On evolution of bed material waves in alluvial rivers

Field and laboratory measurements have shown distinct characteristics of bed sediment waves under differing conditions, whilst their theoretical interpretation has emerged to be equivocal. This note aims to clarify the interpretation of evolution of bed material waves. The complete set of governing equations for the flow–sediment–morphology system is deduced to demonstrate its universally hyperbolic nature, irrespective of the sediment transport functions implemented to close the equations. The hyperbolic nature can admit not only attenuating bed material waves, but also shock‐like waves that are not unusual in the real world. It is suggested that the theory of dispersion/diffusion is not universally appropriate for evolution of bed material waves. Copyright © 2003 John Wiley & Sons, Ltd.     

Further perspectives on the evolution of bed material waves in alluvial rivers

In one‐dimensional mathematical models of ?uvial ?ow, sediment transport and morphological evolution, the governing equations based on mass and momentum conservation laws constitute a hyperbolic system. Succinctly, the hyperbolic nature excludes dispersion or diffusion operators, which is well known in the context of differential equations. There is no doubt that the so‐called ‘dispersion’ argument for bed material wave evolution is questionable, as we have explicitly asserted. Surprisingly, in a recent communication, the authors of the ‘dispersion’ argument suggest that dispersion is not precluded in hyperbolic systems. We provide herein further perspectives to help explain that the dispersion argument is neither appropriate nor necessary for interpreting bed material wave evolution. Also the continuity equations involved are addressed to prompt wider understanding of their signi?cance. In particular, the continuity equation of the water–sediment mixture proposed by the authors of the ‘dispersion’ argument is proved to be incorrect, and inevitably their reasoning based on it is problematic. Copyright © 2005 John Wiley & Sons, Ltd.     

Sediment variability and bed material sampling in gravel-bed rivers

In a 350 m wide reach of the braided, gravel-bed Ashley River, the surface layer of the bed material was sampled in 141 areas of homogeneous graded sediment along seven cross-sections, and 30 kg bulk samples were collected at 86 randomly selected locations along the cross-sections. At one location, a single 854 kg sample composed of 28 subsamples was also collected. Analysis of the single large sample indicate that accurate determination of mean grain size D at that site requires, desirably, a sample of ～ 100 kg, but that samples in which the weight of the largest stone is less than 5 per cent of the total weight have unbiased estimates of D. Spatial variability of bulk material is such that 228 and 50 samples are needed to estimate D to ± 10 and ± 20 per cent respectively of the true value; requirements for estimating inclusive graphic standard duration are only 11 and 3 respectively. The grain-size distribution of the surface layer is only weakly related to the bulk material beneath. The results of ‘Wolman sampling’ along 12 cross-sections at two pace intervals (average 120 stones per cross-section) indicate that estimation of overall surface D to ±10 and ±20 per cent would require sampling along 64 and 14 cross-sections respectively. It is concluded that accurate characterization of bed sediment in gravel-bed rivers is very demanding of labour and resources, and that careful planning is needed to ensure efficiency and meaningful results.     

Particle size distribution of bed materials in the sandy river bed of alluvial rivers

The particle size distribution of bed materials in the sandy river bed of alluvial rivers is important in the study of topics such as friction, river bed evolution, erosion, and siltation. It also can reflect the dependency relation between river bed sediment and flow intensity. In this paper, the critical pattern of sediment movement in the near-wall region of a sandy river bed was analyzed. According to the principle of momentum balance, the critical settling-rising condition of bed material in a sandy river bed was found to be instantaneous turbulent velocity equal to 2.7 times the sediment settling velocity in quiescent water. Based on a vertical instantaneous turbulent velocity with a Gaussian distribution, a theoretical relation for calculating the particle size distribution of bed materials in a sandy river bed without pre-known characteristic grain sizes was developed by solving a stochastic equation. The for-mula is verified using measured data, and the results show that the proposed formula was in accordance with the measured data. This study has theoretical significance and practical value for determining the bed material particle size distribution of the sandy bed of alluvial rivers.     

Bed material transport estimate in large gravel‐bed rivers using the virtual velocity approach

This paper reports on a first attempt of using the virtual velocity approach to assess sediment mobility and transport in two wide and complex gravel‐bed rivers of northern Italy. Displacement length and virtual velocity of spray‐painted tracers were measured in the field. Also, the thickness of the sediment active layer during floods was measured using scour chains and post‐flood morphological changes as documented by repeated survey of channel cross‐sections. The effects of eight and seven floods were studied on the Tagliamento and Brenta Rivers, where 259 and 277 spray‐painted areas were surveyed, respectively. In the Tagliamento River 36% of the spray‐painted areas experienced partial transport, whereas in the Brenta River this accounted for 20%. Whereas, full removal/gravel deposition was observed on 37% and 26% of these areas on the Tagliamento and Brenta Rivers, respectively. The mean displacement length of particles, the thickness of the active layer and the extent of partial transport are well correlated with the dimensionless shear stress. The virtual velocity approach allowed calculation of bed material transport over a wide range of flood magnitudes. Annual coarse sediment transport was calculated up to 150 for the Tagliamento, and 30 × 10³  m³ yr^?1 for the Brenta. The outcomes of this work highlight the relevance of partial transport condition, as it could represent more than 70% of the total bed material transported during low‐magnitude floods, and up to 40% for near‐bankfull events. Results confirm that bed material load tends to be overestimated by traditional formulas. Copyright © 2016 John Wiley & Sons, Ltd.     

Coupled simulation of transient bed evolution in alluvial channels

Abstract

In dealing with the transient sediment transport problem, the commonly used uncoupled model may not be suitable. The uncoupling technique is intended to separate the physical coupling phenomenon of water flow and sediment transport into two independent processes. Very often, as a result, severe numerical oscillation and solution instability problems appear in the simulation of transient sediment transport in alluvial channels. The coupled model, which simultaneously solves water flow continuity, momentum and sediment continuity equations, gives fewer numerical oscillation and solution instability problems. In this article, a coupled model using a matrix double-sweep method to solve the system of nonlinear algebraic equations has been developed. Several test runs designed on the basis of a schematic model have been performed. The numerical oscillation and solution instability problems have been investigated through a comparison with those obtained from an uncoupled model. Based on the proposed case studies, it can be concluded that, for transient bed evolution, the performance of the coupled model is much better than that of the uncoupled model. The numerical oscillation is reduced and the solution is more stable. This newly developed coupled model was also applied to the Cho-Shui River in Taiwan. This application study implied that the effect of the peaky flood wave propagation on the bed evolution could be simulated better by the coupled model than by the uncoupled model.     

The influence of climate change on suspended sediment transport in Danish rivers

The HIRHAM regional climate model suggests an increase in temperature in Denmark of about 3 °C and an increase in mean annual precipitation of 6–7%, with a larger increase during winter and a decrease during summer between a control period 1961–1990 and scenario period 2071–2100. This change of climate will affect the suspended sediment transport in rivers, directly through erosion processes and increased river discharges and indirectly through changes in land use and land cover. Climate‐change‐induced changes in suspended sediment transport are modelled for five scenarios on the basis of modelled changes in land use/land cover for two Danish river catchments: the alluvial River Ansager and the non‐alluvial River Odense. Mean annual suspended sediment transport is modelled to increase by 17% in the alluvial river and by 27% in the non‐alluvial for steady‐state scenarios. Increases by about 9% in the alluvial river and 24% in the non‐alluvial river were determined for scenarios incorporating a prolonged growing season for catchment vegetation. Shortening of the growing season is found to have little influence on mean annual sediment transport. Mean monthly changes in suspended sediment transport between ? 26% and + 68% are found for comparable suspended sediment transport scenarios between the control and the scenario periods. The suspended sediment transport increases during winter months as a result of the increase in river discharge caused by the increase in precipitation, and decreases during summer and early autumn months. Copyright © 2007 John Wiley & Sons, Ltd.     

Modifications of the dispersion relations for surface waves in a layer on a half-space

Summary Dispersion relations for Love and Rayleigh waves in a layer on a half-space are modified by introducing quadratic slownesses instead of velocities. The advantages of this approach are demonstrated on analytical formulae for computing the group velocity.     

Well-balanced numerical modelling of non-uniform sediment transport in alluvial rivers

The last two decades have witnessed the development and application of well-balanced numerical models for shallow flows in natural rivers.However,until now there have been no such models for flows with non-uniform sediment transport.This paper presents a 1D well-balanced model to simulate flows and non-capacity transport of non-uniform sediment in alluvial rivers.The active layer formulation is adopted to resolve the change of bed sediment composition.In the framework of the finite volume Slope Llmiter Centred(SLIC) scheme,a surface gradient method is incorporated to attain well-balanced solutions to the governing equations.The proposed model is tested against typical cases with irregular topography,including the refilling of dredged trenches,aggradation due to sediment overloading and flood flow due to landslide dam failure.The agreement between the computed results and measured data is encouraging.Compared to a non-well-balanced model,the well-balanced model features improved performance in reproducing stage,velocity and bed deformation.It should find general applications for non-uniform sediment transport modelling in alluvial rivers,especially in mountain areas where the bed topography is mostly irregular.     

Dispersive effects of zonally varying topography on quasigeostrophic Rossby waves

Abstract

Dispersion of linear quasigeostrophic plane waves in a stratified ocean with bottom topography is discussed. Particular emphasis is given to cases for which zonal gradients in the sea floor height are important. As such, the relative importance of the topographic and planetary β-effects is strongly dependent on wave vector orientation. The magnitude of the topographic slopes considered is chosen such that these two effects (topographic and planetary β) are of comparable importance. In the interest of simplicity, stratification is taken to be independent of depth. The eigenvalue problem which must be solved to find the free modes of oscillation has already been treated in the literature (in fact, Charney and Flierl (1981) have treated the effects of a more realistic stratification). The aim of this note is to more fully expose, primarily by example, several dispersive properties of these free wave modes which have been largely overlooked.     

Active width of gravel‐bed braided rivers

Previous analyses have identified the active width of braided rivers, the bed area over which bed load flux and short‐term morphological change occurs, as an important element of braiding dynamics and predictions of bed load flux. Here we compare theoretical predictions of active width in gravel‐bed braided rivers with observations from Sunwapta River, and from a generic physical model of gravel braided rivers, to provide general observations of the variation in active width, and to develop an understanding of the causes of variation. Bed topography was surveyed daily along a 150 m reach of the pro‐glacial Sunwapta River for a total of four weeks during summer when flow was above threshold for morphological activity. In the laboratory, detailed digital elevation models (DEMs) were derived from photogrammetric survey at regular intervals during a constant discharge run. From the field and flume observations there is considerable local and circumstantial variation in active width, but also a general trend in average active width with increasing discharge. There is also a clear relationship of active width with active braiding index (number of active branches in the braided channel network), and with dimensionless stream power, which appears to be consistent across the range of data from field and physical models. Thus there is a link between active width and the river morphology and dynamics, and the possibility of a general relationship for estimating active width from channel pattern properties or reach‐scale stream power values, from which approximate bedload flux calculations may be made. The analysis also raises questions about differences between hydraulically‐based numerical model computations of instantaneous active width and observation of time‐integrated morphological active width. Understanding these differences can give insight into the nature of bedload transport in braided rivers and the relationship to morphological processes of braiding. Copyright © 2011 John Wiley & Sons, Ltd.     

Scattering of plane P waves by circular-arc alluvial valleys with saturated soil deposits

This paper presents an analytical solution for two-dimensional scattering and diffraction of plane P waves by circular-arc alluvial valleys with shallow saturated soil deposits. The solution is based on Biot's dynamic theory for saturated porous media, and derived by employing Fourier–Bessel series expansion technique. In this analysis, soil deposits in the circular-arc valley are modeled as saturated porous media based on Biot's dynamic theory, and the circular-arc valley is assumed to be imbedded in an infinite half-space, filled with elastic single-phase media. Numerical results from this solution show that the amplitudes of displacement at the surface of an alluvial valley are mainly relative to the angle of incidence, the dimensionless frequency of incident P wave, the degree of saturation and porosity of soil deposits, and the stiffness and Poisson's ratio of the solid skeleton of the soil deposits. Furthermore, the proposed solution is compared with the previous solution, in which the soil deposit was modeled as an elastic single-phase solid.     

BFO-PSO算法下的弹性波数值模拟

地震波正演模拟是地震反演与成像的基础和关键,有限差分算法广泛应用于地震波数值模拟,差分算子的精度直接影响数值模拟的质量和效率.本文提出一种BFO-PSO算法下的有限差分算子优化方法,并应用其进行弹性波数值模拟.首先,将BFO算法中的趋化、复制、驱散三个步骤引入PSO算法,形成具有更好全局搜索能力和更快收敛速度的BFO-...     

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.     

Simulating the role of tides and sediment characteristics on tidal flat sorting and bedding dynamics

Understanding sediment sorting and bedding dynamics has high value to unravelling the mechanisms underlying geomorphological, geological, ecological and environmental imprints of tidal wetlands and hence to predicting their future changes. Using the Nanhui tidal flat on the Changjiang (Yangtze) Delta, China, as a reference site, this study establishes a schematized morphodynamic model coupling flow, sediment dynamics and bed level change to explore the processes that govern sediment sorting and bedding phenomena. Model results indicate an overall agreement with field data in terms of tidal current velocities, suspended sediment concentrations (SSCs), deposition thicknesses and sedimentary structures. Depending on the variation of tidal current strength, sand-dominated layers (SDLs) and mud-dominated layers (MDLs) tend to form during spring and neap tides, respectively. Thinner tidal couplets are developed during daily scale flood–ebb variations. A larger tidal level variation during a spring–neap tidal cycle, associated with a stronger tidal current variation, favours the formation of SDLs and tidal couplets. A larger boundary sediment supply generally promotes the formation of tidal bedding, though the bedding detail is partially dependent on the SSC composition of different sediment types. Sediment properties, including for example grain size and settling velocity, are also found to influence sediment sorting and bedding characteristics. In particular, finer and coarser sediment respond differently to spring and neap tides. During neap tides, relatively small flow velocities favour the deposition of finer sediment, with limited coarser sediment being transported to the upper tidal flat because of the larger settling velocity. During spring tides, larger flow velocities transport more coarser sediment to the upper tidal flat, accounting for distinct lamination formation. Model results are qualitatively consistent with field observations, but the role of waves, biological processes and alongshore currents needs to be included in further studies to establish a more complete understanding.     

Analytical partial derivatives of the phase- and group velocities for Rayleigh waves propagating in a layer on a half-space

The dispersion relation for Rayleigh waves in a layer on a half-space is modified by introducing the quadratic wave number instead of the phase velocity. The implicit function theorem is then used to derive analytical formulae for the group velocity and for the phase- and group velocity partial derivatives with respect to the parameters of the medium. As two examples, the method is applied to the interpretation of dispersion curves for short-period Rayleigh waves observed in a sedimentary basin of the West Carpathians, and in the Moravo-Silesian region, Czech Republic.     

Currents induced by vertical varied radiation stress in standing waves and evolution of the bed composed of fine sediments

This paper extends the conventional concept of radiation stress （Longuet-Higgins and Stewart, 1964） in progressive water waves to standing waves, so that its vertical profile could be defined and calculated in a new technical way. The hydrodynamic numerical model being coupled with the vertically varying radiation stress in standing waves is used to simulate the currents being induced by standing waves in the vertical section. Numerical modeling of suspended sediment transport is then carried out to simulate the evolution of the bed composed of fine sediments by the currents. The scour and deposition patterns simulated are in qualitative agreement with prior laboratory and field observations.     

Particle transport in gravel-bed rivers: Revisiting passive tracer data

Data from tracer experiments were compiled and analysed in order to explore the role of geomorphological, hydrological and sedimentological constraints on fluvial gravel transport in gravel-bed rivers. A large data set from 217 transport episodes of tagged stones were compiled from 33 scientific papers. Our analyses showed that while magnitude of peak discharge is a major control on gravel transport and mobility, tracer travel distances show some scale dependence on the morphological configuration of the channel. Our results also highlight differences in the way tracers are displaced between step–pool and riffle and pool channels. The riffle–pool sequence seems to be a more efficient trap for travelling gravels than the step–pool pair. In addition, in step–pool channels there are clear differences in tracer transport between observations of first displacements after tracer seeding (unconstrained-stone conditions), and second and subsequent observations of tracer displacements (constrained-stone conditions). The comparison between tracer experiments under constrained conditions and those under unconstrained conditions also highlights the importance of bed state and structures in gravel mobility. The results of this study confirm that sediment transport in gravel-bed rivers is a complex process, whereby sedimentological and geomorphological controls are superimposed on the hydraulic forcing. © 2018 John Wiley & Sons, Ltd.     

Numerical modelling-based comparison of longitudinal dispersion coefficient formulas for solute transport in rivers

River water quality models usually apply the Fischer equation to determine the longitudinal dispersion coefficient (D_x) in solving the advection–dispersion equation (ADE). Recently, more accurate formulas have been introduced to determine D_x in rivers, which could strongly affect the accuracy of the ADE results. A numerical modelling-based approach is presented to evaluate the performance of various D_x formulas using the ADE. This approach consists of a finite difference approximation of the ADE, a MATLAB code and a MS Excel interface; it was tested against the analytical ADE solution and demonstrated using eight well-known D_x formulas and tracer study data for the Chattahoochee River (USA), the Severn (UK) and the Athabasca (Canada). The results show that D_x has an important effect on tracer concentrations simulated with the ADE. Comparison between the simulated and measured concentrations confirms the appropriate performance of Zeng and Huai’s formula for D_x estimation. Use of the newly proposed equations for D_x estimation could enhance the accuracy of solving the ADE.     

地震面波产生的地震动转动分量研究

本文利用弹性波动理论对地面转动分量，即瑞利（Rayleigh)波和乐夫（Love)波产生的转动分量进行了研究，给出了相应的计算公式和计算方法，特别注意到面波的散射效应对转动分量的影响，并将这一特性引入到转动分量的求取中，使问题的解决更切合于实际，最后选取实际地震记录，利用得到的公式计算出地震面波产生的转动分量。