normal and anomalous diffusion of gravel tracer particles in rivers received 12 december 2008 revised 16 november 2009 accepted 10 december 2009 published 4 may 2010 1 one way to study the mechanism of gravel bed load transport is to seed the bed with marked gravel tracer particles within a chosen patch and to follow the pattern of migration and dispersal of particles from this patch in this study we invoke the probabilistic exner equation for sediment conservation of bed gravel formulated in terms of the difference between the rate of entrainment of gravel into motion and the rate of deposition from motion assuming an active layer formulation stochasticity in particle motion is introduced by considering the step length distance traveled by a particle once entrained until it is deposited as a random variable for step lengths with a relatively thin e g exponential tail the above formulation leads to the standard advection diffusion equation for tracer dispersal however the complexity of rivers characterized by a broad distribution of particle sizes and extreme flood events can give rise to a heavy tailed distribution of step lengths this consideration leads to an anomalous advection diffusion equation involving fractional derivatives by identifying the probabilistic exner equation as a forward kolmogorov equation for the location of a randomly selected tracer particle a stochastic model describing the temporal evolution of the relative concentrations is developed the normal and anomalous advection diffusion equations are revealed as its long time asymptotic solution sample numerical results illustrate the large differences that can arise in predicted tracer concentrations under the normal and anomalous diffusion models they highlight the need for intensive data collection efforts to aid the selection of the appropriate model in real rivers

experiments on saltation of sand in water a high speed video system was used to study saltation of sand in an open channel flow high rates of image acquisition provided the information needed to resolve details of the lagrangian properties of particle motion saltation of sand is described in terms of statistical properties of particle trajectories such as mean values and standard deviations of saltation length height and streamwise particle velocity results are compared with available empirical data saltation height seems to be independent of particle size when made dimensionless with the particle diameter however the dimensionless saltation length appears to increase as the particle size decreases particle collision with the bed is also analyzed observations of this process indicate that most of the interactions between saltating particles and the bed are of the collision rebound type which contradicts previous discussions on the subject the estimated value of the dynamic friction coefficient is about half that proposed by bagnold i

the cause of advective slowdown of tracer pebbles in rivers implementation of exner based master equation for coevolving streamwise and vertical dispersion tracer pebbles are often used to study bed load transport processes in gravel bed rivers models have been proposed for their downstream dispersion and also for vertical dispersion but not for the combined effects of downstream and vertical movement here we use the exner based master equation to characterize the transient coevolution of streamwise and vertical advection diffusion of tracer pebbles under equilibrium transport conditions no net aggradation or degradation the coevolution of streamwise and vertical dispersion gives rise to behavior that can differ markedly from that associated with purely streamwise processes with no vertical exchange one example is streamwise advective slowdown particles that are advected downward into zones where the probability of reentrainment becomes asymptotically small are essentially trapped and can no longer participate in streamwise advection as a result the mean streamwise velocity of the tracer plume declines in time qualitative and quantitative comparisons with two field experiments show encouraging agreement despite the simplified boundary conditions in the model

flow pattern and sediment transport in a braided river the torrent de st pierre french alps summary in order to bring some understanding on the mountain stream dynamics we report measurements of flow and sediment transport leveled in a proglacial gravel bed river the torrent de st pierre in the french alps the river exhibits a modest discharge 3 s during most of the glacier melting season a braiding plain developed thanks to the occurrence of a massive landslide providing a small and simplified study area quite similar to recent experimental studies a mass balance was established at the outlet of the braiding plain our measurements indicate that in the range of flows measured the dominating transport mode is suspension though less important bed load transport is far from being negligible dissolved load eventually appears to be very small compared to solid transport analysis of velocity profile measurements shows that in this highly turbulent and shallow stream the use of a logarithmic form fails to recover the velocity profile and to estimate the shear velocity of the flow a uniform chezy like relationship is shown to be valid for the velocity with friction a coefficient considered as constant over the range of our measurements accordingly the only relevant velocity for transport description is the average velocity coupled measurements of bed load and velocity show that bed load transport is related to the average velocity through a power law eventually a correlation between bed load transport and suspended load transport is evidenced and discussed

bedload transport of a bimodal sediment bed 1 despite several decades of investigations accounting for the effect of the wide range of grain sizes composing the bed of rivers on bedload transport remains a challenging problem we investigate this problem by studying experimentally the influence of grain size distribution on bedload transport in the simple configuration of a bimodal sediment bed composed of a mixture of 2 populations of quartz grains of sizes d1 0 7 0 1 mm and d2 2 2 0 4 mm respectively the experiments are carried out in a tilted rectangular flume inside which the sediment bed is sheared by a steady and spatially uniform turbulent flow using a high speed video imaging system we focus on the measurement of the average particle velocity and the surface density of moving particles defined as the number of moving particles per unit surface of the bed these two quantities are measured separately for each population of grains as a function of the dimensionless shear stress or shields number and the fraction of the bed surface covered with small grains we show that the average velocity and the surface density of moving particles obey the same equations as those reported by lajeunesse et al 2010 for a bed of homogeneous grain size once in motion the grains follow therefore similar laws whether the bed is made of uniform sediment or of a bimodal mixture this suggests that the erosion deposition model established by lajeunesse et al 2010 for a bed of uniform sediment can be generalized to the case of a bimodal one the only difference evidenced by our experiments concerns the critical shields number for incipient sediment motion above a uniform sediment bed the latter depends on the particle reynolds number through the shields curve in the case of a bimodal bed our experiments show that the critical shields numbers of both populations of grains decrease linearly with the fraction of the bed surface covered with small grains we propose a simple model to account for this observation

sedimentary bed evolution as a mean reverting random walk implications for tracer statistics sediment tracers are increasingly employed to estimate bed load transport and landscape evolution rates tracer trajectories are dominated by periods of immobility waiting times as they are buried and reexcavated in the stochastically evolving river bed here we model bed evolution as a random walk with mean reverting tendency ornstein uhlenbeck process originating from the restoring effect of erosion and deposition the ornstein uhlenbeck model contains two parameters a and b related to the particle feed rate and range of bed elevation fluctuations respectively observations of bed evolution in flume experiments agree with model predictions in particular the model reproduces the asymptotic t 1 tail in the tracer waiting time exceedance probability distribution this waiting time distribution is similar to that inferred for tracers in natural gravel streams and avalanching rice piles indicating applicability of the ornstein uhlenbeck mean reverting model to many disordered transport systems with tracer burial and excavation

displacement characteristics of coarse fluvial bed sediment 1 previous work highlights the need for data collection to identify appropriate models for temporal evolution of tracer dispersal in rivers results of 64 gravel bed field tracer experiments covering a wide range of flow and sediment supply regimes are compiled here to determine the probabilistic character of gravel transport we focus on whether particle travel distances and waits are thin or heavy tailed while heavy tailed travel distance distributions are observed between successive monitoring events in different hydrological and sediment supply regimes heavy tailedness does not persist through total travel distance over multiple monitoring events suggesting that individual monitoring events occur before particle travel distance exceeds the characteristic correlation length for the channel such that particles that start in fast paths remain in fast paths and particles in slow paths remain in slow paths after a large number of transport events super diffusive spreading was not observed at any of the gravel bed streams continuous time tracking of x y z coordinates of tracers in natural streams is necessary to capture exact step and waiting time distributions

using lagrangian particle saltation observations for bedload sediment transport modelling a lagrangian model for the saltation of sand in water is proposed simulated saltation trajectories neglecting particle rotation and turbulence effects compare fairly well with experimental observations the model for particle motion is coupled with a stochastic model for particle collision with the bed such that a number of realizations of the saltation process can be simulated numerically model predictions of mean values and standard deviations of saltation height length and streamwise particle velocity agree fairly well with experimental observations model predictions of the dynamic friction coefficient are also in good agreement with experimental observations but they underestimate the value of 0 63 proposed by bagnold for this coefficient the saltation model is applied to the estimation of bedload transport rates of sand using a bagnoldean formulation modelled values of the bedload transport rates overestimate those predicted by commonly used bedload formulae which appears to be a consequence of problems in the definition of the dynamic friction coefficient these results seem to indicate a few problems with the bagnoldean formulation particularly regarding the continuum assumption for the bedload layer which would be valid only for very high particle concentrations and small particle diameters and also regarding the evaluation of the shear stress exerted on the bed by the saltating particles 1998 john wiley sons ltd

back to einstein burial induced three range diffusion in fluvial sediment transport individual grains move through gravel bed rivers in cycles of motion and rest with variable characteristics so tracer grains spread apart as they transport downstream in a type of diffusion exper

bedload entrainment travel lengths step lengths rest periods studied with passive iron magnetic and active radio tracer techniques this paper reports results from bedload transport investigations with active radio and passive iron magnetic tracers in the lainbach a step pool mountain river in bavaria southern germany the spatial distributions of the iron tracers after flood events can be best described by exponential or gamma distributions there is some indication of a tendency of size selective transport of the iron tracers but there is also a considerable amount of scatter in the correlations between weight size and travel length owing to the masking influence of other variables such as the shape of the particles and different positions in the river bed the experiments with artificial magnetic tracers showed that elongated pebbles rods had the longest mean transport distance platy ones discs remained relatively close to the starting points the particles from the pool showed the greatest transport lengths and a 100 per cent chance of being eroded the pebble transmitter system petsy consists of transmitters implanted into individual pebbles a computerized receiver a stationary antenna system with an antenna switchboard and a data logging system the particles do not move continuously but in a series of transport steps and non movement intervals a single value for a given size class is not adequate to describe the critical conditions of entrainment under natural circumstances a probability approach is much more suitable the critical unit discharges total discharge divided by active channel width along the measuring reach are dependent on river bed morphology in the steps bedload needs higher unit discharges to be entrained once entrained the transport of bedload is stochastic in nature and the single particle transport is controlled by the step lengths and the duration of rest periods the distributions of both parameters can be approximated by exponential functions applying the stochastic concept proposed by einstein the mean values of the random variables step length and duration of rest period measured with the petsy technique were used for the simulation of spatial distributions of bedload particles from point sources more field and laboratory data are needed to include varying flow and roughness conditions with tracers representing different particle characteristics

numerical simulation of turbulence and sediment transport of medium sand a model of sand transport in water is produced by combining a turbulence resolving large eddy simulation les with a discrete element model dem prescribing the motion of individual grains of medium sand the momentum effect of each particle on the fluid is calculated at the les cell containing the particle and the fluid velocity and pressure interpolated to each particle center is used to derive fluid force on each particle in the dem eleven numerical experiments are conducted of an initially flat bed of particles the experiments span a range of motion from essentially no motion to vigorous suspension hydraulic roughness is found to increase abruptly at the transition from bed load to suspended load transport suspended sediment extracts momentum from the flow and decreases the rate of shear whereas slightly higher in the flow vertical drag by suspended grains damps turbulence and increases the rate of shear vertical sediment diffusivity and effective particle settling velocity are much smaller than is commonly assumed in suspended sediment models the bed load experiments suggest that saltation by itself is a poor model of bed load sand transport in contrast to expectations from saltation models the peak bed load flux occurs at essentially the same level as the bed and grains move slowly in frequent contact with other grains higher and faster moving bed load grains that can be considered to be in saltation represent a smaller portion of the total flux entrainment of bed load grains occurs in response to fluid penetration of the bed by high vorticity turbulence structures embedded within broader high speed fluid regions referred to as a sweeps or high speed wedges

coupled dynamics of the co evolution of gravel bed topography flow turbulence and sediment transport in an experimental channel a series of flume experiments were conducted in a large experimental channel at the st anthony falls laboratory to understand the coupled dynamics of flow and bed forms above the sediment water interface simultaneous high resolution measurements of velocity fluctuations bed elevations and sediment flux at the downstream end of the channel were made for a range of discharges the probability density functions pdfs of bed elevation increments and instantaneous reynolds stress reveal a power law tail behavior and a wavelet cross correlation analysis depicts a strong dependence of these series across a range of scales indicating a feedback between bed form dynamics and near bed turbulence these results complement our previous findings in which the signature of bed form evolution on the near bed velocity fluctuations was confirmed via the presence of a spectral gap and two distinct power law scaling regimes in the spectral density of velocity fluctuations we report herein a strong asymmetry in the probability distribution of bed elevation increments and instantaneous reynolds stresses the latter being further analyzed and interpreted via a quadrant analysis of velocity fluctuations in the longitudinal and vertical directions we also report the presence of intermittency multifractality in bed elevation increments and interpret it in view of the asymmetric nature of the pdfs as the result of scale coupling in other words the geometric asymmetry at the bed form scale gets transferred down to a probabilistic asymmetry at all smaller scales indicating a local anisotropy in the energy transfer finally we propose a predictive relationship between bed form averaged sediment transport rates and bed form averaged instantaneous reynolds stress and validate it using our experimental data

radio tracking gravel particles in a large braided river in new zealand a field test of the stochastic theory of bed load transport proposed by einstein 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

introduction to special section on stochastic transport and emergent scaling on earth s surface rethinking geomorphic transport stochastic theories broad scales of motion and nonlocality 1 in many geomorphic transport systems the time and length scales of motion vary widely particles can be trapped for both short and long periods of time and they can travel large or small distances in very short intervals of time to model such systems we need fresh conceptual and mathematical formalisms the goal of this collection of papers is to challenge existing thinking in geomorphic transport by putting forward new ideas and theories for environmental fluxes from particle transport in a single stream to landslide debris mobilization sediment and water transport on hillslopes dynamic transport on river networks and interpretation of sedimentary deposits over geologic time advanced stochastic theories of transport are proposed the notion of nonlocal flux is introduced and fractional advection diffusion equations are explored as possible models of geomorphic transport

experiments on dispersion of tracer stones under lower regime plane bed equilibrium bed load transport 1 a common approach for estimating the bed load transport rate in gravel bed streams is to relate it to deterministic channel averaged driving parameters and corresponding resistance properties of the bed material notwithstanding the proven success of this approach in modeling various morphodynamic scenarios it does not contain the mechanics necessary to relate the bulk sediment transport rate to the displacement patterns of individual particles experiments on entrainment transport and deposition of tracer stones in a flume described here were designed to address this issue predictors of statistics of bed elevation fluctuations at short timescales total and elevation specific particle entrainment rates particle step lengths mean and associated probability density function for particle virtual velocity and thickness of the active layer were developed the working hypothesis tested in this paper is that the statistics of tracer displacements can be related to channel averaged hydraulic parameters and thus linked to macroscopic aspects of bed load transport

analyzing and modeling sub diffusive transport of bedload along a heterogeneous gravel bed using stochastic and statistical methods abstract bedload transport is one of the main mechanisms for sediment transport in rivers bedload transport may exhibit anomalous dispersion behavior during the formation of clusters on the surface of a heterogeneous river bed which cannot be quantified by the classical fick s law of diffusion this study simplifies the complex bedload transport process to a mass spring damper system which can describe the cluster formation process based on the observed cluster geometry the simulation results are consistent with the morphology of clusters extracted from the experimental gravel bed in our flume the level of spatial heterogeneity of individual clusters is characterized to distinguish the planform morphology of each cluster based on estimation of the hausdorff besicovitch dimension of the cluster area trapping of sediment particles during bedload transport on a heterogeneous gravel bed is quantified using a random walk approach and the birth death emigration immigration markov process sub diffusive dynamics of bedload transport is also modeled simultaneously using the langevin equation that defines statistical properties of bedload sediments further analysis indicates that the microscopic stochastic langevin equation relates to a macroscopic deterministic equation according to the continuous time random walk ctrw theory

statistics of bedload transport over steep slopes separation of time scales and collective motion steep slope streams show large fluctuations of sediment discharge across several time scales these fluctuations may be inherent to the internal dynamics of the sediment transport process a probabilistic framework thus seems appropriate to analyze such a process in this paper we present an experimental study of bedload transport over a steep slope flume for small to moderate shields numbers the sampling technique allows the acquisition of high resolution time series of the solid discharge the resolved time scales range from 10 1 s up to 105 s we show that two distinct time scales can be observed in the probability density function for the waiting time between moving particles we make the point that the separation of time scales is related to collective dynamics proper statistics of a markov process including collective entrainment are derived the separation of time scales is recovered theoretically for low entrainment rates

gondwanatheria and multituberculata mammalia from the late cretaceous of madagascar in addition to four isolated mammalian teeth from the late cretaceous maastrichtian of madagascar described previously and allocated to gondwanatheria marsupialia and mammalia incertae sedis here i put on record five more specimens four of these a virtually complete lower molariform cheek tooth two fragmentary cheek teeth and a fragmentary lower incisor are referred to the sudamericidae gondwanatheria the internal structure of the hypsodont cheek teeth as revealed by micro computed tomography scans to simulate different stages of wear is highly variable limited knowledge of intra individual morphological and size variability in the dentition of sudamericids which are known almost exclusively from isolated teeth precludes a conclusive assessment of whether some or all of the new specimens belong to lavanify miolaka the only previously described sudamericid from madagascar or to a new taxon conservatively therefore pending the recovery of better material all four specimens are referred to sudamericidae gen et sp indet the fifth specimen a molar fragment is tentatively allocated to the multituberculata thereby adding to the controversial specimens that comprise the very sparse and questionable record of this clade on the southern supercontinent gondwana the new specimens do not provide any profound insight into the origins of the highly endemic and imbalanced extant mammalian fauna on madagascar rather they provide only more negative evidence like those previously described they do not represent the basal stocks of any of the five mammalian clades that live on the island today and therefore further support the growing consensus that representatives of the extant clades arrived in the cenozoic

experiments on particle turbulence interactions in the near wall region of an open channel flow implications for sediment transport a high speed video system was used to study the interaction between sediment particles and turbulence in the wall region of an open channel flow with both smooth and transitionally rough beds in smooth flows particles immersed within the viscous sublayer were seen to accumulate along low speed wall streaks apparently due to the presence of quasi streamwise vortices in the wall region larger particles did not tend to group along streaks however their velocity was observed to respond to the streaky structure of the flow velocity in the wall region in transitionally rough flows particle sorting was not observed coherent flow structures in the form of shear layers typically observed in the near wall region interacted with sediment particles lying on the channel bottom resulting in the particles being entrained into suspension although there has been some speculation that this process would not be effective in entraining particles totally immersed in the viscous sublayer the results obtained demonstrate the opposite the entrainment mechanism appears to be the same independent of the roughness condition of the bottom wall smooth or transitionally rough in the latter case however hiding effects tend to preclude the entrainment of particles with sizes finer than that of the roughness elements the analysis of particle velocity during entrainment shows that the streamwise component tends to be much smaller than the local mean flow velocity while the vertical component tends to be much larger than the local standard deviation of the vertical flow velocity fluctuations which would indicate that such particles are responding to rather extreme flow ejection events

direct numerical simulation of bedload transport using a local dynamic boundary condition temporally and spatially averaged models of bedload transport are inadequate to describe the highly variable nature of particle motion at low transport stages the primary sources of this variability are the resisting forces to downstream motion resulting from the geometrical relation pocket friction angle of a bed grain to the grains that it rests upon variability of the near bed turbulent velocity field and the local modification of this velocity field by upstream protruding grains a model of bedload transport is presented that captures these sources of variability by directly integrating the equations of motion of each particle of a simulated mixed grain size sediment bed experimental data from the velocity field downstream and below the tops of upstream protruding grains are presented from these data an empirical relation for the velocity modification resulting from upstream grains is provided to the bedload model the temporal variability of near bed turbulence is provided by a measured near bed time series of velocity over a gravel bed the distribution of pocket friction angles results as a consequence of directly calculating the initiation and cessation of motion of each particle as a result of the combination of fluid forcing and interaction with other particles calculations of bedload flux in a uniform boundary and simulated pocket friction angles agree favourably with previous studies

probability distributions of particle hop distance and travel time over equilibrium mobile bedforms the joint probability distribution of streamwise particle hop distance lateral particle hop distance and travel time constrains the relationships between topographic change and sediment transport

impulse framework for unsteady flows reveals superdiffusive bed load transport 1 sediment transport is an intrinsically stochastic process and measurement of bed load in the environment is further complicated by the unsteady nature of river flooding here we present a methodology for analyzing sediment tracer data with unsteady forcing we define a dimensionless impulse by integrating the cumulative excess shear velocity for the duration of measurement normalized by grain size we analyze the dispersion of a plume of cobble tracers in a very flashy stream over two years the mean and variance of transport distance collapse onto well defined linear and power law relations respectively when plotted against cumulative dimensionless impulse data suggest that the asymptotic limit of bed load tracer dispersion is superdiffusive in line with a broad class of geophysical flows exhibiting strong directional asymmetry advection thin tailed step lengths and heavy tailed waiting times the impulse framework justifies the use of quasi steady flow approximations for long term river evolution modeling

the fluid dynamics of river dunes a review and some future research directions 1 dunes are present in nearly all fluvial channels and are vital in predicting flow resistance sediment transport and deposition within many rivers progress in understanding the fluid dynamics associated with alluvial dunes has been significant in the last 15 years and has witnessed huge advances in field laboratory and numerical investigations progress has been made in detailing the principal features of mean and turbulent flow over asymmetric dunes that possess flow separation in their leesides and how these forms affect both downstream boundary layer structure and stress partitioning over the dune additionally the links between sediment transport over dunes and instantaneous coherent flow structures are being increasingly understood with the feedback of dune three dimensionality upon flow and sediment dynamics over these bed forms beginning to be recognized as vital such research now provides an outstanding background for beginning to address areas of greater complexity that will enable a fuller understanding of these important natural features this review paper summarizes the principal features of mean and turbulent flow over alluvial sand dunes five areas are then highlighted and discussed as a possible focus for future research 1 the influence of dune leeside angle upon flow processes in the dune wake and downstream flow field 2 the influence of three dimensionality in dune shape upon the generation of turbulence and distribution of bed shear stress 3 flow field modification resulting from bed form superimposition and amalgamation 4 the scale and topology of dune related turbulence and its interactions with sediment transport and the flow surface and 5 the influence of suspended sediment on the dune flow field and dune morphology

mass transfer in unmetamorphosed carbonates and during low grade metamorphism of arenites s u m m a r y study of stylolites in silurian carbonates of southern ontario and of spaced cleavage in lower palaeozoic meta arenites of nova scotia shows that diffusional or infiltrational mass transfer has been the dominant mechanism for dimensional change the carbonates show a quite specific pattern of stylolite growth in and normal to the mean plane of the stylolite and there is always a low porosity halo about each stylolite implied shortening usually exceeds the amplitude of any teeth in stylolites and may reach 5 of the local sequence in the meta arenites increased inequancy decreased long axis fluctuation of quartz grains lithon to cleavage coupled with virtually constant grain dimension parallel to cleavage suggest gross loss of volume modal and chemical analyses suggest that an average cleavage zone represents a dilation of 50 expressed as shortening normal to cleavage bulk loss is about 10 almost all sio2 in both cases mass removal begins at zero or low levels of overall deformation for the carbonates total deformation is near zero the process shuts down by self suffocation in the meta arenites the process was probably partly driven by the conditions associated with greenschist level metamorphism in both cases collapse across the surfaces of dissolution is nicely adjusted to keep the gross shortening approximately homogeneous

generation of evenly spaced pressure solution seams during late diagenesis a kinetic theory stylolites and pressure solution seams can form during diagenesis of rocks subjected to stress through a feedback involving texture and pore fluid solute concentration this feedback destabilizes the state of uniform texture represented here only by porosity for simplicity a mathematical kinetic model that includes pressure solution diffusion and reprecipitation predicts the spontaneous generation even in initially uniform rocks of regions alternatingly in space more and less soluble a region that becomes more soluble also becomes simultaneously more porous the kinetic theory predicts that stylolites can form at roughly constant spacings this agrees with many field and petrographic observations bedding planes between beds that have initially different texture are shown by the theory to be the focus of a porosity instability that can lead to the formation of a stylolite and to the generation of more stylolites within each bed this prediction agrees with the observation that many stylolites have developed at bedding planes

stochastic incipient motion criterion for spheres under various bed packing conditions incipient motion criteria based solely on time averaged bed shear stress may underpredict sediment transport the focus of this study is on the stochastic aspect of the problem of incipient motion specifically the role of near bed turbulent structures and bed packing density on the commencement of sediment motion is investigated the cornerstone of the proposed model is based on the concept that the particle motion is governed by the intermittent nature of near bed turbulence based on this mechanism in this article we provide a quantitative model for predicting the commencement of sediment entrainment for the first time under three representative bed packing densities corresponding to the isolated wake interference and skimming flow regimes the performance of the proposed model is compared to published experimental data and the conventional approach that is based on the consideration that flow parameters are statistically well represented by a normal distribution

bedload a granular phenomenon bedload the transport of sediment remaining in contact with the stream bed has mainly been studied from the perspective of the correlation between fluid driving forces and the responding sediment flux yet grain grain interactions are important and bedload should also be considered as a granular phenomenon we review progress made recently in the study of granular flows especially on segregation and rheology that better illuminates the nature of bedload granular flows may exhibit gas like or fluid like flow or quasi solid deformation all three conditions might be duplicated in bedload understanding of intense bedload transport occurring continuously in a layer several grains deep typical of sand beds might greatly benefit from results in granular physics as illustrated by grain inspired bedload results however processes restricted to the surface of the bed when particles move intermittently and the bed becomes structured while characteristic in gravel bed channels are not well addressed in granular physics mutual study of these phenomena may benefit both physics and fluvial geomorphology we intend therefore to contribute to an enhanced dialogue between granular physics and bedload science communities copyright 2010 john wiley sons ltd