Morphodynamic Theory of Sediment Distribution in Mixed Bedrock-Alluvial Channels
Abstract:Abrasion by saltating sediment has been shown to be an important mechanism of incision in bedrock rivers. Because sediment can abrade the bed as well as shield bedrock from erosion, it is necessary to understand how sediment becomes spatially distributed in mixed bedrock-alluvial rivers if we want to be able to predict their morphodynamic evolution. This presentation will discuss two analytical approaches to explore the controls on the spatial patterns of sediment distribution in mixed bedrock-alluvial rivers.
The first approach focuses sediment distribution in straight channels. The local sediment transport rate is modeled as proportional to the areal concentration of sediment available on the bed, and the sediment continuity equation is reformulated to account for temporal changes in areal concentration of sediment on nonalluviated surfaces. We perform a linear stability analysis and show that an initially uniform distribution of the areal concentration of sediment on the bed is unstable to small perturbations. Our analysis suggests that the difference in roughness between sediment and bare bedrock forces the system to organize such that the sediment on the bed will tend to become locally concentrated, which is in general agreement with experimental observations.
The second approach addresses the importance of channel curvature on the formation of point bars in mixed bedrock-alluvial channels. We present a nonlinear asymptotic theory of fully developed flow and bed topography in a channel of constant curvature to calculate the three-dimensional flow field in a channel bend, the shape of the cross section (including the point bar and exposed bedrock), and the slope and depth in the bend necessary to transport the sediment supply from upstream. Our model results suggest that in mixed bedrock-alluvial bends, there is a characteristic relationship between the degree of curvature, the amount of sediment supplied from upstream, the morphology of the point bar, and the amount of bedrock exposure. This points to a potentially useful model application in which sediment supply might be calculated from local measurements of bar morphology and channel curvature.