‘Bedload’ dynamics: Grain impacts,momentum transfer and derivation of a grain froude number

A test is proposed for Bagnold's postulate that the normal weight stress due to moving ‘bedload’ is balanced by a solid transmitted stress due to the rate of change of momentum produced by grain impacts on unit area of the stationary bed. The test involves derivation of an expression for normal momentum transfer due to saltating grains at moderate transport stages when grain-to-grain collisions and partial suspension during saltation may be ignored. A dimensionless number, Φ, (a grain Froude Number) is derived, given by ū²/g where ū is the mean grain forward velocity, g is the gravitational acceleration and L? is the length of a single saltation ‘jump’. Equilibrium demands that Φ be unity during bedload transport involving saltating grains if Bagnold's postulate is correct. Experimental data shows Φ < 1, the discrepancy between theory and experiment being due to the existence of lift forces acting upon bedload grains. Bagnold's postulate is correct for concentrated dispersions of grains, as in grain flows, when fluid lift forces may be neglected due to high particle concentration.     

Least action principle,equilibrium states,iterative adjustment and the stability of alluvial channels

The energy based least action principle (LAP) has proven to be very successful for explaining natural phenomena in both classical and modern physics. This paper briefly reviews its historical development and details how, in three ways, it governs the behaviour and stability of alluvial rivers. First, the LAP embodies the special stationary equilibrium state of motion and so its incorporation with the principle of energy conservation explains why so many optimizing hypotheses have been proposed in fluvial geomorphology. Second, the variational approach underlying the LAP provides a more straightforward and simpler fuzzy‐object orientated method for solving river regime problems than do the various complex Newtonian formulations. Third, it is shown that in fluvial systems with surplus energy the surplus can be expended with slope and/or channel geometry adjustments, with the degree of channel geometry adjustment quantified by the dimensionless numbers F for depth dominated adjustment and H for width/depth dominated adjustment. Different planforms are preferred at different energy levels, with H providing a quantitative measure of the flow's efficiency for moving sediment. In rivers with insufficient energy, the interactions of endogenous and exogenous factors are shown to be capable, in certain circumstances, of achieving a stationary equilibrium condition which acts as the attractor state. Importantly, this study describes how iterative changes enable systems to achieve such a stable equilibrium. Copyright © 2007 John Wiley & Sons, Ltd.     

Variation of Froude number versus depth during the passage of internal solitary waves from the in-situ observation and a numerical model

There are few studies on the variation of Froude number versus depth during the passage of internal solitary waves (ISWs). In this paper, according to the limited observational data of the ISWs near the Dongsha Islands in the northern South China Sea (SCS), it is found that, during the passage of an ISW, the local Froude number near the main thermocline gets maximum and the flow is supercritical, with the Froude number decreasing gradually upward and downward, whilst before and after the passage of the ISW, the local Froude number is less than 1 and the flow is subcritical in the entire water column. Since the observational current data are only available in the upper ocean, a two-dimensional continuously stratified nonlinear model is employed here to study the variation of Froude number versus depth during the passage of an ISW. The modeled ISW induced current field agrees well with that observed during the passage of the observational ISW. It is found that, even during the passage of the ISW, although the Froude number is larger than 1 in the upper layer, it is less than 1 in the lower layer, and the duration when the Froude number is larger than 1 also changes with depth. Thus, it is suggested that, once the Froude number near the main thermocline is larger than 1, the passage of ISWs could be identified. Moreover, it would be better to choose a sampling interval of no more than 1/4 passage period of the ISW during an in-situ observation of ISWs.     

Assessment of geomorphological bank evolution of the alluvial threshold rivers based on entropy concept parameters

The complex stream bank profiles in alluvial channels and rivers that are formed after reaching equilibrium has been a popular topic of research for many geomorphologists and river engineers. The entropy theory has recently been successfully applied to this problem. However, the existing methods restrict the further application of the entropy parameter to determine the cross-section slope of the river banks. To solve this limitation, we introduce a novel approach in the extraction of the equation based on the calculation of the entropy parameter (λ) and the transverse slope of the bank profile at threshold channel conditions. The effects of different hydraulic and geometric parameters are evaluated on a variation of the entropy parameter. Sensitivity analysis on the parameters affecting the entropy parameter shows that the most effective parameter on the λ-slope multiplier is the maximum slope of the bank profile and the dimensionless lateral distance of the river banks.     

Relationship between the equilibrium morphology of river islands and flow-sediment dynamics based on the theory of minimum energy dissipation

River islands are vital geomorphic units in alluvial rivers, and the variation of their morphology and position plays a significant role in regulating flow-sediment transport and channel stability. Based on the theories of minimum energy dissipation theory of fluid movement and river morphodynamics, this study uses the river islands in anabranching channels to analyze the relationship between the shape coefficient of river island and the flow-sediment dynamics under stable equilibrium conditions...     

Coupled estimation of the energy slope and associated sand-silt transport during high stream power events in alluvial rivers

A coupled routing for the transport capacity and the energy slope is introduced through the definition of the control factor m whose value is linked to the bed form configuration.The coupling aims to further incorporate the interactions occurring in alluvial rivers and thus enhance the prediction of the fine sediment fluxes,especially during high stream power events.Based on a predictive rule for the control factor m that only involves water depth,velocity and bedform constitutive texture,the novel method is confronted to observations collected in one of the most strongly dynamic alluvial river namely the Lower Yellow River.Comparisons between time series of measured and computed concentrations illustrate that during high velocity events the main dynamics of the sediment transport is correctly reproduced.The main advantage of the present approach is to supply consistent time evolutions of sediment concentrations without making use of any detailed shear information.     

Adjustment and recovery of unstable alluvial channels: Identification and approaches for engineering management

The management of riverine environments is shown to require a knowledge and awareness of the complex interactions between fluvial and mass-wasting processes, riparian vegetation, and channel form. Identification of the cause of instability rather than the local symptoms, and knowledge of the temporal and spatial aspects of channel adjustment are central to the application of (1) appropriate analyses to estimate future channel changes, (2) appropriate mitigation measures, and (3) the protection of river-crossing structures and adjacent land. Conceptual models of channel evolution and bank-slope development are particularly valuable for interpreting past and present processes, applying appropriate computational techniques to estimate future channel changes, and implementing strategies to mitigate the impacts of processes likely to dominate the channel in the future. Techniques for identification and analysis of channel instability are interdisciplinary and provide a mechanism for estimating changes in channel-bed elevation and channel width with time. Features of channel form and associated riparian vegetation can be used as diagnostic criteria to identify channel processes, the stage of channel evolution and the magnitude and extent of instability. Changes in bed elevation with time can be represented using an exponential function; changes in channel width with time can be calculated using slope stability equations and (or) projection of a temporary angle of stability from a low-angle surface termed the ‘slough line’ that supports re-establishment of woody vegetation. These techniques, in combination with knowledge of the state of channel evolution, can then be used to assess the appropriateness of various mitigation measures to control on-going channel adjustments and to protect river-crossing structures.     

Modelling the effect of vegetation on channel pattern in bedload rivers

We modify a simple numerical stream‐pattern model to examine the effect of sediment stabilization by roots on the channel pattern of bedload rivers. In the model, vegetation enhances bank resistance to erosion, causing the development of a single channel instead of a rapidly changing, multiple channel (braided) pattern. Net aggradation resulting from a high sediment supply, however, causes frequent avulsions that destroy vegetation locally, leading to the development of a multiple‐channel pattern. A stability diagram representing multiple model runs predicts whether a river will exhibit single or multiple channels, based on plant‐enhanced bank strength, and on the time scale of plant development relative to a time scale for change in unvegetated channels. A second stability diagram predicts the way in which the amplitude and period of a fluctuating imposed sediment load influence whether a single or multiple‐channel pattern develops. Copyright © 2003 John Wiley & Sons, Ltd.     

The chronology and stratigraphy of the alluvial terraces of the river Dane Valley,Cheshire, N.W. England

Three groups of alluvial terraces together with the modern floodplain mark the Postglacial development of the middle part of the Dane Valley, Cheshire. These are a High terrace group of late Pleistocene age, a Middle terrace group of late Pleistocene to early Holocene age, a Low terrace of mid–late Holocene age, and a modern (post ca. 1840 AD) floodplain. A chronology of erosion, deposition, and landform development since mid-Holocene times is established in this paper on the basis of terrace morphology, stratigraphy, sedimentology, soil analysis, magnetic mineral analysis, and four radiocarbon dates. After dissection of the Middle terrace during the early to mid-Holocene, a long period of lateral activity by the river was followed by a major aggradation phase, which formed the Low terrace surface. This was followed by dissection during the last ca. 300 years and the development of the modern floodplain since ca. 1840 AD. Various explanations for the changes during the Holocene are considered; the Low terrace aggradation appears to be related to a major phase of mediaeval soil erosion.     

Knickpoint recession rate and catchment area: the case of uplifted rivers in Eastern Scotland

Knickpoint behaviour is a key to understanding both the landscape responses to a base‐level fall and the corresponding sediment fluxes from rejuvenated catchments, and must be accommodated in numerical models of large‐scale landscape evolution. Knickpoint recession in streams draining to glacio‐isostatically uplifted shorelines in eastern Scotland is used to assess whether knickpoint recession is a function of discharge (here represented by its surrogate, catchment area). Knickpoints are identified using DS plots (log slope versus log downstream distance). A statistically significant power relationship is found between distance of headward recession and catchment area. Such knickpoint recession data may be used to determine the values of m and n in the stream power law, E = KA^mSⁿ. The data have too many uncertainties, however, to judge definitively whether they are consistent with m = n = 1 (bedrock erosion is proportional to stream power and KPs should be maintained and propagate headwards) or m = 0·3, n = 0·7 (bedrock incision is proportional to shear stress and KPs do not propagate but degrade in place by rotation or replacement). Nonetheless, the E Scotland m and n values point to the dominance of catchment area (discharge) in determining knickpoint retreat rates and are therefore more consistent with the stream power law formulation in which bedrock erosion is proportional to stream power. Copyright © 2005 John Wiley & Sons, Ltd.     

The influence of sediment size,relative grain size and channel slope on initiation of sediment motion in boulder bed rivers. A lichenometric study

Sediment transport of four boulder bed rivers is studied using lichenometry. The presence of lichens on boulders in the river channel is used to date the last mobilization of the blocks. Using size frequency diagrams and regional growth curves calibrated with dated reference points it is possible to determine the flood event responsible for the last mobilization of each boulder with lichens present. The specific stream power of flood events over the last 60 years is then calculated, and thresholds of sediment transport based on the sediment size are calculated. The results from the four studied rivers are compared to similar relationships in the literature. Sediment motion thresholds appear to be very variable within the same type of river (mountainous boulder bed rivers). The critical specific stream power necessary to mobilize a particle of a given diameter may vary by up to 10 times from one river to the next. Bed sediment size and river slope may explain this large range of stream powers. Calculation of the relative size of the transported particles (D_i/D₅₀) also shows that both hiding and protrusion effects, as well as channels slope, are important factors in sediment transport. Copyright © 2010 John Wiley & Sons, Ltd.     

Luminescence dating without sand lenses: An application of OSL to coarse-grained alluvial fan deposits of the Lost River Range,Idaho, USA

Optically stimulated luminescence (OSL) dating is increasingly used to estimate the age of fluvial deposits. A significant limitation, however, has been that conventional techniques of sampling and dose rate estimation are suitable only for thick (>60 cm) layers consisting of sand size or finer grains. Application of OSL dating to deposits lacking such layers remains a significant challenge. Alluvial fans along the western front of the Lost River Range in east-central Idaho, USA are one example. Deposits are typically pebble to cobble sheetflood gravels with a sandy matrix but thin to absent sand lenses. As a result, the majority of samples for this project were collected by excavating matrix material from gravelly deposits under light-safe tarps or at night. To examine the contributions of different grain-size fractions to calculated dose-rates, multiple grain-size fractions were analyzed using ICP–MS, high resolution gamma spectrometry and XRF. Dose rates from bulk sediment samples were 0.4–40% (mean of 18%) lower than dose-rate estimates from the sand-size fractions alone, illustrating the importance of representative sampling for dose rate determination. We attribute the difference to the low dose-rate contribution from radio-nuclide poor carbonate pebbles and cobbles that occur disproportionately in clast sizes larger than sand. Where possible, dose rates were based on bulk sediment samples since they integrate the dose-rate contribution from all grain sizes. Equivalent dose distributions showed little evidence for partial bleaching. However, many samples had significant kurtosis and/or overdispersion, possibly due to grain-size related microdosimetry effects, accumulation of pedogenic carbonate or post-depositional sediment mixing. Our OSL age estimates range from 4 to 120 ka, preserve stratigraphic and geomorphic order, and show good agreement with independent ages from tephra correlation and U-series dating of pedogenic carbonate. Furthermore, multiple samples from the same deposit produced ages in good agreement. This study demonstrates that with modified sampling methods and careful consideration of the dose rate, OSL dating can be successfully applied to coarse-grained deposits of climatic and tectonic significance that may be difficult to date by other methods.     

A test of equilibrium theory and a demonstration of its practical application for predicting the morphodynamics of the Yangtze River

Taking the width/depth ratio of a river channel as an independent variable, a variational analysis of basic flow relationships shows that alluvial‐channel flow adjusts channel geometry to achieve stationary equilibrium when the condition of maximum flow efficiency (MFE) is satisfied. As a test of the veracity of MFE and to examine if this theory of self‐adjusting channel morphodynamics can be practically applied to large river systems, this study examines the degree of correspondence between theoretically determined equilibrium channel geometries and actual measurements along the middle and lower Yangtze River. Using four different forms of the Meyer‐Peter and Müller bedload relation and relations of flow continuity and resistance we show that the Meyer‐Peter and Müller bedload relation modified on the basis of MFE theory predicts channel dimensions most accurately when applied to the middle and lower Yangtze River. This provides convincing evidence supporting MFE equilibrium theory. Copyright © 2014 John Wiley & Sons, Ltd.     

A practical method for analysis of river waves and for kinematic wave routing in natural channel networks

The behaviour of river waves is described using a simplified dimensionless form of the momentum equation in conjunction with the continuity equation. Three dimensionless parameters were derived based on a quantitative linear analysis. These parameters, which depend on the Froude number of the steady uniform flow and the geometric characteristics of the river, permit quantification of the influence of inertia and pressure in the momentum equation. It was found that dynamic and diffusion waves occur mainly on gentle channel slopes and the transition between them is characterized by the Froude number. On the other hand, the kinematic wave has a wide range of applications. If the channel slope is greater than 1%, the kinematic wave is particularly suitable for describing the hydraulics of flow. Since slopes in natural channel networks are often greater than 1%, an analytical solution of the linearized kinematic wave equation with lateral inflow uniformly distributed along the channel is desirable and was therefore derived. The analytical solution was then implemented in a channel routing module of an existing simple rainfall–runoff model. The results obtained using the analytical solution compared well with those obtained from a non‐linear kinematic wave model. Copyright © 2000 John Wiley & Sons, Ltd.     

Accuracy of the kinematic wave and diffusion wave approximations for time-independent flows with infiltration included

Errors in the kinematic wave and diffusion wave approximation for time-independent (or steady-state) cases of channel flow with infiltration were derived for three types of boundary conditions: zero flow at the upstream end, and critical flow depth and zero depth gradient at the downstream end. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors of less than 1·4% for KF²₀≥7·5, and up to 14% for KF²₀≤0·75 for the upstream boundary condition of zero discharge and finite depth, where K is the kinematic wave number and F₀ is the Froude number. The kinematic wave approximation was reasonably accurate except at the channel boundaries and for small values of KF²₀ (≤1). The accuracy of these approximations was significantly influenced by the downstream boundary, both in terms of the magnitude of the error and the segment of the channel reach for which these approximations would be applicable. © 1998 John Wiley & Sons, Ltd.     

On the incipient formation of bars and channels on alluvial fans

The morphodynamics of topographic expansion has been recently investigated both experimentally, by Sittoni et al., (2014) Shaw et al., (2018), and numerically Sittoni et al., 2014. Here, we study the basic mechanism that governs the evolution of topographic and expansions and explore the instability of the bottom topography under conditions of steady but spatially expanding flow. We model the expanding flow via a by configuration where water and sediments are supplied from a central hole and flow on a cone shaped surface confined by lateral walls. The governing equations are the shallow-water equations coupled with the Exner equation, written in cylindrical coordinates. We initially approach the problem analytically by considering the conditions required for the basic state, consisting of a pure radial flow and bottom profile, to lose stability to small amplitude perturbations. This analysis suggests that more than one mode may be unstable, encouraging us to extend the analysis to the nonlinear regime. We do this through numerical modeling of the full governing equations, which allows us to predict the establishment of a bar pattern whose features are similar to those experimentally observed. Two prominent features of the finite-amplitude bar pattern are (1) bar apices are distributed at a radial distance from the inflow consistent with work of Shaw et al. (2018); and (2) that the flow aspect ratio of the interbar areas remain high without provoking further instability. Both features imply that in general expansion acts to reduce bar development relative to an equivalent rectilinear flow. © 2019 John Wiley & Sons,  Ltd.     

On the influence of stratification and tidal forcing upon mixing in sill regions

A cross-sectional non-hydrostatic model with idealized topography was used to examine the processes influencing tidal mixing in the region of sills. Initial calculations with appropriate parameters for the sill at the entrance to Loch Etive showed that the model could reproduce the main features of the observed mixing in the region. In particular, the hydraulic jump in the sill region was reproduced, as was an intense mid-water jet that was observed to separate from the lee side of the sill. Shear instabilities associated with the jet appeared to be a source of mixing within the thermocline. In addition, internal lee waves were generated on the lee side of the sill, with the observed amplification because of trapping during the flood stage. Their magnitude and hence the mixing increased with increasing Froude number (F _r). In the case of vertically varying buoyancy frequency, its value near the sill top determined the F _r number, with its value below influencing internal waves magnitude at depth. At high F _r values particularly with strong currents, short waves and overturning occurred.     

Stable channel analysis with sediment transport for rivers in Malaysia: A case study of the Muda,Kurau, and Langat rivers

Assessments of a stable channel were done to evaluate the conditions of three rivers in Malaysia,using an analytical method that modifies the stable channel flowchart developed by Chang(1988) and Ariffin(2004).The analytical approach was selected to calculate the suitable dimensions for a stable channel,using equations that describe the physical relation of sediment transport,flow resistance,and dynamic equilibrium.Measured field data were used as the input data for the stable channel program,wh...     

The role of lithology,catchment size and the alluvial zone on the hydrogeochemistry of two intermittent Mediterranean streams

Hydrology and solute concentrations of two intermittent Mediterranean streams draining two nested catchments were compared. The two catchments were mainly underlain by granitic rocks and different types of sericitic schists. Only the lowland catchment had an alluvial zone and a well‐developed riparian forest. The rainfall–runoff relationship and the correlation between daily flow concentrations showed that hydrological behaviour was similar at both sites during most of the year. However, reverse fluxes were detected during the wetting and drying up periods only in the stream with an alluvial zone. The intermittence in stream flow also had effects on absolute solute concentrations, temporal solute dynamics and streamwater stoichiometry. Streamwater chemistry was not affected by drainage area, except for cations produced mainly by bedrock dissolution (i.e. calcium and magnesium) that increased with increasing catchment size. Differences in the relationship among cations and anions were detected between the two streams, which could be attributed to biogeochemical processes occurring in the alluvial zone. The multivariate model used in this study showed that stoichiometry was more useful than absolute concentrations when analyzing the influence of different lithologies on streamwater chemistry. Such differences were amplified in autumn, likely due to a low hydrological connectivity between the two nested catchments. Copyright © 2007 John Wiley & Sons, Ltd.