Bed Morphodynamics Research Articles

Computational modeling of dissipation and regeneration of fluvial sand dunes under variable discharges

AbstractIt is observed, during flood events, that bed forms initially grow in height and make the riverbed rougher. But later, under high discharge, the bed forms grow longer with the opposite effect of making the riverbed smoother. After the discharge drops to a lower value, new bed forms regenerate on top of the elongated bed forms. This mechanism leads to a significant variation in the bed roughness and the water stage and hence determines the behavior of floods and the risk of flood disasters. This work presents detailed modeling of bed forms under discharge hydrographs and simulates the conditions under which the bed is flattened out in the upper plane bed regime. The flow was simulated by large‐eddy simulation, and the sediments were considered as rigid spheres and modeled in a Lagrangian framework. The bed morphodynamics were the result of entrainment and deposition of sediment particles. We examined several discharge hydrographs. In the first case, we increased the discharge linearly and then kept it constant after reaching the upper plane bed condition. The dunes were generated and grew during the rising stage of discharge. When the flow conditions reached the upper plane bed regime, high‐frequency ripples were generated and helped to flatten the bed. The results also showed that in contrast with mechanisms in the dune regime, the flattening of the bed was associated with a distinct pattern of sediment transport which deposited sediment mainly in the lee side of the dunes and led to flattening of the bed. After flattening, the sediments were mainly transported in suspension mode. As long as flow conditions stayed in the upper plane bed regime, the bed remained flat with small high‐frequency ripples. We also examined two other scenarios: one with an immediate falling stage of discharge after the rising stage and the other with a period of constant discharge between the rising and falling stages. Dunes were regenerated during the falling stage of discharge for both cases. In the first case, the dunes were regenerated before the bed was flattened because of a time lag between the flow and the bed deformation. Bed flattening was followed by dune regeneration in the second case. Moreover, a significant reduction in the form drag coefficient was observed after the flattening in the second case. The reduction in form drag led to a reduction in the flood intensity. The model showed its ability to reproduce the key phenomena of the development of subaqueous dunes under conditions of a passing flood wave.

Intra‐event scale bar–bank interactions and their role in channel widening

AbstractChannel bars and banks strongly affect the morphology of both braided and meandering rivers. Accordingly, bar formation and bank erosion processes have been greatly explored. There is, however, a lack of investigations addressing the interactions between bed and bank morphodynamics, especially over short timescales. One major implication of this gap is that the processes leading to the repeated accretion of mid‐channel bars and associated widenings remain unsolved. In a restored section of the Drau River, a gravel‐bed river in Austria, mid‐channel bars have developed in a widening channel. During mean flow conditions, the bars divert the flow towards the banks. One channel section exhibited both an actively retreating bank and an expanding mid‐channel bar, and was selected to investigate the morphodynamic processes involved in bar accretion and channel widening at the intra‐event timescale. We repeatedly surveyed riverbed and riverbank topography, monitored riverbank hydrology and mounted a time‐lapse camera for continuous observation of riverbank erosion processes during four flow events. The mid‐channel bar was shown to accrete when it was submerged during flood events, which at the subsequent flow diversion during lower discharges narrowed the branch along the bank and increased the water surface elevation upstream from the riffle, which constituted the inlet into the branch. These changes of bed topography accelerated the flow along the bank and triggered bank failures up to 20 days after the flood events. Four analysed flow events exhibited a total bar expansion from initially 126 m2 to 295 m2, while bank retreat was 6 m at the apex of the branch. The results revealed the forcing role of bar accretion in channel widening and highlighted the importance of intra‐event scale bed morphodynamics for bank erosion, which were summarized in a conceptual model of the observed bar–bank interactions. Copyright © 2015 John Wiley & Sons, Ltd.

Coupling channel evolution monitoring and RFID tracking in a large, wandering, gravel-bed river: Insights into sediment routing on geomorphic continuity through a riffle–pool sequence

Bedload transport and bedform mobility in large gravel-bed rivers are not easily monitored, especially during floods. Large reaches present difficulties in bed access during flows for flow measurements. Because of these logistical issues, the current knowledge about bedload transport processes and bedform mobility lacks field-based information, while this missing information would precisely match river management needs. The lack of information linking channel evolution and particle displacements is even more striking in wandering reaches. The Durance River is a large, wandering, gravel-bed river (catchment area: 14,280km2; mean width: 240m), located in the southern French Alps and highly impacted by flow diversion and gravel mining. In order to improve current understanding of the link between sediment transport processes and river bed morphodynamics, we set up a sediment particle survey in the channel using Radio Frequency Identification (RFID) tracking and topographic surveys (GPS RTK and scour chains) for a 4-year recurrence interval flood. By combining topographic changes before and after a flood, intraflood erosion/deposition patterns from scour chains, differential routing of tracer particles, and spatial distribution of bed shear stress through a complex reach, this paper aims to define the critical shear stress for significant sediment mobility in this setting. Gravel tracking highlights displacement patterns in agreement with bar downstream migration and transport of particles across the riffle within this single flood event. Because no velocity measurements were possible during flood, a Telemac three-dimensional model helped interpret particle displacements by estimating spatial distribution of shear stresses and flow directions at peak flow. Although RFID tracking in a large, wandering, gravel-bed river does have some technical limitations (burial, recovery process time-consuming), it provides useful information on sediment routing through a riffle–pool sequence.

Extreme scenarios for the evolution of a soft bed interacting with a fluid using the Value at Risk of the bed characteristics

We show how to introduce the Value at Risk (VaR) concept in the analysis of the adaptation of the shape of a soft bed to a flow knowing the Probability Density Function (PDF) of the responses of the shape to flow perturbations (bed receptivity). Our aim is to quantify our confidence on simulation scenarios by an available morphodynamic model for the shape. The approach permits to perform this task at low complexity as it does not require any sampling of the bed receptivity parameter space. The paper goes beyond stationarity for the variability of the bed receptivity by linking its dynamics to the bottom morphodynamics through an original transport equation for the local bed receptivity standard deviation. The approach has been applied to the analysis of bed morphodynamics based on minimization principles. The results show the importance of including uncertainty information during the coupling and not only eventually through simple margins on the results.

Numerical simulation of river meandering with self-evolving banks

[1] In this study, the natural process of river meandering is captured in a computational model that considers the effects of bank erosion, the process of land accretion along the inner banks of meander bends, and the formation of channel cutoffs. The methodology for predicting bank erosion explicitly includes a submodel treating the formation and eventual removal of slump blocks. The accretion of bank material on the inner bank is modeled by defining the time scale over which areas that are originally channel become land. Channel cutoff formation is treated relatively simply by recomputing the channel alignment at a single model time step when migrating banks meet. The model is used to compute meandering processes in both steady and unsteady flows. The key features of this new model are the ability (a) to describe bank depositional and bank erosional responses separately, (b) to couple them to bed morphodynamics, and thus (c) to describe coevolving river width and sinuosity. Two cases of steady flow are considered, one with a larger discharge (i.e., “bankfull”) and one with a smaller discharge (i.e., “low flow”). In the former case, the shear stress is well above the critical shear stress, but in the latter case, it is initially below it. In at least one case of constant discharge, the planform pattern can develop some sinuosity, but the pattern appears to deviate somewhat from that observed in natural meandering channels. For the case of unsteady flow, discharge variation is modeled in the simplest possible manner by cyclically alternating the two discharges used in the steady flow computations. This model produces a rich pattern of meander planform evolution that is consistent with that observed in natural rivers. Also, the relationship between the meandering evolution and the return time scale of floods is investigated by the model under the several unsteady flow patterns. The results indicate that meandering planforms have different shapes depending on the values of these two scales. In predicting meander evolution, it is important to consider the ratio of these two time scales in addition to such factors as bank erosion, slump block formation and decay, bar accretion, and cutoff formation, which are also included in the model.

Detailed simulation of morphodynamics: 2. Sediment pickup, transport, and deposition

The paper describes a numerical model for simulating sediment transport with eddy‐resolving 3‐D models. This sediment model consists of four submodels: pickup, transport over the bed, transport in the water column and deposition, all based on a turbulent flow model using large‐eddy simulation. The sediment is considered as uniform rigid spherical particles. This is usually a valid assumption for sand‐bed rivers where underwater dune formation is most prominent. Under certain shear stress conditions, these particles are picked up from the bed due to an imbalance of gravity and flow forces. They either roll and slide on the bed in a sheet of sediment or separate from the bed and get suspended in the flow. Sooner or later, the suspended particles settle on the bed again. Each of these steps is modeled separately, yielding a physics‐based process model for sediment transport, suitable for the simulation of bed morphodynamics. The sediment model is validated with theoretical findings such as the Rouse profile as well as with empirical relations of sediment bed load and suspended load transport. The current model shows good agreement with these theoretical and empirical relations. Moreover, the saltation mechanism is simulated, and the average saltation length, height, and velocity are found to be in good agreement with experimental results.

Applicability of the De Marchi Hypothesis for Side Weir Flow in the Case of Movable Beds

Side weirs are widely used hydraulic structures typically designed and studied in the case of fixed bed conditions. In the case of subcritical flows, the hydraulics of side weirs can be modelled by using the classical De Marchi hypothesis. In the present work, a generalization of this hypothesis is developed for the case of side weirs over movable beds. Experiments showing the effects and feedbacks between the spilling discharge and the bed morphodynamics are presented. The application of the experimental observations to the generalized De Marchi hypothesis clearly show that the functioning of side weirs on a movable bed can be modelled by using this hypothesis. These findings could be instrumental for the design and verification of these structures. DOI: 10.1061/(ASCE)HY.1943-7900.0000566. © 2012 American Society of Civil Engineers. CE Database subject headings: Weirs; Experimentation; Channel flow; Movable bed models. Author keywords: Weirs; Subcritical flow; Experimentation; Channel flow.

A simplified 2D model for meander migration with physically-based bank evolution

The rate of migration, calculated by numerical models of river meandering, is commonly based on a method that relates the rate of migration to near-bank excess velocity multiplied by a dimensionless coefficient. Notwithstanding its simplicity, since the early 1980s this method has provided important insight into the long-term evolution of meander planforms through theoretical exercises. Its use in practice has not been as successful, because the complexity of the physical processes responsible for bank retreat, the heterogeneity in floodplain soils, and the presence of vegetation, make the calibration of the dimensionless coefficient rather challenging. This paper presents a new approach that calculates rates of meander migration using physically-based streambank erosion formulations. The University of Illinois RVR Meander model, which simulates meandering-river flow and bed morphodynamics, is integrated with algorithms for streambank erosion of the US Department of Agriculture channel evolution computer model CONCEPTS. The performance of the proposed approach is compared to that of the more simple classic method through the application to several test cases for idealized and natural planform geometry. The advantages and limitations of the approach are discussed, focusing on simulated planform pattern, the impact of soil spatial heterogeneity, the relative importance of the different processes controlling bank erosion (hydraulic erosion, cantilever, and planar failure), the requirements for obtaining stable migration patterns (centerline filtering and interpolation of bank physical properties), and the capability of predicting the planform evolution of natural rivers over engineering time scales (i.e., 50 to 100years). The applications show that the improved physically-based method of bank retreat is required to capture the complex long-term migration patterns of natural channels, which cannot be merely predicted from hydrodynamics only.

Curvilinear immersed boundary method for simulating coupled flow and bed morphodynamic interactions due to sediment transport phenomena

The fluid–structure interaction curvilinear immersed boundary (FSI-CURVIB) numerical method of Borazjani et al. [3] is extended to simulate coupled flow and sediment transport phenomena in turbulent open-channel flows. The mobile channel bed is discretized with an unstructured triangular mesh and is treated as a sharp-interface immersed boundary embedded in a background curvilinear mesh used to discretize the general channel outline. The unsteady Reynolds-averaged Navier–Stokes (URANS) equations closed with the k − ω turbulence model are solved numerically on a hybrid staggered/non-staggered grid using a second-order accurate fractional step method. The bed deformation is calculated by solving the sediment continuity equation in the bed-load layer using an unstructured, finite-volume formulation that is consistent with the CURVIB framework. Both the first-order upwind and the higher-order hybrid GAMMA schemes [12] are implemented to discretize the bed-load flux gradients and their relative accuracy is evaluated through a systematic grid refinement study. The GAMMA scheme is employed in conjunction with a sand-slide algorithm for limiting the bed slope at locations where the material angle of repose condition is violated. The flow and bed deformation equations are coupled using the partitioned loose-coupling FSI-CURVIB approach [3]. The hydrodynamic module of the method is validated by applying it to simulate the flow in an 180° open-channel bend with fixed bed. To demonstrate the ability of the model to simulate bed morphodynamics and evaluate its accuracy, we apply it to calculate turbulent flow through two mobile-bed open channels, with 90° and 135° bends, respectively, for which experimental measurements are available.

Adaptive quadtree simulation of sediment transport

Morphodynamic change is a key factor in the development of river systems. This paper describes a two-dimensional model of fluvial bed morphodynamics, with the flow hydrodynamics represented by the hyperbolic non-linear shallow water equations and the bed morphodynamics by the bed deformation equation. Bed load transport is estimated using a simple expression. Suspended sediment transport is not considered. The model uses a deviatoric form of the non-linear shallow water equations that mathematically balances the source and flux gradient terms at equilibrium, including the effects of non-uniform bed topography. The governing equations are solved in a decoupled way, using a Godunov-type finite-volume solver for the non-linear shallow water equations and second-order finite differences for the bed deformation equation, both based on adaptive quadtree grids. The evolution of a sandbar in an open channel is tested against generalised approximate analytical solutions. The numerical predictions on adaptive quadtree grids are found to be in excellent agreement with the approximate analytical solutions within the range of validity of the latter. Results are also presented for the evolution of a sand dune and a sandpit. It is demonstrated that the de-coupled shallow flow and bed morphodynamics calculations are computationally efficient and accurate. It is shown that the use of adaptive quadtree grids leads to a much improved computational performance over that on an equivalent fine resolution fixed uniform grid.

Discussion of “Effect of Seepage-Induced Nonhydrostatic Pressure Distribution on Bed-Load Transport and Bed Morphodynamics” by Simona Francalanci, Gary Parker, and Luca Solari

Discussion of “Effect of Seepage-Induced Nonhydrostatic Pressure Distribution on Bed-Load Transport and Bed Morphodynamics” by Simona Francalanci, Gary Parker, and Luca Solari

Closure to “Effect of Seepage-Induced Nonhydrostatic Pressure Distribution on Bed-Load Transport and Bed Morphodynamics” by Simona Francalanci, Gary Parker, and Luca Solari

Closure to “Effect of Seepage-Induced Nonhydrostatic Pressure Distribution on Bed-Load Transport and Bed Morphodynamics” by Simona Francalanci, Gary Parker, and Luca Solari

One‐dimensional numerical modeling of sediment transport and bed deformation in open channels

A one‐dimensional numerical model for simulating unsteady flow and sediment transport in open channels is presented and tested. The flow hydrodynamics is represented by the shallow water equations, and the bed morphodynamics is represented by the Exner equation and an additional equation describing the nonequilibrium sediment transport. Sediment size distribution is represented by the median grain diameter and the standard deviation, instead of the usual modeling with multiple particle size classes. Various methods for computing bed elevation changes at a cross section due to erosion or deposition of sediment are proposed and tested, including an innovative approach that relates the spatial pattern of erosion and deposition rates to boundary shear stress distribution, which is calculated by the Merged Perpendicular Method. An explicit finite difference scheme is employed for solving the water and sediment governing equations. The pertinence of the model is examined for two hypothetical cases. The model is then tested on one set of laboratory experiments on bed degradation under steady flow, showing excellent model data fit, and indicating that incorporating a nonequilibrium sediment transport equation into the model structure is an important element in reproducing the bed degradation process. Finally, the model is applied to simulate the morphological changes taking place in the Ha!Ha! River (Quebec) after the failure of the Ha!Ha! Dyke on July 1996. Relevant results can be obtained in terms of changes in longitudinal bed profile and cross‐sectional geometry as well as water levels, although some discrepancies are obtained between the simulated and surveyed cross‐sectional geometries, mainly because bank failure and channel widening are not modeled.

Experiments in a high‐amplitude Kinoshita meandering channel: 2. Implications of bend orientation on bed morphodynamics

Experiments carried out under flat smooth bed condition in a periodic, asymmetric, Kinoshita meandering channel showed that bend skewness controls the three‐dimensional mean flow (e.g., primary and secondary flow) and turbulence structure (e.g., location of shear layers and turbulent shear stresses). In this paper, similar hydraulic conditions are used to perform movable‐bed experiments with uniform sediment size in order to study the effect of bend orientation on bed morphodynamics. Two main differences between the upstream‐ and downstream‐skewed meander configurations are found: (1) for the case of bends oriented upstream valley, the bed forms are produced just upstream of the bend apex, whereas for the case of bends oriented downstream valley they are observed around the upstream inflection point, and (2) the downstream‐skewed condition produces the deepest scour region, which is located downstream of the bend apex. A comparison with observations at two bends on the Wabash River, Illinois, shows some remarkable similarities with the bed morphology observed in the Kinoshita channel. Further analysis of the bed form celerity, bed load transport during evolution, and superimposition of migrating bed forms and their implications on bend migration are presented.

One-dimensional modelling of fluvial bed morphodynamics

An understanding of fluvial processes is vital for river management systems. This paper describes a one-dimensional model of fluvial bed morphodynamics, with the flow hydrodynamics represented by the hyperbolic nonlinear shallow water equations and the bed morphodynamics by the bed deformation equation, with an empirical formula used for the bed load. Suspended sediment transport is not considered. The model uses a deviatoric form of the nonlinear shallow water equations that mathematically balances the source and flux gradient terms at equilibrium, and inherently caters for non-uniform bed topography. The governing equations are solved in an uncoupled way, using a Godunov-type finite volume solver for the nonlinear shallow water equations and second-order finite differences for the bed deformation equation. Generalised approximate analytical solutions and numerical predictions are presented for the evolution of a hump in an open channel. The numerical model predictions on converged grids are found to be in excellent agreement with the approximate analytical solutions within the range of validity of the approximate analytical model. It is demonstrated that uncoupling the shallow flow and bed morphodynamics calculations is computationally efficient and accurate. Results from a detailed parameter study are presented in order to interpret further the underlying physics of hump migration, and the influence studied of a morphodynamic time-scale related to the speed of bed change.

Effect of Seepage-Induced Nonhydrostatic Pressure Distribution on Bed-Load Transport and Bed Morphodynamics

Bed-load transport is commonly evaluated in the condition of a hydrostatic pressure distribution of the flow field; while this condition is reasonable for quasi-steady, quasi-uniform rectilinear flows, it cannot be satisfied in a large variety of flow conditions, i.e., near an obstacle as in the case of a bridge pier. The dimensionless Shields number, which contains the assumption of a hydrostatic pressure distribution in its denominator, therefore cannot be strictly applied to evaluate bed-load transport in all the configurations where nonhydrostatic pressure distributions are observed. In the present work, a generalization of the Shields number is proposed for the case of nonhydrostatic pressure distribution produced by groundwater flow. Experiments showing the effects of vertical groundwater flow on the bed morphodynamics are presented. The comparison between the experimental observations and numerical results, obtained by means of a morphodynamic model which employs the new formulation of the Shields number, suggests that the proposed generalization of the Shields number is able to account the effect of the nonhydrostatic pressure distribution on the bed-load transport.