.The frequency of occurrence of the extreme flows in the proposed particle tracking model can be explicitly accounted for by the Poisson process when evaluating particle movement.The ensemble mean and variance of particle trajectory can be obtained from the proposed stochastic models via simulations.The ensemble mean and variance of particle velocity are verified with available data.Applicability of the proposed stochastic particle tracking models for sediment transport modeling is also discussed.  相似文献   

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