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\begin{document}

\title{Scaling laws in Aeolian sand transport under low sand availability}



\author[1,1,1]{Sandesh Kamath}%
\author[2,2,2]{Yaping Shao}%
\author[3,3,3]{Eric Ribeiro Parteli}%
\affil[1]{Institute of Geophysics and Meteorology, University of Cologne}%
\affil[2]{University of Cologne}%
\affil[3]{University of Duisburg-Essen}%


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  \date{June 13, 2024}


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\begin{abstract}
Previous studies of wind-blown sand have considered either fully
erodible or non-erodible soils, but the transport over sparsely
sand-covered soils is still poorly understood. The quantitative modeling
of this transport is important for the parametrization of Aeolian
processes under low sand availability. Here we show, by means of
particle-based numerical simulations, that the Aeolian sand transport
rate Q scales with the wind shear velocity u* as Q = a.{[}1 + b .
(u*/u*t - 1){]} .[?](d/g) . \selectlanguage{greek}ρ\selectlanguage{english}f. (u*\selectlanguage{ngerman}² \selectlanguage{english}- u\selectlanguage{english}*t2), where u\selectlanguage{english}*t is the minimal
threshold u\selectlanguage{english}* for sustained transport, d is particle size, g is gravity
and \selectlanguage{greek}ρ\selectlanguage{english}f is air density, while u*t and the empirical parameters a and b
depend on the sand cover thickness. Our model explains the transition
from the quadratic to cubic scaling of Q with u* as soil conditions
change from fully erodible to rigid and provides constraints for
modeling Aeolian transport under low sand availability.%
\end{abstract}%



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