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\title{The vertical structure and entrainment of subglacial melt water plumes}



\author[1]{Hans Burchard}%
\author[2]{Karsten Bolding}%
\author[3]{Adrian Jenkins}%
\author[4]{Martin Losch}%
\author[5]{Markus Reinert}%
\author[6]{Lars Umlauf}%
\affil[1]{Leibniz Institiute for Baltic Sea Research Warnemünde}%
\affil[2]{Bolding \& Bruggeman ApS}%
\affil[3]{BAS}%
\affil[4]{Alfred Wegener Institute for Polar and Marine Research}%
\affil[5]{Leibniz Institute for Baltic Sea Research}%
\affil[6]{Leibniz-Institute for Baltic Sea Research (IOW)}%


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  \date{May 24, 2024}


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\begin{abstract}
Basal melting of marine-terminating glaciers, through its impact on the
forces that control the flow of the glaciers, is one of the major
factors determining sea level rise in a world of global warming.
Detailed quantitative understanding of dynamic and thermodynamic
processes in melt-water plumes underneath the ice-ocean interface is
essential for calculating the subglacial melt rate. The aim of this
study is therefore to develop a numerical model of high spatial and
process resolution to consistently reproduce the transports of heat and
salt from the ambient water across the plume into the glacial ice. Based
on boundary layer relations for momentum and tracers, stationary
analytical solutions for the vertical structure of subglacial
non-rotational plumes are derived, including entrainment at the plume
base. These solutions are used to develop and test convergent numerical
formulations for the momentum and tracer fluxes across the ice-ocean
interface. After implementation of these formulations into a
water-column model coupled to a second-moment turbulence closure model,
simulations of a transient rotational subglacial plume are performed.
The simulated entrainment rate of ambient water entering the plume at
its base is compared to existing entrainment parameterizations based on
bulk properties of the plume. A sensitivity study with variations of
interfacial slope, interfacial roughness and ambient water temperature
reveals substantial performance differences between these bulk
formulations. An existing entrainment parameterization based on the
Froude number and the Ekman number proves to have the highest predictive
skill. Recalibration to subglacial plumes using a variable drag
coefficient further improves its performance.%
\end{abstract}%



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