Mixed bedrock-alluvial rivers can exhibit partial alluvial cover, which may play an important role in controlling bedrock erosion rates and landscape evolution. However, numerical morphodynamic models generally are unable to predict the pattern of alluviation in these channels. Hence we present a new two-dimensional depth-averaged morphodynamic model that can be applied to both fully alluvial and mixed bedrock-alluvial channels, and we use the model to gain insight into the mechanisms responsible for the development of sediment patches and patterns of bedrock alluviation. The model computes hydrodynamics, sediment transport, and bed evolution, using a roughness partitioning that accounts for differential roughness of sediment and bedrock, roughness due to sediment transport, and form drag. The model successfully replicates observations of bar development and migration from a fully alluvial flume experiment, and it models persistent sediment patches observed in a mixed bedrock-alluvial flume experiment. Numerical experiments in which the form drag, sediment transport roughness, and ripple factor correction were neglected did not successfully reproduce the observed persistent sediment cover in the mixed bedrock-alluvial case, suggesting that accounting for these different roughness components is critical to successfully model sediment dynamics in bedrock channels.

Understanding the development and spatial distribution of alluvial patches in mixed bedrock-alluvial rivers is necessary to predict the mechanisms of the interactions between sediment transport, alluvial cover, and bedrock erosion. This study aims to analyze patterns of bedrock alluviation using a 2D morphodynamic model, and to use the model results to better understand the mechanisms responsible for alluvial patterns observed experimentally. A series of simulations are conducted to explore how alluvial patterns in mixed bedrock-alluvial channels form and evolve for different channel slopes and antecedent sediment layer thicknesses. In initially bare bedrock low-slope channels, the model predicts a linear relationship between sediment cover and sediment supply because areas of subcritical flow enable sediment deposition, while in steep-slope channels the flow remains fully supercritical and the model predicts so-called runaway alluviation. For channels initially covered with sediment, the model predicts a slope-dependent sediment supply threshold above which a linear relationship between bedrock exposure and sediment supply develops, and below which the bedrock becomes fully exposed. For a given sediment supply, the fraction of bedrock exposure and average alluvial thickness converge toward the equilibrium value regardless of the initial cover thickness so long as it exceeds a minimum threshold. Steep channels are able to maintain a continuous strip of sediment under sub-capacity sediment supply conditions by achieving a balance between increased form drag as bedforms develop and reduced surface roughness as the portion of alluvial cover decreases. In lower-slope channels, alluvial patches are distributed sporadically in regions of the subcritical flow.