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

Abstract

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.

The SPACE 1.0 model: a Landlab component for 2-D calculation of sediment transport, bedrock erosion, and landscape evolution

“…Lague (2010) and Zhang et al (2015) followed a similar approach, further modifying the sediment mass conservation framework to include below-capacity sediment transport. Exner sediment transport in bedrock-alluvial systems was expanded to 2-D by Nelson and Seminara (2012) and Inoue et al (2016Inoue et al ( , 2017, though the specifics of calculating sediment flux differ between the model of Nelson and Seminara (2012) and the latter two. The Exner-based conservation framework allows calculation of bed cover by sediment as a function of the ratio of sediment flux to transport capacity (q s /q c ) (Inoue et al, 2014).…”

“…Fowler et al (2007) incorporated an equation for bed abrasion by bed load, assuming that abrasion rates should scale with the velocity of the bed load layer and should decline with increasing bed load layer thickness (yielding a form of the tools and cover effects). Several workers have adapted forms of the saltationabrasion bedrock erosion model of Dietrich (1998, 2004) in conjunction with sediment mass conservation to incorporate both the tools and cover effects into models of bedrock-alluvial river erosion (Turowski, 2009;Nelson and Seminara, 2011;Inoue et al, 2014Inoue et al, , 2016Inoue et al, , 2017. Turowski (2009) combined a stochastic erosion-deposition model with a saltation-abrasion-style incision rule and explored the sensitivity of bed cover and bedrock erosion rate to changes in sediment transport.…”

“…They used a modified Exner equation for sediment mass conservation incorporating both mobile bed load and an alluvial layer, and a saltation-abrasion-style bedrock incision rule (Sklar and Dietrich, 2004;Chatanantavet and Parker, 2009). Inoue et al (2016Inoue et al ( , 2017 expanded the sediment conservation and bedrock erosion formulations of Inoue et al (2014) to 2-D to allow spatial variability in alluvial thickness and bedrock erosion along both the channel length and width. Inoue et al (2017) advanced the model of Inoue et al (2016) by incorporating a simple parameterization for bedrock bank erosion to investigate meander bend migration.…”

Numerical Modelling of Cohesive Bank Migration

“…Following this line, most of the models which address the morphological evolution of the rivers couple hydrodynamic and bed evolution submodels with a bank erosion submodel, so they are able to predict changes in both bed and bank form, comprehending also bank failure (e.g., [28][29][30][31][32][33][34][35][36][37]). Nevertheless, their approach can differ significantly from one another.…”

“…Some authors, for example, conduct a proper bank stability investigation, considering a limit equilibrium analysis for planar or rotational slip failure [29,30] or a cantilever failure [30]. Others evaluate a bank erosion/accretion rate, which gives rise to the displacement of bank top and a consequent mesh modification [31,32,[35][36][37] or, in a similar way, they couple a bed scouring with an intermittent bank erosion model, which shift the bank while keeping the same initial angle of repose [28]. Another approach consists in coupling the basal erosion due to hydrodynamic forces with a bank failure model, which triggers when the bank slope exceeds a critical angle [33,34,38,39].…”