Numerical modelling of two-dimensional morphodynamics with applications to river bars and bifurcations

We study the numerical approximation of the two-dimensional morphodynamic model governed by the shallow water and Exner equations to simulate reach-scale two-dimensional morphodynamics of bedload-dominated alluvial rivers. The solution strategy relies on a full coupling of the governing equations within each time step. The resulting system of governing equations contains nonconservative products related to the longitudinal and lateral bed slopes and source terms related to friction. The full problem is solved numerically on unstructured triangular grids, simultaneously updating the principal part and adding the source terms (friction) using a splitting technique.The principal part is solved by means of a novel second-order accurate upwind-biased centred scheme of the finite volume type, while the source terms are added to the problem by solving a system of ordinary differential equations. A new algorithm for treating the wetting-and-drying is also proposed.The model is applied to well-established test problems in order to verify the accuracy of the proposed method, the robustness of the wetting-and-drying algorithm and the ability of the model in dealing with transcritical flows. Finally we test the model ability to reproduce two dimensional morphodynamic processes occurring at the scale of tens of channel widths in bedload dominated alluvial rivers with homogeneous grain size. This is achieved by comparing model outcomes with those of analytical theories and flume experiments on the same morphodynamic processes. These selected “benchmarks” include migrating free bars spontaneously developing in straight reaches, steady bars forced by abrupt river planform changes and the dynamics of channel bifurcations.     

Bedload transport in shallow water models: Why splitting (may) fail, how hyperbolicity (can) help

In this paper, we are concerned with sediment transport models consisting of a shallow water system coupled with the so called Exner equation to describe the evolution of the topography. We show that, for some bedload transport models like the well-known Meyer-Peter and Müller model, the system is hyperbolic and, thus, linearly stable, only under some constraint on the velocity. In practical situations, this condition is hopefully fulfilled. Numerical approximations of such system are often based on a splitting method, solving first shallow water equation on a time step and, updating afterwards the topography. It is shown that this strategy can create spurious/unphysical oscillations which are related to the study of hyperbolicity. Using an upper bound of the largest eigenvector may improve the results although the instabilities cannot be always avoided, e.g. in supercritical regions.     

2-D SIMULATION OF CHANNEL FLOWS WITH MOVEABLE BED

1 INTRODUCTIONFor many hydraulic engineering problems, the analysis of flow and bed level variations in openchannels is a fundamental prerequisite. forcal methOds fOr alluvial rivers are well develoPednowadays as far as onediInensional descriPtions are concemed. A cOmPrhensive analysis of Ihe wellknown models is Presented by Habersack(l998). HOwever, for a number of Problems such as channelwidening, flow pattem close to sPuds and etc. a more deailed knowledge of the bed level behavio…     

A one‐dimensional process‐based approach to study reservoir sediment dynamics during management operations

A comprehensive understanding of the dynamics of erosion and sedimentation in reservoirs under different management conditions is required to anticipate sedimentation issues and implement effective sediment management strategies. This paper describes a unique approach combining fluvial geomorphology tools and morphodynamic modeling for analyzing the sediment dynamics of an elongated hydropower reservoir subjected to management operations: the Génissiat Reservoir on the Rhône River. Functional sub‐reaches representative of the reservoir morphodynamics were delineated by adapting natural river segmentation methods to elongated reservoirs. The segmentation revealed the link between the spatial and temporal reservoir changes and the variability of longitudinal flow conditions during reservoir management operations. An innovative modeling strategy, incorporating the reservoir segmentation into two sediment transport codes, was implemented to simulate the dynamics of erosion and sedimentation at the reach scale during historic events. One code used a bedload approach, based on the Exner equation with a transport capacity formula, and the other used a suspended load approach based on the advection–dispersion equation. This strategy provided a fair quantification of the dynamics of erosion and sedimentation at the reach scale during different management operations. This study showed that the reservoir morphodynamics is controlled by bedload transport in upper reaches, graded suspended load transport of sand in middle reaches and suspended load transport of fine sediments in lower reaches. Eventually, it allowed a better understanding of the impact of dam management on sediment dynamics. Copyright © 2017 John Wiley & Sons, Ltd.     

Modelling dam-break flows over mobile beds using a 2D coupled approach

Dam-break flows usually propagate along rivers and floodplains, where the processes of fluid flow, sediment transport and bed evolution are closely linked. However, the majority of existing two-dimensional (2D) models used to simulate dam-break flows are only applicable to fixed beds. Details are given in this paper of the development of a 2D morphodynamic model for predicting dam-break flows over mobile beds. In this model, the common 2D shallow water equations are modified, so that the effects of sediment concentrations and bed evolution on the flood wave propagation can be considered. These equations are used together with the non-equilibrium transport equations for graded sediments and the equation of bed evolution. The governing equations are solved using a matrix method, thus the hydrodynamic, sediment transport and morphological processes can be jointly solved. The model employs an unstructured finite volume algorithm, with an approximate Riemann solver, based on the Roe-MUSCL scheme. A predictor–corrector scheme is used in time stepping, leading to a second-order accurate solution in both time and space. In addition, the model considers the adjustment process of bed material composition during the morphological evolution process. The model was first verified against results from existing numerical models and laboratory experiments. It was then used to simulate dam-break flows over a fixed bed and a mobile bed to examine the differences in the predicted flood wave speed and depth. The effects of bed material size distributions on the flood flow and bed evolution were also investigated. The results indicate that there is a great difference between the dam-break flow predictions made over a fixed bed and a mobile bed. At the initial stage of a dam-break flow, the rate of bed evolution could be comparable to that of water depth change. Therefore, it is often necessary to employ the turbid water governing equations using a coupled approach for simulating dam-break flows.     

Well-balanced high-order centered schemes on unstructured meshes for shallow water equations with fixed and mobile bed

In this paper, we study the numerical approximation of the two-dimensional morphodynamic model governed by the shallow water equations and bed-load transport following a coupled solution strategy. The resulting system of governing equations contains non-conservative products and it is solved simultaneously within each time step. The numerical solution is obtained using a new high-order accurate centered scheme of the finite volume type on unstructured meshes, which is an extension of the one-dimensional PRICE-C scheme recently proposed in Canestrelli et al. (2009) [5]. The resulting first-order accurate centered method is then extended to high order of accuracy in space via a high order WENO reconstruction technique and in time via a local continuous space–time Galerkin predictor method. The scheme is applied to the shallow water equations and the well-balanced properties of the method are investigated. Finally, we apply the new scheme to different test cases with both fixed and movable bed. An attractive future of the proposed method is that it is particularly suitable for engineering applications since it allows practitioners to adopt the most suitable sediment transport formula which better fits the field data.     

Parsimonious sediment transport equations based on Bagnold's stream power approach

It is increasingly recognized that effective river management requires a catchment scale approach. Sediment transport processes are relevant to a number of river functions but quantifying sediment fluxes at network scales is hampered by the difficulty of measuring the variables required for most sediment transport equations (e.g. shear stress, velocity, and flow depth). We develop new bedload and total load sediment transport equations based on specific stream power. These equations use data that are relatively easy to collect or estimate throughout stream networks using remote sensing and other available data: slope, discharge, channel width, and grain size. The new equations are parsimonious yet have similar accuracy to other, more established, alternatives. We further confirm previous findings that the dimensionless critical specific stream power for incipient particle motion is generally consistent across datasets, and that the uncertainty in this parameter has only a minor impact on calculated sediment transport rates. Finally, we test the new bedload transport equation by applying it in a simple channel incision model. Our model results are in close agreement to flume observations and can predict incision rates more accurately than a more complicated morphodynamic model. These new sediment transport equations are well suited for use at stream network scales, allowing quantification of this important process for river management applications. Copyright © 2017 John Wiley & Sons, Ltd.     

Hydrodynamic and sediment dynamic modifications of tidal flow in the near-field area of offshore breakwaters

Numerical modeling was used in order to study the effect of tidal currents within a breakwater scheme that has reached morphodynamic equilibrium. Tidal flow is simulated, using a downscaling procedure from a regional numerical model, in order to investigate the small-scale hydrodynamic modifications caused by the structures in the absence of waves. Sediment transport processes at different stages of the neap and spring tidal cycle are also considered over the entire scheme. Significant modifications to the tidal currents were identified, caused by the presence of the following structures: (1) obstruction of the main tidal flow and (2) flow channelization between the structures and the coastline, leading to flow acceleration over the salients. Furthermore, the effect of the modified tidal regime on bedload sediment transport processes was investigated. The design characteristics of the scheme (i.e., gap width, offshore distance, and relative angle with respect to the tidal currents) are found to influence locally the tidal flow and the bedload transport, over the top of the salients, modulating their growth. Despite being located in a mixed-energy, wave-dominated environment, the shear stress ratio between currents and waves show a dominance of tidal processes at the sheltered areas of the scheme (i.e., behind the breakwaters) that diminishes as the incident wave period increases. Hence, in order to correctly predict the morphological evolution of such coast under the influence of coastal protection schemes, the tidal processes have to be studied in addition to the wave processes.     

Reconciled bedload sediment transport rates in ephemeral and perennial rivers

It has been thought for some time that bedload sediment transport rates may differ markedly in ephemeral and perennial rivers and, supporting this thought, there has been observation of very high rates of bedload transport by flash floods in the ephemeral river Nahal Yatir. However, until now, there has been no quantitative model resolving the observation, nor a theory capable of explaining why bedload transport rates by unsteady flash floods can be reasonably well described by bedload transport capacity formulae initially derived for steady flows. Here a time scale analysis of bedload transport is presented as pertaining to Nahal Yatir, which demonstrates that bedload transport can adapt sufficiently rapidly to capacity determined exclusively by local flow regime, and accordingly the transport capacity formulations developed for steady flows can be applied even under unsteady flows such as flash floods. Complementing the time scale analysis, a series of computational exercises using a coupled shallow water hydrodynamic model are shown to adequately resolve the observation of the very high rates of bedload transport by flash floods in Nahal Yatir. While bedload transport rates in ephemeral and perennial rivers differ remarkably when evaluated against a pure flow parameter such as specific stream power, they are essentially reconciled if assessed with a physically sensible parameter incorporating not only the flow regime but also the sediment particle size. The present finding underpins the practice of fluvial geomorphologists relating measured bedload transport to local flow and sediment characteristics only, irrespective of whether the flow is unsteady or steady. Copyright © 2010 John Wiley & Sons, Ltd.     

MODELING SEDIMENT PROCESSES ON SMALL WATERSHEDS:A CONCEPTUAL FRAMEWORK Ⅰ. BROAD SHALLOW FLOW PROCESSE

A conceptual modeling framework for developing process-based mathematical models of sediment generation, transport, and deposition on broad shallow flow areas is presented. The governing equations relevant to process-based modeling of broad shallow flow sediment processes on small watersheds are presented and the effects of space and time averaging on the predictive equations are described. Starting from the most general one-dimensional, unsteady model of sediment processes, simpler model structures are obtained and the successive simplifications made on the governing equations in order to obtain simpler and less detailed formulations are described. Specific model formulations are given for illustrative purposes and applications of these models to erosion and sediment yield prediction from broad shallow flow areas are shown using sediment data from rainfall simulator plots. In spite of some progress made in the development of process-based erosion and sediment yield models from broad shallow flow areas, further developmental modeling efforts must be based on a clear separation between hydrologic and hydraulic processes, and the soil properties which are significant for each.     

TWO DIMENSIONAL NUMERICAL SIMULATION OF FLOW AND GEO-MORPHOLOGICAL PROCESSES NEAR HEADLANDS BY USING UNSTRUCTURED GRID

1 INTRODUCTION In recent years, due to the increase in population and industrial developments, mankind has faced manyproblems associated with rivers, coastal waters and reservoirs. Some of these problems are flood control,water supply, power generation, and irrigation. In addition, making new hydraulic structures changesnatural conditions. Prediction of these changes is necessary for designing such constructions. For solutionof these problems usually an assessment of flow pattern, sedim…     

Oscillatory bedload transport: Data review and simple formulation

This review displays over 700 rates of sediment transport by oscillatory flow from 20 sources. Sediments include fine sands to pebbles, both of quartz and of lightweight materials, and the transport rates in water range over seven orders of magnitude. Most data are average gross (to and fro) bedload rates collinear with laboratory flow over a horizontal sediment bed, although other situations with net transport, suspended load, or oblique field waves are considered.As peak flow velocity nears twice the threshold velocity for sediment motion, bedload appears to be fully developed and the transport rate is near that given by a simple formula including flow frequency and peak velocity, and sediment size and density. At lesser peak velocities, bedload rates are markedly smaller and distinctly different regimes of sediment mobilization and transport may be identified.     

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.     

Formation of stationary alternate bars in a steep channel with mixed-size sediment: A flume experiment

Alternate bars were formed by sediment transport in a flume with Froude-modelled flow and relative roughness characteristic of gravel-boulder channels with steep slopes. The flume (0.3 m wide × 7.5 m long) was filled with a sand-gravel mixture, which was also fed into the top of the flume at a constant rate under constant discharge. Channel slope was set at 0.03. Initially, coarse particles accumulated on incipient bar heads near one side of the flume and diverted flow and bedload transport across the flume toward a pool scoured against the opposite flume wall downstream. Sorting in the pool directed coarse particles onto the next bar head downstream. Alternate sequences of pools and coarse bar heads were thereby linked down the entire flume by interactions of sediment sorting, flow, and channel morphology. During episodes of bar construction, unsorted bedload invaded interior bar surfaces and was deposited. Persistent deposition of coarse particles on bar heads prevented downstream migration of bars by inhibiting bar-head erosion and bedload transport over bars. Likely factors leading to bar-head stabilization in modelled gravel-bed channels are coarse mixed-size sediment, steep channel gradients, and shallow depths.     

A model based on Hirano-Exner equations for two-dimensional transient flows over heterogeneous erodible beds

In order to study the morphological evolution of river beds composed of heterogeneous material, the interaction among the different grain sizes must be taken into account. In this paper, these equations are combined with the two-dimensional shallow water equations to describe the flow field. The resulting system of equations can be solved in two ways: (i) in a coupled way, solving flow and sediment equations simultaneously at a given time-step or (ii) in an uncoupled manner by first solving the flow field and using the magnitudes obtained at each time-step to update the channel morphology (bed and surface composition). The coupled strategy is preferable when dealing with strong and quick interactions between the flow field, the bed evolution and the different particle sizes present on the bed surface. A number of numerical difficulties arise from solving the fully coupled system of equations. These problems are reduced by means of a weakly-coupled strategy to numerically estimate the wave celerities containing the information of the bed and the grain sizes present on the bed. Hence, a two-dimensional numerical scheme able to simulate in a self-stable way the unsteady morphological evolution of channels formed by cohesionless grain size mixtures is presented. The coupling technique is simplified without decreasing the number of waves involved in the numerical scheme but by simplifying their definitions. The numerical results are satisfactorily tested with synthetic cases and against experimental data.     

LES-DEM simulations of sediment transport

In this work, a fully-coupled Computational Fluid Dynamics (CFD) model and Discrete Element Method (DEM) are used to simulate a unidirectional turbulent open-channel flow over the full range of sediment transport regimes. The fluid and particles are computed on separate grids using a dual-grid formulation to maintain consistency and avoid instability issues. The results of coupling the dispersed phase to a multiphase flow solver that uses volume-averaged Navier-Stokes equations are compared to those obtained from coupling through drag to a single flow solver. The current work also examines the applicability and limitations of lumping particles as a representative particle to reduce the cost of simulations. Insight to the impact of different turbulent events to the entrainment of particles is also given. The simulation results of sediment transport from both coupling techniques show good agreement with empirical formulas in the bedload regime, but under-predict sediment transport in the suspended load regime. In the suspended load regime, using partial coupling, the rate of sediment transport was found to be under-predicted as compared to full-coupling. The deviation in results in the suspended load regime was found to increase with increases in the applied shear stress. Both coupling methods revealed the same effect on the friction factor where friction increases in the bedload regime and decreases in the suspended load regime reaching a maximum at the transition between regimes. This result is contrary to past studies which have shown a discrete jump in the friction factor at the transition. Lumping particles as representative particles is shown to reduce the simulation cost by more than a factor of 5 when using a scaling factor of 2. By doing a quadrant analysis on information obtained from particle and flow field results, it was found that most of the particles are entrained by more frequent sweep events.     

Fully coupled methods for multiphase morphodynamics

We present numerical methods for a system of equations consisting of the two dimensional Saint–Venant shallow water equations (SWEs) fully coupled to a completely generalized Exner formulation of hydrodynamically driven sediment discharge. This formulation is implemented by way of a discontinuous Galerkin (DG) finite element method, using a Roe Flux for the advective components and the unified form for the dissipative components. We implement a number of Runge–Kutta time integrators, including a family of strong stability preserving (SSP) schemes, and Runge–Kutta Chebyshev (RKC) methods. A brief discussion is provided regarding implementational details for generalizable computer algebra tokenization using arbitrary algebraic fluxes. We then run numerical experiments to show standard convergence rates, and discuss important mathematical and numerical nuances that arise due to prominent features in the coupled system, such as the emergence of nondifferentiable and sharp zero crossing functions, radii of convergence in manufactured solutions, and nonconservative product (NCP) formalisms. Finally we present a challenging application model concerning hydrothermal venting across metalliferous muds in the presence of chemical reactions occurring in low pH environments.     

Experimental investigation of sediment transport in partially ice-covered channels

It is important to understand the effects of ice cover on sediment transport in cold climates, where sub-freezing temperatures affect water bodies for a significant part of the year. The literature contains many studies on sediment transport in open channel flow, and several studies on sediment transport in completely ice-covered flow. There has been little or no research on sediment transport in partially ice-covered channels. In the current study, laboratory experiments were done in a rectangular flume to quantify the impact of border ice presence on the sediment transport rate. The effects of ice cover extent and changing flow strengths on sediment transport distribution also were investigated, and the results were compared to those for fully ice-covered and open channel flow. The ice coverage ratios considered were 0 (representing the open water condition), 0.25, 0.50, 0.67, and 1 (representing fully ice-covered flow). The partial ice cover was found to impact the sediment transport distribution within the channel. The effect of ice coverage extent on sediment transport distribution was more significant at lower flow strengths and became negligible at higher flow strengths. The conventional equations for sediment transport in open channel flow and fully ice-covered flow that relate the dimensionless bedload transport rate to the flow strength were found to be applicable to estimate the total cross-section-averaged bedload transport for partially ice-covered flow when modified appropriately. Empirical coefficients for these equations were determined using the experimental data.     

Assessment of the performance of numerical modeling in reproducing a replenishment of sediments in a water-worked channel

The artificial replenishment of sediment is used as a method to re-establish sediment continuity downstream of a dam. However, the impact of this technique on the hydraulics conditions, and resulting bed morphology, is yet to be understood. Several numerical tools have been developed during last years for modeling sediment transport and morphology evolution which can be used for this application. These models range from 1D to 3D approaches: the first being over simplistic for the simulation of such a complex geometry; the latter requires often a prohibitive computational effort. However, 2D models are computationally efficient and in these cases may already provide sufficiently accurate predictions of the morphology evolution caused by the sediment replenishment in a river. Here, the 2D shallow water equations in combination with the Exner equation are solved by means of a weak-coupled strategy. The classical friction approach considered for reproducing the bed channel roughness has been modified to take into account the morphological effect of replenishment which provokes a channel bed fining. Computational outcomes are compared with four sets of experimental data obtained from several replenishment configurations studied in the laboratory. The experiments differ in terms of placement volume and configuration. A set of analysis parameters is proposed for the experimental-numerical comparison, with particular attention to the spreading, covered surface and travel distance of placed replenishment grains. The numerical tool is reliable in reproducing the overall tendency shown by the experimental data. The effect of fining roughness is better reproduced with the approach herein proposed. However, it is also highlighted that the sediment clusters found in the experiment are not well numerically reproduced in the regions of the channel with a limited number of sediment grains.     

MODELING SEDIMENT PROCESSES ON SMALL WATERSHEDS: A CONCEPTUAL FRAMEWORK Ⅱ. CONCENTRATED FLOW PROCESSES

L INTRODUCTIONThe purpose of this paper is to present a general modeling framework that can serveas a conceptual basis for developing sediment process models by concentrated flow systems on small watersheds. A survey of fundamental principles for developing sedimentprocess models is made with particular emphasis on the effects of space and time averaging on the governing equations. Starting from the most general one--dimensional,unsteady model of sediment processes, simpler model structur…