Finite amplitude bars in mixed bedrock-alluvial channels

Abstract

We present a nonlinear asymptotic theory of fully developed flow and bed topography in a wide channel of constant curvature to describe finite amplitude perturbations of bottom topography, subject to an inerodible bedrock layer. The flow field is evaluated at the leading order of approximation as a slowly varying sequence of locally uniform flows, slightly perturbed by a weak curvature-induced secondary flow. Using the constraint of constant fluid discharge and sediment flux, we calculate an analytical solution for the cross-sectional profile of flow depth and bed topography, and we determine the average slope in the bend necessary to transport the sediment supplied from a straight, alluvial, upstream reach. Both fully alluvial bends and bends with partial bedrock exposure are shown to require a larger average slope than a straight upstream reach; the relative slope increase is much larger for mixed bedrock-alluvial bends. Curvature and sediment supply are shown to have a strong effect on the characteristics of the point bars in mixed bedrock-alluvial channels. Higher curvature bends produce bars of larger amplitude and more bedrock exposure through the cross section, and increasing the sediment supply leads to taller and wider point bars. Differences in the relative roughness of sediment and bedrock have a smaller, secondary effect on point bar characteristics. Our analytical approach can potentially be extended to the case of arbitrary, yet slowly varying, curvature, and should ultimately lead to an improved understanding of the formation of meanders in bedrock channels.

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

“…These results, which are summarized in Figure , are consistent with those of Nelson et al (), who studied point bar behavior in a mixed bedrock‐alluvial channel bend and found that decreasing sediment supply leads to narrower point bars. Their model, however, applies only to alluvial deformation of a fixed bed, and cannot handle vertical and lateral bedrock erosion associated with sediment transport.…”

“…the ratio k sb /k sa , has been observed to affect the areal fraction of alluvial cover (Chatanantavet and Parker, 2008;Inoue et al, 2014;Johnson, 2014) and the characteristics of alternate bars (Nelson and Seminara, 2012). In a curved bedrock channel, however, the influence of relative roughness on the characteristics of a point bar is small (Nelson et al, 2014). To simplify our simulations here, the hydraulic roughness height for bedrock k sb is taken to be equal to the hydraulic The abrasion coefficient for bedrock β is taken to be 0.025 m -1 in all the simulations.…”

“…the mechanism of saltation-abrasion (Sklar and Dietrich, 2004). In the model of Nelson et al (2014), the bedrock near the inner bank is fully covered by an alluvial point bar. In many mixed bedrock-alluvial channels, however, the inner bank bedrock is not fully covered by alluvium (e.g.…”

Consequences of Abrading Bed Load on Vertical and Lateral Bedrock Erosion in a Curved Experimental Channel

“…All these effects help to increase the abrasion on the outer bank by moving sediment. Nelson et al (2014) and Inoue, Parker, and Stark (2017) calculated the shape and thickness of alluvial cover in a bend in a mixed bedrock-alluvial river. They showed that the height and width of the point bar increase with increasing sediment supply.…”

A Froude‐scaled model of a bedrock‐alluvial channel reach: 2. Sediment cover

“…Field observations [ Hodge et al ., ], flume experiments [ Chatanantavet and Parker , ; Hodge et al ., ], and theoretical analyses [ Hodge et al ., ; Nelson and Seminara , ; Nelson et al ., ] have demonstrated that the most stable configuration of sediment on a bedrock surface is in patches, producing a spatial pattern of discrete alluvial and bedrock areas. Despite this, within‐reach‐scale patterns of sediment cover in bedrock‐alluvial rivers have not received significant attention.…”