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\begin{document}

\title{Computational Simulations of Bed Surface Variability 1 and Particle
Entrainment in a Gravelbed River}



\author[1]{Kimberly Hill}%
\author[1]{Amirreza Ghasemi}%
\author[1]{Sanaz Borhani}%
\author[2]{Enrica Viparelli}%
\affil[1]{University of Minnesota}%
\affil[2]{University of South Carolina}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\begin{abstract}
Key Points: 8 * Bed heights of bedload-dominated rivers modeled by
Distinct Element Method (DEM) 9 simulations follow a Gaussian
distribution. 10 * The standard deviation of bed height, s \selectlanguage{greek}η , \selectlanguage{english}increases
as the shear stress increases. 11 * Peak entrainment of bed particles
occurs at a distance 2s \selectlanguage{greek}η \selectlanguage{english}above the average bed 12 height. Abstract 14
We investigate the statistics of bed height variability and particle
entrainment height un-15 der steady state bedload transport conditions
using distinct element method (DEM) sim-16 ulations. We do so in the
context of a theoretical probabilistic formulation derived to 17 better
capture spatial variation in sediment exchange between bed material load
and al-18 luvial deposits (Parker et al., 2000). Using DEM simulations,
we set the foundation for 19 a physics-based closure of this
probabilistic framework toward its practical implemen-20 tation. Towards
this, we perform DEM simulations for bedload transport under simi-21 lar
boundary conditions to those of Wong et al. (2007) laboratory
experiments: a bed 22 of gravel particles of median grain size 7.1mm
with lognormal grain size distribution trans-23 ported under bed shear
stresses ranging from \selectlanguage{greek}τ \selectlanguage{english}0 = 8.70 to 13.7 Pa. We first validate 24 these
simulations by demonstrating that they capture measurable transport and
height 25 variations from experimental measurements. We then compute the
statistics of both the 26 bed height and entrainment height as they vary
with bed shear stress. We find that vari-27 abilites in both bed height
and entrainment height variabilities follow Gaussian distri-28 butions,
for which: (1) the standard deviation of bed height variability s \selectlanguage{greek}η
\selectlanguage{english}increases with 29 shear stress, and (2) the peak entrainment height
occurs a distance of twice the stan-30 dard deviation of bed height
variability (2s \selectlanguage{greek}η\selectlanguage{english}) above the mean bed height. We discuss 31 implications
of these results and next steps for understanding these transport
statistics 32 under a broader range of conditions. 33%
\end{abstract}%



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