Three-dimensional modeling of bank erosion and morphological changes in the Shishou bend of the middle Yangtze River

This paper presents a three-dimensional (3-D) numerical model to simulate morphological changes in alluvial channels due to bank erosion. A method for the simulation of bank erosion is established. This is incorporated into a 3-D mathematical model for turbulent flow and non-uniform, non-equilibrium sediment transport. This model is applied to simulate morphological changes in the Shishou bend of the middle Yangtze River in China, where serious bank erosions occurred during the last two decades. The double-layer sediment structure of the riverbank on the middle Yangtze River is taken into account in the bank erosion module. Both cohesive and non-cohesive bank material in the different layers are considered. The bank erosion module also includes other factors affecting the rate of bank erosion, such as the longitudinal length of failed bank, the thickness of each layer in the double-layer structure, and the erosion-resisting effect of cohesive material from the top layer of failed bank. A locally-adaptive grid system is proposed to efficiently simulate the lateral migration of alluvial channel due to bank erosion. The predictive capability of the 3-D model is examined by laboratory data. Simulated processes of bank erosion agree with field observations in the Shishou bend during the period of October 1996–October 1998, and the bank erosion module plays a significant role in simulating morphological changes of the study reach. In addition, the equivalent channel-forming discharge, which is defined as a constant discharge that can create the same amount of bank erosion in an alluvial channel as that created by natural runoff processes during the same period of time, is proposed to improve calculation efficiency for feasibility studies.     

MITIGATION OF SEDIMENTATION HAZARDS DOWNSTREAM FROM RESERVOIRS

1 INTRODUCTION Increasing attention is being given to sedimentation hazards downstream from reservoirs as dams built during the past century accumulate progressively greater volumes of sediment. The sediment storage both decreases reservoir capacity and operating efficiency of the dam, and creates a 搒ediment-shadow?downstream where sediment-starved flows commonly erode channel boundaries and create long-term channel instabilities. Numerous studies have documented downstream channel change…     

Numerical simulation of channel pattern changes Part Ⅰ: Mathematical model

This paper presents a computational fluid dynamics model for simulation of twodimensional (2-D) water flow, sediment transport, bank failure processes, and the subsequent channel pattern changes. Effects of secondary currents at channel bends are included in the modified momentum conservation equation of water flow. An improved bank failure model is applied to calculate bank failure due to riverbed erosion, and to simulate lateral migration and planform changes of alluvial channels. The water flow model has been validated using laboratory measurements of flow in consecutive bends designed by the authors, in addition to flume test data from the literature.     

Numerical simulation of channel pattern changes Part I: Mathematical model

This paper presents a computational fluid dynamics model for simulation of two- dimensional (2-D) water flow, sediment transport, bank failure processes, and the subsequent channel pattern changes. Effects of secondary currents at channel bends are included in the modified momentum conservation equation of water flow. An improved bank failure model is applied to calculate bank failure due to riverbed erosion, and to simulate lateral migration and planform changes of alluvial channels. The water flow model has been validated using laboratory measurements of flow in consecutive bends designed by the authors, in addition to flume test data from the literature.     

Morphodynamics of a bedrock‐alluvial meander bend that incises as it migrates outward: approximate solution of permanent form

In meandering rivers cut into bedrock, erosion across a channel cross‐section can be strongly asymmetric. At a meander apex, deep undercutting of the outer bank can result in the formation of a hanging cliff (which may drive hillslope failure), whereas the inner bank adjoins a slip‐off slope that connects to the hillslope itself. Here we propose a physically‐based model for predicting channel planform migration and incision, point bar and slip‐off slope formation, bedrock abrasion, the spatial distribution of alluvial cover, and adaptation of channel width in a mixed bedrock‐alluvial channel. We simplify the analysis by considering a numerical model of steady, uniform bend flow satisfying cyclic boundary conditions. Thus in our analysis, ‘sediment supply’, i.e. the total volume of alluvium in the system, is conserved. In our numerical simulations, the migration rate of the outer bank is a specified parameter. Our simulations demonstrate the existence of an approximate state of dynamic equilibrium corresponding to a near‐solution of permanent form in which a bend of constant curvature, width, cross‐sectional shape and alluvial cover distribution migrates diagonally downward at constant speed, leaving a bedrock equivalent of a point bar on the inside of the bend. Channel width is set internally by the processes of migration and incision. We find that equilibrium width increases with increasing sediment supply, but is insensitive to outer bank migration rate. The slope of the bedrock point bar varies inversely with both outer bank migration rate and sediment supply. Although the migration rate of the outer bank is externally imposed here, we discuss a model modification that would allow lateral side‐wall abrasion to be treated in a manner similar to the process of bedrock incision. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical modelling of channel migration with application to laboratory rivers

The paper presents the development of a morphological model and its application to experimental model rivers.The model takes into account the key processes of channel migration,including bed deformation,bank failure and wetting and drying.Secondary flows in bends play an important role in lateral sediment transport,which further affects channel migration.A new formula has been derived to predict the near-bed secondary flow speed,in which the magnitude of the speed is linked to the lateral water level gradient.Since only non-cohesive sediment is considered in the current study,the bank failure is modelled based on the concept of submerged angle of repose.The wetting and drying process is modelled using an existing method.Comparisons between the numerical model predictions and experimental observations for various discharges have been made.It is found that the model predicted channel planform and cross-sectional shapes agree generally well with the laboratory observations.A scenario analysis is also carried out to investigate the impact of secondary flow on the channel migration process.It shows that if the effect of secondary flow is ignored,the channel size in the lateral direction will be seriously underestimated.     

A coupled hierarchical modeling approach to simulating the geomorphic response of river systems to anthropogenic climate change

Anthropogenic climate change is expected to change the discharge and sediment transport regime of river systems. Because rivers adjust their channels to accommodate their typical inputs of water and sediment, changes in these variables can potentially alter river morphology. In this study, a hierarchical modeling approach was developed and applied to examine potential changes in reach‐averaged bedload transport and spatial patterns of erosion and deposition for three snowmelt‐dominated gravel‐bed rivers in the interior Pacific Northwest. The modeling hierarchy was based on discharge and suspended‐sediment load from a basin‐scale hydrologic model driven by a range of downscaled climate‐change scenarios. In the field, channel morphology and sediment grain‐size data for all three rivers were collected. Changes in reach‐averaged bedload transport were estimated using the Bedload Assessment of Gravel‐bedded Streams (BAGS) software, and the Cellular Automaton Evolutionary Slope and River (CAESAR) model was used to simulate the spatial pattern of erosion and deposition within each reach to infer potential changes in channel geometry and planform. The duration of critical discharge was found to control bedload transport. Changes in channel geometry were simulated for the two higher‐energy river reaches, but no significant morphological changes were found for a lower‐energy reach with steep, cohesive banks. Changes in sediment transport and river morphology resulting from climate change could affect the management of river systems for human and ecological uses. Copyright © 2015 John Wiley & Sons, Ltd.     

Channel morphologic processes of a highly sinuous bend approaching neck cutoff by bank erosion in the middle Yangtze River

The distal reach of the Lower Jingjiang River(LJR)in the middle of the Yangtze River consists of five adjacent bends,among which the Qigongling Bend is a U-shaped meander with a mean sinuosity of 2.2 and the narrowest neck 525 m in width.This bend is slowly approaching neck cutoff owing to progressive bank erosion.An abnormal phenomenon has occurred in this bend since the Three Gorges Reservoir(TGR)began to operate in 2003 which is erosion in the inner bank zone and deposition in the outer bank zone.This problem has not been fully understood because of the interplay of changes in water-sediment,bank erosion,and artificial bank revetment.In this study,aerial and remote sensing images,hydrological data,channel topography,and an existing bank erosion model are used to reveal channel morphodynamics of this bend and the trend of the potential neck cutoff induced by bank erosion.The study results show that the clear water released from the TGR has provided by forcefully eroded the point bar of inner bank but failed to scour the outer bank due to the protection of bank revetment since the 1990 s.Thus far,the outer bank zone near the bend apex has increasingly widened in conjunction with the formation of 2 emerging sand bars.Consequently,the thalweg of the main channel has laterally shifted toward the inner bank by roughly 800 m.More severely,the rate of bank retreat on the upstream side of the bend neck was about 4.5 m/yr in 2010-2019,but the downstream side of this neck was experienced slight deposition.Bank erosion could be accelerated by progressively increasing erosion and eventually trigger the occurrence of neck cutoff in the next few decades,thereby significantly altering the quasi-equilibrium regime of channel morphodynamics in the LJR.     

Three‐dimensional flow structure and patterns of bed shear stress in an evolving compound meander bend

Compound meander bends with multiple lobes of maximum curvature are common in actively evolving lowland rivers. Interaction among spatial patterns of mean flow, turbulence, bed morphology, bank failures and channel migration in compound bends is poorly understood. In this paper, acoustic Doppler current profiler (ADCP) measurements of the three‐dimensional (3D) flow velocities in a compound bend are examined to evaluate the influence of channel curvature and hydrologic variability on the structure of flow within the bend. Flow structure at various flow stages is related to changes in bed morphology over the study timeframe. Increases in local curvature within the upstream lobe of the bend reduce outer bank velocities at morphologically significant flows, creating a region that protects the bank from high momentum flow and high bed shear stresses. The dimensionless radius of curvature in the upstream lobe is one‐third less than that of the downstream lobe, with average bank erosion rates less than half of the erosion rates for the downstream lobe. Higher bank erosion rates within the downstream lobe correspond to the shift in a core of high velocity and bed shear stresses toward the outer bank as flow moves through the two lobes. These erosion patterns provide a mechanism for continued migration of the downstream lobe in the near future. Bed material size distributions within the bend correspond to spatial patterns of bed shear stress magnitudes, indicating that bed material sorting within the bend is governed by bed shear stress. Results suggest that patterns of flow, sediment entrainment, and planform evolution in compound meander bends are more complex than in simple meander bends. Moreover, interactions among local influences on the flow, such as woody debris, local topographic steering, and locally high curvature, tend to cause compound bends to evolve toward increasing planform complexity over time rather than stable configurations. Copyright © 2016 John Wiley & Sons, Ltd.     

Interaction between meander dynamics and floodplain heterogeneity in a large tropical sand‐bed river: the Rio Beni,Bolivian Amazon

The evolution of meandering river floodplains is predominantly controlled by the interplay between overbank sedimentation and channel migration. The resulting spatial heterogeneity in floodplain deposits leads to variability in bank erodibility, which in turn influences channel migration and planform development. Despite the potential significance of these feedbacks, few studies have quantified their impact upon channel evolution and floodplain construction in dynamic settings (e.g. locations characterized by rapid channel migration and high rates of overbank sedimentation). This study employs a combination of field observations, geographic information system (GIS) analysis of satellite imagery and numerical modelling to investigate these issues along a 375 km reach of the Rio Beni in the Bolivian Amazon. Results demonstrate that the occurrence of clay‐rich floodplain deposits promotes a significant reduction in channel migration rates and distinctive styles of channel evolution, including channel straightening and immobilization of bend apices leading to channel narrowing. Clay bodies act as stable locations limiting the propagation of planform disturbances in both upstream and downstream directions, and operate as ‘hinge’ points, around which the channel migrates. Spatial variations in the erodibility of clay‐rich floodplain material also promote large‐scale (10–50 km) differences in channel sinuosity and migration, although these variables are also likely to be influenced by channel gradient and tectonic effects that are difficult to quantify. Numerical model results suggest that spatial heterogeneity in bank erodibility, driven by variable bank composition, may force a substantial (c. 30%) reduction in average channel sinuosity, compared to situations in which bank strength is spatially homogeneous. Copyright © 2015 John Wiley & Sons, Ltd.     

Unexpected sedimentation patterns upstream and downstream of the Three Gorges Reservoir: Future risks

This paper summarizes the latest developments, future prospects, and proposed countermeasures of reservoir sedimentation and channel scour downstream of the Three Gorges Reservoir (TGR) on the Yangtze River in China. Three key results have been found.(1) The incoming sediment load to the TGR has been significantly lower than expected.(2) The accumulated volume of sediment deposition in the TGR is smaller than expected because the overall sediment delivery ratio is relatively low, and the deposition in the near-dam area of the TGR is still developing.(3) River bed scour in the river reaches downstream of the Gezhouba Dam is still occurring and channel scour has extended to reaches as far downstream as the Hukou reach. Significantly, sedimentation of the TGR is less problematic than expected since the start of operation of the TGR on the one hand;on the other hand, the possible increases in sediment risks from dependence on upstream sediment control, deposition in the reservoir, and scour along middle Yangtze River should be paid more attention.(1) Sediment trapped by dams built along the upper Yangtze River and billion tons of loose materials on unstable slopes produced by the Wenchuan Earthquake could be new sediment sources for the upper Yangtze River. More seriously, possible release of this sediment into the upper Yangtze River due to new earthquakes or extreme climate events could overwhelm the river system, and produce catastrophic consequences.(2) Increasing sediment deposition in the TGR is harmful to the safety and efficiency of project operation and navigation.(3) The drastic scour along the middle Yangtze River has intensified the down-cutting of the riverbed and erosion of revetment, it has already led to increasing risk to flood control structures and ecological safety. It is suggested to continue the Field Observation Program, to initiate research programs and to focus on risks of sedimentation.     

Rates,distributions and mechanisms of change in meander morphology over decadal timescales,River Dane,UK

This paper analyses types and rates of change in river meander morphology and the links between mechanisms of change and emergent behaviour of planform morphology. It uses evidence of four dates of aerial photography combined with annual field mapping and ground photography to examine the morphological changes and mechanisms of change in a series of bends on an active meandering river, the River Dane in NW England, over a 25 year period. This unique data set allows insight into the spatial and temporal variability of bank line movement and component processes. Bank lines were mapped photogrametrically from air photos of 1984, 1996, 2001 and 2007 and the digitised courses compared in ArcGIS to produce calculations of erosional and depositional areas and rates. Most bends exhibit morphological change that largely follows the autogenic sequence, identified in qualitative models of meander development, from low sinuosity curves through simple symmetric and asymmetric bends to compound forms with lobe development in the apex region. Rates of erosion and bankline movement increase through this sequence until the compound phase. Relationships of amounts of movement to various curvature measures of bend morphology are complex. Several new loops, distinct from compound bend behaviour, have developed during the study period in formerly straight sections. Mechanisms of morphological change are illustrated for four types of bends: new, rapid growth bend; sharp‐angled bend with mid‐channel bar development; symmetric migrating bend; and simple to compound bend development. The changes take place in phases that are not simply related to discharge but to inherent sequences and feedbacks in development of bars and bend morphology and timescales for these are identified. Overall, emergent behaviour of systematic planform change, moderated by channel confinement and boundary features, is produced from spatially and temporally varied channel processes. Copyright © 2010 John Wiley & Sons, Ltd.     

DEPTH-AVERAGED 2-D CALCULATION OF FLOW AND SEDIMENT TRANSPORT IN CURVED CHANNELS

The helical flow significantly affects the flow, sediment transport and morphological evolution in curved channels. A semi-empirical formula is proposed to determine the cross-stream distribution of the helical flow intensity in the developed regions of a channel bend. It is then used to evaluate the dispersion terms in the depth-averaged 2-D momentum equations and suspended-load transport equation as well as the bed-load transport angle, thus enhancing the depth-averaged 2-D model to account for the effect of helical flow. The tests in several experimental and field cases show that the enhanced depth-averaged 2-D model can much more reasonably predict the shifting of main flow from inner bank to outer bank, the erosion along outer bank and deposition along inner bank than the depth-averaged 2-D model without considering this effect.     

Stochastic erosion of composite banks in alluvial river bends

The erosion of composite river banks is a complex process involving a number of factors including fluvial erosion, seepage erosion, and cantilever mass failure. To predict the rate of bank erosion with these complexities, a stochastic bank erosion model is suitable to define the probability distribution of the controlling variables. In this study, a bank erosion model in a river bend is developed by coupling several bank erosion processes with an existing hydrodynamic and morphological model. The soil erodibility of cohesive bank layers was measured using a submerged jet test apparatus. Seasonal bank erosion rates for four consecutive years at a bend in the Brahmaputra River, India, were measured by repeated bankline surveys. The ability of the model to predict erosion was evaluated in the river bend that displayed active bank erosion. In this study, different monsoon conditions and the distribution functions of two variables were considered in estimating the stochastic bank erosion rate: the probability of the soil erodibility and stochastic stage hydrographs for the nth return period river stage. Additionally, the influences of the deflection angle of the streamflow, longitudinal slope of river channel, and bed material size on bank erosion rate were also investigated. The obtained stochastic erosion predictions were compared with the observed distribution of the annual‐average bank erosion rate of 45 river bends in the Brahmaputra River. The developed model appropriately predicted the short‐term morphological dynamics of sand‐bed river bends with composite banks. Copyright © 2014 John Wiley & Sons, Ltd.     

Using a historical aerial photograph analysis to inform trout habitat restoration efforts

Restoration of the upper Strawberry River included bank stabilization techniques because it was assumed that excessive bank erosion was degrading spawning habitat for Bonneville cutthroat trout (BCT). Using a long‐term aerial photograph record, the historical range of variability in bank erosion rates and channel geometry was determined, and this information was used to assess present‐day conditions and the rationale for restoration. Relative to historical variability, the channel planform was relatively stable and bank erosion rates were the lowest recorded in the post‐disturbance era. Although a historical loss of riparian vegetation coincided with a shift to a wider and more sinuous channel, lateral migration rates declined and the channel narrowed as riparian cover increased in the decades before restoration, indicating a process of natural recovery. Furthermore, it was found that the percentage of fine sediment in the streambed before restoration was insufficient to affect BCT spawning success. Together these results suggest that bank erosion and fine sediment did not affect the quality of spawning habitat or the abundance of BCT on the upper Strawberry River. The results highlight how a historical analysis can be used to identify the sources of habitat degradation and inform the selection of restoration goals and strategies. Copyright © 2011 John Wiley & Sons, Ltd.     

Modeling the impact of dam removal on channel evolution and sediment delivery in a multiple dam setting

Dam removal can generate geomorphic disturbances, including channel bed and bank erosion and associated abrupt/pulsed release and downstream transfer of reservoir sediment, but the type and rate of geomorphic response often are hard to predict. The situation gets even more complex in systems which have been impacted by multiple dams and a long and complex engineering history. In previous studies one-dimensional (1-D) models were used to predict aspects of post-removal channel change. However, these models do not consider two-dimensional (2-D) effects of dam removal such as bank erosion processes and lateral migration. In the current study the impacts of multiple dams and their removal on channel evolution and sediment delivery were modeled by using a 2-D landscape evolution model (CAESAR-Lisflood) focusing on the following aspects: patterns, rates, and processes of geomorphic change and associated sediment delivery on annual to decadal timescales. The current modeling study revealed that geomorphic response to dam removal (i.e., channel evolution and associated rates of sediment delivery) in multiple dam settings is variable and complex in space and time. Complexity in geomorphic system response is related to differences in dam size, the proximity of upstream dams, related buffering effects and associated rates of upstream sediment supply, and emerging feedback processes as well as to the presence of channel stabilization measures. Modeled types and rates of geomorphic adjustment, using the 2-D landscape evolution model CAESAR-Lisflood, are similar to those reported in previous studies. Moreover, the use of a 2-D method showed some advantages compared to 1-D models, generating spatially varying patterns of erosion and deposition before and after dam removal that provide morphologies that are more readily comparable to field data as well as features like the lateral re-working of past reservoir deposits which further enables the maintenance of sediment delivery downstream.     

Modelling of meander migration in an incised channel

An updated linear computer model for meandering rivers with incision has been developed. The model simulates the bed topography, flow field, and bank erosion rate in an incised meandering channel. In a scenario where the upstream sediment load decreases （e.g., after dam closure or soil conservation）, alluvial river experiences cross section deepening and slope flattening. The channel migration rate might be affected in two ways： decreased channel slope and steeped bank height. The proposed numerical model combines the traditional one-dimensional （1D） sediment transport model in simulating the channel erosion and the linear model for channel meandering. A non-equilibrium sediment transport model is used to update the channel bed elevation and gradations. A linear meandering model was used to calculate the channel alignment and bank erosion/accretion, which in turn was used by the 1D sediment transport model. In the 1D sediment transport model, the channel bed elevation and gradations are represented in each channel cross section. In the meandering model, the bed elevation and gradations are stored in two dimensional （2D） cells to represent the channel and terrain properties （elevation and gradation）. A new method is proposed to exchange information regarding bed elevations and bed material fractions between 1D river geometry and 2D channel and terrain. The ability of the model is demonstrated using the simulation of the laboratory channel migration of Friedkin in which channel incision occurs at the upstream end.     

Reach-scale changes in channel geometry and dynamics due to the coastal backwater effect: the lower Trinity River,Texas

In this paper we use multiple field surveys spanning several decades to systematically evaluate the geomorphic consequences of a change in flow hydraulics from uniform flow to backwater flow for the lower Trinity River in east Texas, USA. Spatial changes in lateral migration rate, channel geometry, and point bar size correspond to two distinct geomorphic zones. Within the upstream uniform flow reach, the river channel is defined by fully developed point bars and a high rate of lateral channel migration. This zone transitions where the median channel bottom elevation drops below sea level. At this point flow is affected by the backwater influence of the Trinity Bay water surface elevation, as opposed to being bed slope control dominated. The change in hydraulics within the backwater zone is reflected in the channel morphology, which is characterized by smaller point bars, narrower and more symmetrical cross-sectional channel geometry, lower channel migration rates, and little to no bend deformation or cutoffs. Studying the connection between channel geometry, river bend kinematics, sediment transport, and fluid mechanics in each zone provides a deeper understanding of the relationship between channel shape and river mechanics. © 2019 John Wiley & Sons, Ltd.     

Hydraulic and geomorphic processes in an overbank flood along a meandering,gravel‐bed river: implications for chute formation

Hydraulic interactions between rivers and floodplains produce off‐channel chutes, the presence of which influences the routing of water and sediment and thus the planform evolution of meandering rivers. Detailed studies of the hydrologic exchanges between channels and floodplains are usually conducted in laboratory facilities, and studies documenting chute development are generally limited to qualitative observations. In this study, we use a reconstructed, gravel‐bedded, meandering river as a field laboratory for studying these mechanisms at a realistic scale. Using an integrated field and modeling approach, we quantified the flow exchanges between the river channel and its floodplain during an overbank flood, and identified locations where flow had the capacity to erode floodplain chutes. Hydraulic measurements and modeling indicated high rates of flow exchange between the channel and floodplain, with flow rapidly decelerating as water was decanted from the channel onto the floodplain due to the frictional drag provided by substrate and vegetation. Peak shear stresses were greatest downstream of the maxima in bend curvature, along the concave bank, where terrestrial LiDAR scans indicate initial floodplain chute formation. A second chute has developed across the convex bank of a meander bend, in a location where sediment accretion, point bar development and plant colonization have created divergent flow paths between the main channel and floodplain. In both cases, the off‐channel chutes are evolving slowly during infrequent floods due to the coarse nature of the floodplain, though rapid chute formation would be more likely in finer‐grained floodplains. The controls on chute formation at these locations include the flood magnitude, river curvature, floodplain gradient, erodibility of the floodplain sediment, and the flow resistance provided by riparian vegetation. Copyright © 2015 John Wiley & Sons, Ltd.     

A new framework for modeling the migration of meandering rivers

Many models of river meander migration rely upon a simple formalism, whereby the eroding bank is cut back at a rate that is dictated by the flow, and the depositing bank then migrates passively in response, so as to maintain a constant bankfull channel width. Here a new model is presented, in which separate relations are developed for the migration of the eroding bank and the depositing bank. It is assumed that the eroding bank consists of a layer of fine‐grained sediment that is cohesive and/or densely riddled with roots, underlain by a purely noncohesive layer of sand and/or gravel. Following erosion of the noncohesive layer, the cohesive layer fails in the form of slump blocks, which armor the noncohesive layer and thereby moderate the erosion rate. If the slump block material breaks down or is fluvially entrained, the protection it provides for the noncohesive layer diminishes and bank erosion is renewed. Renewed bank erosion, however, rejuvenates slump block armoring. At the depositing bank, it is assumed that all the sediment delivered to the edge of vegetation due to the transverse component of sediment transport is captured by encroaching vegetation, which is not removed by successive floods. Separate equations describing the migration of the eroding and depositing banks are tied to a standard morphodynamic formulation for the evolution of the flow and bed in the central region of the channel. In this model, the river evolves toward maintenance of roughly constant bankfull width as it migrates only to the extent that the eroding bank and depositing bank ‘talk’ to each other via the medium of the morphodynamics of the channel center region. The model allows for both (a) migration for which erosion widens the channel, forcing deposition at the opposite bank, and (b) migration for which deposition narrows the channel forcing erosion at the opposite bank. Copyright © 2010 John Wiley & Sons, Ltd.