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\begin{document}

\title{Numerical simulations of meanders migrating laterally as they incise
into bedrock}



\author[1]{Takuya Inoue}%
\author[2]{Jagriti Mishra}%
\author[3]{Gary Parker}%
\affil[1]{Civil Engineering Research Institute for Cold Regions}%
\affil[2]{Hokkaido University}%
\affil[3]{University of Illinois at Urbana Champaign}%


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  \date{June 17, 2024}


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\begin{abstract}
The problem of meandering in mixed bedrock-alluvial rivers is more
challenging than that of purely alluvial streams, in that alluvial, bed
incisional and bank incisional morphodynamics must be accounted for.
Here we present a numerical formulation that addresses heretofore
unanswered questions. Bed incision is based on abrasion due to saltating
grains. The model satisfies mass conservation of alluvium over a
partially-covered bedrock surface. Bank incision is treated in terms of
a measure of incipient collision of bedload particles with the bank. It
is assumed that land accretes along the inside of point bars when the
water depth falls below a specified shallow value. All but one of the
runs are performed with repetitive two-step hydrographs. Runs starting
from a low-amplitude sine-generated curve indicate that sinuosities at
least as high as 2.5 can be achieved. The rate of increase of sinuosity
declines in time, but does not vanish. For the same hydrograph,
increasing the initial thickness of alluvium on the bed causes the rate
of vertical bedrock incision to decline, and bend sinuosity to increase
at a faster rate. At a sufficiently high thickness, the channel migrates
laterally without bed lowering. Bend shape can change dramatically with
increasing alluvial thickness, with high thickness favoring more regular
bend trains. For the same initial alluvial thickness, increasing the
peak flow of the hydrograph causes the vertical incision rate and the
rate of sinuosity growth to increase. The model thus captures a wide
range of behavior associated with bedrock meandering.%
\end{abstract}%



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