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\begin{document}

\title{Multiplicative noise and intermittency in bedload sediment transport}



\author[1]{Santiago Benavides}%
\author[1]{Eric Deal}%
\author[2]{J Taylor Perron}%
\author[3]{Jeremy Venditti}%
\author[1]{Qiong Zhang}%
\author[1]{Ken Kamrin}%
\affil[1]{Massachusetts Institute of Technology}%
\affil[2]{MIT---EAPS}%
\affil[3]{Simon Fraser University}%


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  \date{May 29, 2024}


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\begin{abstract}
Sediment transport in rivers near the threshold of grain motion is
characterized by rare but large transport events. This intermittency
makes it difficult to relate average sediment flux to average flow
conditions, or to define an unambiguous threshold for grain entrainment.
Although intermittent sediment transport can be observed and
characterized, its origins are unclear. In this study we investigate
bedload sediment transport near the threshold of grain motion in an
experimental flume to examine the origins of intermittency. We apply
image-processing techniques to high-speed video of grains in a narrow
flume, which allows us to track individual particles and measure
statistics of particle motion. Bedload sediment transport near the
threshold of grain motion is very low, allowing us to approximate the
time evolution of the sediment flux via a polynomial expansion,
including a linear growth rate and a nonlinear term which saturates the
growth. We introduce a noisy coefficient to the linear growth rate term
(``multiplicative noise''), rather than adding the noise to the
equation, to model the inherent fluctuations in the system. We
demonstrate that multiplicative noise near the threshold of grain motion
can account for the observed intermittency. We use analytical results
from bifurcation theory in the presence of multiplicative noise to
analyze our experimental results, quantifying the noise responsible for
the intermittency and calculating the critical shear stress for grain
entrainment in a novel way that is consistent with the physics of grain
motion at low transport stages.%
\end{abstract}%



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