spatially averaged open channel flow over rough bed in this paper it is suggested that the double averaged in temporal and in spatial domains momentum equations should be used as a natural basis for the hydraulics of rough bed open channel flows especially with small relative submergence the relationships for the vertical distribution of the total stress for the simplest case of 2d steady uniform spatially averaged flow over a rough bed with flat free surface are derived these relationships explicitly include the form induced stresses and form drag as components of the total stress using this approach we define three types of rough bed flows 1 flow with high relative submergence 2 flow with small relative submergence and 3 flow over a partially inundated rough bed the relationships for the double averaged velocity distribution and hydraulic resistance for all three flow types are derived and compared with measurements where possible the double averaged turbulent and form induced intensities and stresses for the case of regular spherical segment type roughness show the dominant role of the double averaged turbulence stresses and form drag in momentum transfer in the near bed region

hydrodynamics of steep streams with planar coarse grained beds turbulence flow resistance and implications for sediment transport the hydraulics of steep mountain streams differ from lower gradient rivers due to shallow and rough flows energetic subsurface flow and macro scale form drag from immobile boulders and channel and bed forms heightened flow resistance and reduced sediment transport rates in steep streams are commonly attributed to macro scale form drag however little work has explored steep river hydrodynamics in the absence of complex bed geometries here we present theory for the vertical structure of flow velocity in steep streams with planar rough beds that couples surface and subsurface flow we test it against flume experiments using a bed of fixed cobbles over a wide range of bed slopes 0 4 30 experimental flows have a nearly logarithmic velocity profile far above the bed flow velocity decreases less than logarithmically towards the bed and is non zero at the bed surface velocity profiles match theory derived using a hybrid eddy viscosity model in which the mixing length is a function of height above the bed and bed roughness subsurface flow velocities are large 1 m s and follow a modified darcy brinkman forchheimer relation that accounts for channel slope and shear from overlying surface flow near bed turbulent fluctuations decrease for shallow rough flows and scale with the depth averaged flow velocity rather than bed shear velocity flow resistance for rough planar beds closely matches observations in natural steep streams despite the lack of bed or channel forms in the experiments suggesting that macro scale form drag is smaller than commonly assumed in stress partitioning models for sediment transport

a mixing layer theory for flow resistance in shallow streams 1 a variety of surface roughness characterizations have emerged from nineteenth and twentieth century studies of channel hydraulics when the water depth h is much larger than the characteristic roughness height ks roughness formulations such as manning s n and the friction factor f can be explicitly related to the momentum roughness height zo in the log law formulation for turbulent boundary layers thereby unifying roughness definitions for a given surface however when h is comparable to or even smaller than ks the log law need not be valid using a newly proposed mixing layer analogy for the inflectional velocity profile within and just above the roughness layer a model for the flow resistance in shallow flows is developed the key model parameter is the characteristic length scale describing the depth of the kelvin helmholtz wave instability it is shown that the new theory originally developed for canopy turbulence recovers much of the earlier roughness results for flume experiments and shallow gravel streams this study is the first to provide such a unifying framework between canopy atmospheric turbulence and shallow gravel stream roughness characterization the broader implication of this study is to support the merger of a wealth of surface roughness characterizations independently developed in nineteenth and twentieth century hydraulics and atmospheric sciences and to establish a connection between roughness formulations across traditionally distinct boundary layer types

influence of bed patchiness slope grain hiding and form drag on gravel mobilization in very steep streams steep streams are a major portion of channel networks and provide a link to transport sediment from hillslopes to lower gradient rivers despite their importance key unknowns remain perhaps foremost of which is evaluating in steep streams empirical laws for fluvial sediment transport developed for low gradient rivers to address this knowledge gap we painted sediment in situ over 3 years to monitor incipient sediment motion and sediment patch development in five small drainage areas of 0 04 2 km 2 and steep slopes of 5 37 tributaries of elder creek california united states we found that channel beds organized into size sorted sediment patches which displayed active fluvial transport of gravel annually consistent year to year patch median grain sizes partial transport of bed material and significantly higher values of critical shields stress for incipient sediment motion compared to that observed for lower gradient rivers the high critical shields stresses up to 0 5 for the median grain size agree within a factor of 3 to theoretical predictions which account for slope dependent hydraulics grain hiding and sediment patches for grains of approximately the same size as the roughness length scale slope dependent hydraulics and bed patchiness are the dominant controls on critical shields stress values while grain hiding is important for grains larger or smaller than the roughness length scale form drag exists in our monitored tributaries but has a smaller influence than the above effects our field observations show fluvial processes contribute to sediment mobilization in steep channels which are often considered to be dominated by debris flows

velocity distribution and bed roughness in high gradient streams a model for the velocity field over a poorly sorted bed is derived herein and applied to flow in steep streams with coarse gravel beds in such streams large clasts often are comparable in size to stream depth and act as obstacles to the flow the effect of these obstacles on a flow is estimated by partitioning total stress proportional to the depth slope product into a purely fluid component and a form drag component associated with flow around the obstacles an eddy viscosity closure is used with a length scale dependent on both distance from the boundary and wake dimension resulting velocity profiles agree well with profiles measured by marchand et al 1984 in nine mountain streams in colorado model runs for a range of conditions reveal that the velocity distribution depends primarily on d84z and flow depth h d84z is the length of the vertically oriented axis of clasts at the 84th percentile of the grain size distribution calculated values of mean velocity normalized by shear velocity are well represented by a simple log linear relationship in terms of relative roughness d84 h

bed load transport flume experiments on steep slopes experiments were conducted over uniform gravel bed materials to obtain 143 friction factor values under bed load equilibrium flow conditions in an attempt to add to the scarce data available on slopes between 1 and 9 for shields numbers between 0 08 and 0 29 analyses showed that when only flows over flat beds are considered a distinction must be made between flows with and without bed load more particularly fitting flow resistance equations indicated that the roughness parameter increases by a factor of 2 5 from clear water flow to intense bed load transport between these two states the flow resistance can be approximated by a constant for a given slope

stabilizing self organized structures in gravel bed stream channels field and experimental observations stable reticulate structures which we call stone cells have been observed in cobble gravel channel beds with low bed material transport rates experiments show that such structures develop simultaneously with the armor layer during an extended period when flows do not exceed the shields threshold by more than 2 times so that bed material transport is low they are constructed by particles moving from less stable positions into more stable configurations against each other intermediate developments include clusters and stone lines they reduce sediment transport by orders of magnitude and are evidently a major stability promoting mechanism in gravel channels the timescale for their development suggests that the boundaries of many gravel bed channels are not in equilibrium with recent competent flows but reflect the history of recent dominant flows

applicability of bed load transport models for mixed size sediments in steep streams considering macro roughness in steep mountain streams macro roughness elements typically increase both flow energy dissipation and the threshold of motion compared to lower gradient channels reducing the part of the flow energy available for bed load transport bed load transport models typically take account of these effects either by reducing the acting bed shear stress or by increasing the critical parameters for particle entrainment here we evaluate bed load transport models for mixed size sediments and models based on a median grain size using a large field data set of fractional bed load transport rates we derive reference shear stresses and bed load transport relations based on both the total boundary shear stress and a reduced or effective shear stress that accounts for flow resistance due to macro roughness when reference shear stresses are derived from the total boundary shear stress they are closely related to channel slope but when they are derived from the effective shear stress they are almost invariant with channel slope the performance of bed load transport models is generally comparable when using the total shear stress and a channel slope related reference shear stress or when using the effective shear stress and a constant reference shear stress however dimensionless bed load transport relations are significantly steeper for the total stress approach whereas they are similar to the commonly used fractional wilcock and crowe wc transport model for the effective stress approach this similarity in the relations allows the wc model developed for lower gradient streams to be used in combination with an effective shear stress approach in steep mountain streams

flow resistance in steep streams an experimental study 1 frequently an assessment of the mean water velocity in a stream is necessary to estimate the discharge associated with a particular flow depth or conversely the mean depth associated with a particular discharge in the absence of a direct measurement of flow velocity a flow resistance approach which establishes the relation between depth and velocity can be applied two approaches have been used in the past traditional approaches based on the use of a resistance coefficient e g darcy weisbach or dimensionless hydraulic geometry approaches to examine if one approach is more appropriate for steep streams data from 31 flume experiments conducted to examine flow resistance in self formed cascade channels were analyzed a dimensionless hydraulic geometry approach developed using at a station data to characterize the q exponent and between site data to characterize the exponent on the channel slope term was more accurate than more traditional approaches the developed relation was similar to the established rational relation v g0 2q0 6s 0 4s0 2 suggesting that the rational relation has merit the approach does not utilize a flow partitioning approach since in steep streams with small relative depths the grains themselves generate form and spill resistance the observation that a single dimensionless hydraulic geometry flow resistance relation can describe measurements across a range of grain sizes and bed slopes 3 21 suggests that steep streams may follow a single scaling relation similar to the regime equations associated with lowland rivers

feedback between bed load transport and flow resistance in gravel and cobble bed rivers 1 to calculate bed load engineers often use flow resistance equations that provide estimates of bed shear stress in these equations on the basis of the estimate of the appropriate hydraulic radius associated with the bed only the bed roughness ks is commonly set as a constant whatever the bed load intensity however several studies have confirmed the existence of feedback mechanisms between flow resistance and bed load suggesting that a flow dependent bed roughness should be used therefore using a data set composed of 2282 flume and field experimental values this study investigated the importance of these feedback effects new flow resistance equations were proposed for three flow domains domain 1 corresponds to no bed load and a constant bed roughness ks d where d is a representative grain diameter whereas domain 3 corresponds to a high bed load transport rate over a flat bed with a constant bed roughness ks 2 6d between these two domains a transitional domain 2 was identified for which the bed roughness evolved from d to 2 6d with increasing flow conditions in this domain the darcy weisbach resistance coefficient f can be approximated using a constant for a given slope the results using this new flow resistance equation proved to be more accurate than those using equations obtained from simple fittings of logarithmic laws to mean values the data set indicates that distinguishing domains 2 and 3 is still relevant for bed load in particular the data indicate a slope dependence in domain 2 but not in domain 3 a bed load model based on the tractive force concept is proposed finally flow resistance and bed load equations were used together to calculate both shear stress and bed load from the flow discharge the slope and the grain diameter for each run of the data set efficiency tests indicate that new equations implicitly taking a feedback mechanism into account can reduce the error by a factor of 2 when compared to other equations currently in use showing that feedback between flow resistance and bed load can improve field bed load modeling

flow resistance estimation in mountain rivers examination of the flow resistance of high gradient gravel and boulder bed rivers using data collected in british mountain rivers with slopes of 0 4 4 shows that there are differences in resistance variation between mountain and lowland rivers and that between site variations do not necessarily reflect at a site variations comparison of data with the familiar resistance equation relating the dracy weisbach friction factor to the logarithm of relative submergence shows that the equation tends to overestimate the resistance in uniform flow the equation also tends to underestimate the rate of change of resistance at a site as discharge varies with high gradients the influences of nonuniform channel profile sediment size distribution channel slope and sediment transport are reviewed but the data do not allow any quantification of these effects instead an empirical approach based on the available data is presented allowing the friction factor to be calculated from the relative submergence with an error of up to n25 to n35 a summary of the field data is included

flow turbulence over fixed and weakly mobile gravel beds characteristics of turbulence structure in quasi 2d flows with static and weakly mobile gravel beds are presented three sets of measurements with acoustic doppler velocimeters in an irrigation canal were used two with subcritical bed shear stress static beds and one with the bed shear stress o close to critical oc weakly mobile bed the analyses included vertical distributions of local mean velocities turbulence intensities turbulent shear stresses velocity auto and cross spectra the quadrant method and high order velocity moments a number of properties of turbulence intensities high order moments streamwise bursting parameters and velocity spectra appeared to be similar for all three flows but some properties were different the most important one was an observed reduction in the von karman constant for the flow with weakly mobile bed comparison of these results with other studies and analogies with drag reducing flows suggest that at o oc 1 the drag on the bed for a given granula

vertical effective stress as a control on quartz cementation in sandstones abstract temperature controlled precipitation kinetics has become the overwhelmingly dominant hypothesis for the control of quartz cementation in sandstones here we integrate quantitative petrographic data high spatial resolution oxygen isotope analyses of quartz cement basin modelling and a kinetic model for quartz precipitation to suggest that the supply of silica from stress sensitive intergranular pressure dissolution at grain contacts is in fact a key control on quartz cementation in sandstones we present data from highly overpressured sandstones in which despite the current burial temperature of 190 c quartz cement occurs in low amounts 4 6 1 2 of bulk volume in situ oxygen isotope data across quartz overgrowths suggest that cementation occurred over 100 ma and a temperature range of 80 150 c during which time high fluid overpressures resulted in consistently low vertical effective stress we argue that the very low amounts of quartz cement can only be explained by the low vertical effective stress which occurred throughout the burial history and which restricted silica supply as a result of a low rate of intergranular pressure dissolution at grain contacts

theoretical development on the effects of changing flow hydraulics on incipient bed load motion 1 several decades of flume and field measurements have indicated that in rough turbulent flows the critical shields stress increases with increasing slope and associated decreasing relative depth this result contradicts the usual consideration of a decreased critical shields value on very steep slopes because of increased gravitational effects however recent studies have demonstrated that these experimental results could be reproduced with a force balance model if the classical logarithmic velocity profile was replaced with a velocity profile that was more compatible with available velocity measurements over gravel beds these measurements indicate the existence of a roughness layer that is a zone of almost constant velocity close to the bed whose properties mean velocity and turbulence depended on the flow s relative depth unfortunately velocity profile measurements for low relative depth associated with steep slopes are scarce and it is still difficult to include such flow properties in a force balance model flow resistance data on the basis of depth average velocity measurements are very common and cover a wide range of slopes and relative depths in this paper these data are used to fit a velocity profile including a roughness layer when used in a force balance model for incipient motion it adequately reproduced a data set composed of 270 critical shields values measured in a flume with near uniform sediments the relevance of this research to field problems is discussed using a data set composed of 92 critical shields stresses obtained from field measurements finally a model is proposed for field applications taking into account the slope effect

influence of relative submergence on spatial variance and form induced stress of gravel bed flows 1 spatial flow variance has a strong control on sediment transport sediment water interface exchange mechanisms and the distribution and behavior of aquatic organisms in rivers thus being able to quantify spatial flow variance and how it varies with different water levels is important for understanding how fluvial processes change during periods of time varying flow in this paper laboratory flume measurements of near bed flow velocity were used to quantify spatial flow variance and form induced stress and their variation with flow submergence within and above the surface of porous gravel beds with differing grain roughness the analysis revealed spatial flow variance was usually four or five times higher within the roughness layer than above a rise in relative submergence resulted typically in a decrease in spatial variance relative to bed shear velocity in streamwise form induced intensity streamwise turbulence intensity and form induced momentum flux both within and above the roughness layer flow submergence had no consistent influence on spatial variance in the vertical flow direction and in reynolds stress form induced stress was significant within the roughness layer more so at shallow depths the greater significance was driven primarily by higher spatial flow variance in time averaged streamwise velocity at these depths the implication is the relative role of momentum transfer mechanisms within the roughness layer and thus sediment water interface exchange processes in rivers will change during periods of time varying flows

velocity characteristics along a small step pool channel this paper summarizes measurements of velocity along three reaches of a small mountain channel with step pool bedforms a one dimensional electromagnetic current meter was used to record velocity fluctuations at 37 fixed measurement points during five measurement intervals spanning the peak of the annual snowmelt hydrograph measurement cross sections were located upstream from a bed step at the step lip downstream from the step and in a uniform gradient run data analyses focused on characteristics of velocity profiles and on correlations between velocity characteristics and the potential control variables bedform type reach gradient and flow depth to test the hypothesis that velocity characteristics are related to channel bedform types anova and ancova tests were performed for the average velocity and coefficient of variation of point velocity data results indicate that high frequency velocity variations correlate to some degree with both channel characteristics and discharge velocity became more variable as stage increased particularly at low gradient reaches with less variable bed roughness velocity profiles suggest that locations immediately downstream from bed steps are dominated by wake turbulence from mid profile shear layers locations immediately upstream from steps at step lips and in runs are dominated by bed generated turbulence adverse pressure gradients upstream and downstream from steps may be enhancing turbulence generation whereas favourable pressure gradients at steps are suppressing turbulence the bed generated turbulence and skin friction of runs appear to be less effective energy dissipators than the wake generated turbulence and form drag of step pool bedforms copyright 2000 john wiley sons ltd

a phenomenological model for the flow resistance over submerged vegetation 1 the bulk velocity ub in streams is conventionally estimated from manning s equation but difficulties remain in parameterizing the roughness coefficient n when the streambed is covered with vegetation a two layer velocity model is proposed to determine n and ub for the submerged vegetation case the modeled n is derived as a function of flow and vegetation properties that can be inferred from remote sensing platforms such as canopy height leaf area density and flow depth the main novelty in the proposed formulation is that the shear stress is related to the mean velocity profile by considering both ejective and sweeping motions by dominant eddies the proposed model is tested against a large data set from the literature and is shown to perform well particularly for rigid vegetation poorer model performance for flexible vegetation can be partially attributed to the shape of the assumed mean velocity profile the roughness coefficient n is found to be robust to variations in the average spacing between canopy elements allowing the model to be applied to heterogeneous canopies

is the critical shields stress for incipient sediment motion dependent on channel bed slope data from laboratory flumes and natural streams show that the critical shields stress for initial sediment motion increases with channel slope which indicates that particles of the same size are more stable on steeper slopes this observation is contrary to standard models that predict reduced stability with increasing slope due to the added downstream gravitational force processes that might explain this discrepancy are explored using a simple force balance model including increased drag from channel walls and bed morphology variable friction angles grain emergence flow aeration and changes to the local flow velocity and turbulent fluctuations surprisingly increased drag due to changes in bed morphology does not appear to be the cause of the slope dependency because both the magnitude and trend of the critical shields stress are similar for flume experiments and natural streams and significant variations in bed morphology in flumes is unlikely instead grain emergence and changes in local flow velocity and turbulent fluctuations seem to be responsible for the slope dependency due to the coincident increase in the ratio of bed roughness scale to flow depth i e relative roughness a model for the local velocity within the grain roughness layer is proposed based on a 1 d eddy viscosity with wake mixing in addition the magnitude of near bed turbulent fluctuations is shown to depend on the depth averaged flow velocity and the relative roughness extension of the model to mixed grain sizes indicates that the coarser fraction becomes increasingly difficult to transport on steeper slopes

self adjustment of stream bed roughness and flow velocity in a steep mountain channel understanding how channel bed morphology affects flow conditions and vice versa is important for a wide range of fluvial processes and practical applications we investigated interactions between bed roughness and flow velocity in a steep glacier fed mountain stream riedbach ct valais switzerland with almost flume like boundary conditions bed gradient increases along the 1 km study reach by roughly 1 order of magnitude s 3 41 with a corresponding increase in streambed roughness while flow discharge and width remain approximately constant due to the glacial runoff regime streambed roughness was characterized by semivariograms and standard deviations of point clouds derived from terrestrial laser scanning reach averaged flow velocity was derived from dye tracer breakthrough curves measured by 10 fluorometers installed along the channel commonly used flow resistance approaches darcy weisbach equation and dimensionless hydraulic geometry were used to relate the measured bulk velocity to bed characteristics as a roughness measure d84 yielded comparable results to more laborious measures derived from point clouds flow resistance behavior across this large range of steep slopes agreed with patterns established in previous studies for both lower gradient and steep reaches regardless of which roughness measures were used we linked empirical critical shear stress approaches to the variable power equation for flow resistance to investigate the change of bed roughness with channel slope the predicted increase in d84 with increasing channel slope was in good agreement with field observations

particle friction angles in steep mountain channels sediment transport rates in steep mountain channels are typically an order of magnitude lower than predicted by models developed for lowland rivers one hypothesis for this observation is that particles are more stable in mountain channels due to particle particle interlocking or bridging across the channel width this hypothesis has yet to be tested however because we lack direct measurements of particle friction angles in steep mountain channels here we address this data gap by directly measuring the minimum force required to dislodge sediment pebbles to boulders and the sediment weight in mountain channels using a handheld force gauge at eight sites in california with reach averaged bed angles ranging from 0 5 to 23 and channel widths ranging from 2 m to 16 m we show that friction angles in natural streams average 68 and are 16 larger than those typically measured in laboratory experiments which is likely due to particle interlocking and burial results also show that larger grains are disproportionately more stable than predicted by existing models and that grains organized into steps are twice as stable as grains outside of steps however the mean particle friction angle does not vary systematically with bed slope these results do not support systematic increases in friction angle in steeper and narrower channels to explain the observed low sediment transport rates in mountain channels instead the spatial pattern and grain size dependence of particle friction angles may indirectly lower transport rates in steep narrow channels by stabilizing large clasts and channel spanning steps which act as momentum sinks due to form drag

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

a vortex based model of velocity and shear stress in a partially vegetated shallow channel 1 this paper presents a method for predicting the distributions of velocity and shear stress in shallow channels with a boundary of emergent vegetation experiments in a laboratory channel with model vegetation show that the velocity profile exhibits a distinct two layer structure consisting of a rapidly varying shear layer across the vegetation interface and a more gradual boundary layer in the main channel in addition coherent vortices are observed which span both layers and are the dominant contributors to lateral momentum fluxes from these observations we propose a model for the vortex induced exchange and find expressions for the width of momentum penetration into the vegetation the velocity and shear stress at the vegetation edge and the width of the boundary layer in the main channel these variables along with a momentum balance in the main channel comprise a modeling framework which accurately reproduces the observed velocity and shear stress distributions the predictions for the velocity and shear stress can provide a basis for modeling flood conveyance overbank sediment transport and scalar residence time in the vegetated layer

calculating bed load transport in steep boulder bed channels 1 steep rough channels occupy a large fraction of the total channel length in mountainous regions most sediment mobilized on hillslopes must pass through these streams before reaching lower gradient channels steep channels have wide grain size distributions that are composed of finer more mobile sediment and large rarely mobile grains the large grains can bear a significant portion of the total shear stress and thereby reduce the stress available to move the finer sediment conventional bed load transport equations often overpredict the sediment flux in steep channels by several orders of magnitude we hypothesize that sediment transport equations overpredict the sediment flux because they do not 1 account for the stress borne by rarely mobile grains 2 differentiate between highly and rarely mobile sediment and 3 account for the limited availability of mobile sediment here we modify a conventional bed load transport equation to include these three effects we use measurements of the flow bed properties and sediment flux in a small steep flume to test this equation we supply gravel at a constant rate through fields of regularly spaced immobile spheres and measure the bed coverage by gravel and sphere protrusion the percent of the sphere that protrudes above the gravel deposit for a given sphere spacing the proportion of the bed covered by gravel increases and the sphere protrusion decreases with greater sediment supply thus bed coverage and immobile grain protrusion may serve as proxies for sediment availability in steep rough streams unlike most transport equations that we tested our modified bed load equation predicts sediment fluxes to within an order of magnitude of the measured values our results demonstrate that accurately predicting bed load transport in steep rough streams may require accounting for the effects of local sediment availability coverage by mobile sediment and drag due to rarely mobile particles

roughness of loose rock riprap on steep slopes a study was conducted to determine the roughness of rock riprap laid on steep slopes tests were conducted in a 1 07 m wide flume and two 2 74 m wide field scale structures using angular riprap with median diameters d50 ranging from 52 to 278 mm and bed slopes s0 ranging from 0 028 to 0 333 m m empirical relationships were developed to predict the manning roughness coefficient as a function of d50 and s0 the darcy weisbach friction factor was predicted as a function of d d84 the relative submergence newly developed equations are applicable for riprap placed on slopes from 2 8 33 roughness coefficients calculated using the developed equations were compared with roughness coefficients calculated using equations developed from observations on natural mountain streams

velocity distribution in the roughness layer of rough bed flows several models for the vertical distribution of the double averaged in time and in the plane parallel to the mean bed longitudinal velocity in the flow region between roughness troughs and roughness tops are suggested we found that the same model for velocity distribution may be applicable to a range of flow conditions and roughness types which share some common features the suggested models for velocity distribution in the near bed region are 1 constant velocity 2 exponential velocity distribution and 3 linear velocity distribution the measured velocity distributions may be approximated by a single model or by a combination of models depending on roughness geometry and flow conditions the validity of these models for velocity distribution is supported by laboratory data

air concentrations of submerged and unsubmerged hydraulic jumps in a bedrock step pool channel 1 the classical hydraulic jump which is a hydraulic jump formed in a horizontal smooth and prismatic laboratory flume has often been used for estimating hydraulic and morphologic characteristics of mountain river channels however most studies utilizing classical hydraulic jump relationships have neglected the role of aerated flows and jump types prevalent in natural systems by developing a methodology to survey digitize and visualize air concentrations for jumps in bedrock rivers we present new data for submerged jumps and sloping jumps in a bedrock step pool channel as with laboratory research our results indicated peak mean and local air concentrations of natural jumps were skewed by submergence of the jump roller beneath the free surface however unlike laboratory research cross stream variations were significant for both jumps varying up to 20 across the jump width traces through each jump thalweg also indicated the classical hydraulic jump was a poor analogue for estimating surficial air concentrations

resistance equation for large scale roughness a theory of flow resistance for large scale roughness is developed the main points of which are supported by a flume study from which the outline of a process based resistance equation is determined rivers with large scale roughness have steep slopes and depths of the same order of magnitude as the bed material size flow resistance depends on the form drag of the roughness elements and their disposition in the channel theoretical considerations show resistance to be a function of reynolds number froude number roughness geometry and channel geometry these processes are examined using the results of flume experiments based on five different roughness beds and a wide range of flows semi empirical analysis supports the theory and allows the development of a theoretical power law resistance equation which accounts for most of the processes a summary of the data is presented for use in other research studies

controls on fluvial evacuation of sediment from earthquake triggered landslides large earthquakes in active mountain belts can trigger landslides which mobilize large volumes of clastic sediment delivery of this material to river channels may result in aggradation and flooding while sediment residing on hillslopes may increase the likelihood of subsequent landslides and debris flows despite recognition of these processes the controls on the residence time of coseismic landslide sediment in river catchments remain poorly understood here we assess the residence time of fine grained 5 mm day 1 together with previous observations from the c e 1999 chi chi earthquake in taiwan our results demonstrate the importance of landslide density and runoff intensity in setting the duration of earthquake triggered landslide impacts on river systems

influence of external forcings on abrupt millennial scale climate changes a statistical modelling study the last glacial period was punctuated by a series of abrupt climate shifts the so called dansgaard oeschger do events the frequency of do events varied in time supposedly because of changes in background climate conditions here the influence of external forcings on do events is investigated with statistical modelling we assume two types of simple stochastic dynamical systems models double well potential type and oscillator type forced by the northern hemisphere summer insolation change and or the global ice volume change the model parameters are estimated by using the maximum likelihood method with the ngrip hbox ca 2 record the stochastic oscillator model with at least the ice volume forcing reproduces well the sample autocorrelation function of the record and the frequency changes of warming transitions in the last glacial period across miss 2 3 and 4 the model performance is improved with the additional insolation forcing the bic scores also suggest that the ice volume forcing is relatively more important than the insolation forcing though the strength of evidence depends on the model assumption finally we simulate the average number of warming transitions in the past four glacial periods assuming the model can be extended beyond the last glacial and compare the result with an iberian margin sea surface temperature sst record martrat et al in science 317 5837 502 507 2007 the simulation result supports the previous observation that abrupt millennial scale climate changes in the penultimate glacial mis 6 are less frequent than in the last glacial miss 2 4 on the other hand it suggests that the number of abrupt millennial scale climate changes in older glacial periods miss 6 8 and 10 might be larger than inferred from the sst record

analytical solution of the depth averaged flow velocity in case of submerged rigid cylindrical vegetation a new model for the depth averaged velocity for flow in presence of submerged vegetation is developed the model is based on a two layer approach where flow above and through the vegetation layer is described separately vegetation is treated as a homogeneous field of identical cylindrical stems and the flow field is considered stationary and uniform it is demonstrated that scaling considerations of the bulk flow field can be used to avoid complications associated with smaller scale flow processes and that still the behavior of depth averaged flow over vegetation is described accurately the derived scaling expression of the average flow field is simple in form it follows fundamental laws of fluid flow and it shows very good agreement with laboratory flume experiments the new model can be used for quick evaluation of a river s hydraulic response in cases where vegetated floodplains are inundated

variation in the reference shields stress for bed load transport in gravel bed streams and rivers 1 the present study examines variations in the reference shear stress for bed load transport r using coupled measurements of flow and bed load transport in 45 gravel bed streams and rivers the study streams encompass a wide range in bank full discharge 1 2600 m3 s average channel gradient 0 0003 0 05 and median surface grain size 0 027 0 21 m a bed load transport relation was formed for each site by plotting individual values of the dimensionless transport rate w versus the reach average dimensionless shear stress the reference dimensionless shear stress r was then estimated by selecting the value of corresponding to a reference transport rate of w 0 002 the results indicate that the discharge corresponding to r averages 67 of the bank full discharge with the variation independent of reach scale morphologic and sediment properties however values of r increase systematically with average channel gradient ranging from 0 025 0 035 at sites with slopes of 0 001 0 006 to values greater than 0 10 at sites with slopes greater than 0 02 a corresponding relation for the bank full dimensionless shear stress bf formulated with data from 159 sites in north america and england mirrors the relation between r and channel gradient suggesting that the bank full channel geometry of gravel and cobble bedded streams is adjusted to a relatively constant excess shear stress bf r across a wide range of slopes

prediction of sediment transport in step pool channels 1 in mountainous drainage networks sediment mobilized on hillslopes must first pass through steep streams before reaching lower gradient channels the bed of steep channels is typically composed of large relatively immobile boulders and finer more mobile gravel most sediment transport equations overpredict sediment flux in steep streams by several orders of magnitude because they do not account for the stress borne by immobile grains and the limited availability of the more mobile sediment we previously developed and tested in flume experiments a sediment transport equation that accounts for these two effects here we modify the parker 1990 bed load equation to include the resistance borne by steps and selective transport of the relatively mobile sediment using a range of hiding functions we test a number of resistance equations and hiding functions combined with our modified and the original parker equations against measured flow and sediment transport in three steep channels our modified sediment transport equation generally predicts the transported sediment volumes to within an order of magnitude of the measured values whereas the unmodified equations do not the most accurate sediment flux predictions were obtained from using our modified equation combined with a hiding function that calculates highly selective transport of the relatively mobile sediment furthermore this hiding function has a critical shields stress that is similar to those reported for lower gradient channels the effects of the immobile steps on flow and sediment transport are not adequately captured by simply increasing the critical shields stress to values reported in steep streams

selective sorting and abrasion of river gravel ii applications most gravel rivers show a tendency for characteristic grain size to decrease in the downstream direction over scales of tens or hundreds of kilometers it has been surmised that this downstream fin