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\begin{document}

\title{On the form drag coefficient under ridged ice: Laboratory experiments
and numerical simulations from ideal scaling to real ice conditions}



\author[1]{Yongheng Zu}%
\author[1]{Peng Lu}%
\author[2]{Matti Lepparanta}%
\author[3]{Bin Cheng}%
\author[1]{Zhijun Li}%
\affil[1]{Dalian University of Technology}%
\affil[2]{University of Helsinki}%
\affil[3]{Finnish Meteorological Institute}%


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  \date{June 05, 2024}


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\begin{abstract}
The bottom topography of ridged sea ice differs largely from that of
other sea ice types. The form drag on ridge keels plays an important
role affecting sea ice drift and deformation. We have carried out
laboratory experiments and numerical simulations for a ridge model in a
flume in order to better understand the characteristics of the form
drag. The experimental setup covered both laminar and turbulent
conditions. The local form drag coefficient of a keel, Cd, varied with
the keel depth h and slope angle \selectlanguage{greek}α \selectlanguage{english}in the turbulent regime. The
numerical model extended the experimental results to independence of the
water depth in order to achieve an analogy for ocean conditions. The
results showed Cd= 0.68ln(\selectlanguage{greek}α/\selectlanguage{english}7.8),R2= 0.998, 10@ [?] \selectlanguage{greek}α\selectlanguage{english}[?] \selectlanguage{english}90@, \selectlanguage{english}Cd ranging
from 0.14 to 1.66, when keel depth is much smaller than mixed layer
depth. In the Arctic Ocean, keel slope angles are within the range of
10@--\selectlanguage{english}50@ \selectlanguage{english}where Cd increases monotonously and becomes the dominant part
of the total ice-water drag coefficient when \selectlanguage{greek}α \selectlanguage{english}[?] \selectlanguage{english}20@. \selectlanguage{english}When h/Lr (the
ratio of keel depth to spacing) was high (h/Lr\textgreater{}0.01), the
ratio of air-ice to ice-water drag coefficient first decreased and then
increased with \selectlanguage{greek}α \selectlanguage{english}and reached the minimum at \selectlanguage{greek}α \selectlanguage{english}[?] \selectlanguage{english}30@. \selectlanguage{english}The variation of Cd
with \selectlanguage{greek}α \selectlanguage{english}(10@--\selectlanguage{english}50@\selectlanguage{english}) affects the momentum transfer of drifting sea ice, and
we suggest that Cd under ridged sea ice to be tuned to 0.14--1.26 in
multi-category sea ice models.%
\end{abstract}%



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