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\begin{document}

\title{A mechanistic model for lateral erosion of bedrock channel banks by
bedload particle impacts}



\author[1]{Tingan Li}%
\author[2]{Theodore K. Fuller}%
\author[3]{Leonard S. Sklar}%
\author[4]{Karen B. Gran}%
\author[1]{Jeremy G. Venditti}%
\affil[1]{Simon Fraser University}%
\affil[2]{St. Anthony Falls Laboratory, University of Minnesota}%
\affil[3]{Concordia University}%
\affil[4]{University of Minnesota Duluth}%


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  \date{May 21, 2024}


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\begin{abstract}
Bedrock rivers get wider by lateral erosion. Lateral erosion is widely
thought to occur when the bed is covered by alluvium, which deflects the
downstream transport of bedload particles into channel walls. Here we
develop a model for lateral bedrock erosion by bedload particle impacts.
The lateral erosion rate is the product of the volume eroded per
particle impact and the impact rate on the wall. The volume eroded per
particle impact is modelled by tracking the motion of bedload particles
from collision with roughness elements to impacts on the wall. The
impact rate on the wall is zero if the bedload particle deflected by
roughness elements cannot reach the wall. Otherwise, the impact rate on
the wall is the same with that on roughness elements. The model further
incorporates the co-evolution of wall morphology, shear stress and
erosion rate. The model predicts the undercut wall shape observed in
physical experiments. The non-dimensional lateral erosion rate is used
to explore how lateral erosion varies under different relative sediment
supply (ratio of supply to transport capacity) and transport stage
conditions. Maximum lateral erosion rates occur at high relative
sediment supply rates (\textasciitilde{} 0.7) and moderate transport
stages (\textasciitilde{}10). The competition between lateral and
vertical erosion is investigated by coupling the saltation-abrasion
vertical erosion model with our lateral erosion model. The results
suggest that vertical erosion dominates under near 75\% of supply and
transport stage conditions, but is outpaced by lateral erosion near the
threshold for full bed coverage.%
\end{abstract}%



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