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\begin{document}

\title{A parameterization of local and remote tidal mixing}



\author[1]{Casimir de Lavergne}%
\author[2]{Clément Vic}%
\author[1]{Gurvan Madec}%
\author[3]{Fabien Roquet}%
\author[4]{Amy Waterhouse}%
\author[5]{Caitlin Whalen}%
\author[1]{Yannis Cuypers}%
\author[1]{Pascale Bouruet-Aubertot}%
\author[2]{Bruno Ferron}%
\author[6]{Toshiyuki Hibiya}%
\affil[1]{LOCEAN Laboratory, Sorbonne Université-CNRS-IRD-MNHN, Paris, France}%
\affil[2]{LOPS Laboratory, UBO-IFREMER-CNRS-IRD, Plouzané, France}%
\affil[3]{Department of Marine Sciences, University of Gothenburg, Gothenburg, Sweden}%
\affil[4]{Scripps Institution of Oceanography, University of California, La Jolla, California}%
\affil[5]{Applied Physics Laboratory, University of Washington, Seattle, Washington}%
\affil[6]{Department of Earth and Planetary Science, Graduate School of Science, The University of Tokyo, Tokyo, Japan}%


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  \date{May 25, 2024}


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\begin{abstract}
Vertical mixing is often regarded as the Achilles' heel of ocean models.
In particular, few models include a comprehensive and energy-constrained
parameterization of mixing by internal ocean tides. Here, we present an
energy-conserving mixing scheme which accounts for the local breaking of
high-mode internal tides and the distant dissipation of low-mode
internal tides. The scheme relies on four static two-dimensional maps of
internal tide dissipation, constructed using mode-by-mode Lagrangian
tracking of energy beams from sources to sinks. Each map is associated
with a distinct dissipative process and a corresponding vertical
structure. Applied to an observational climatology of stratification,
the scheme produces a global three-dimensional map of dissipation which
compares well with available microstructure observations and with
upper-ocean finestructure mixing estimates. This relative agreement,
both in magnitude and spatial structure across ocean basins, suggests
that internal tides underpin most of observed dissipation in the ocean
interior at the global scale. The proposed parameterization is therefore
expected to improve understanding, mapping and modelling of ocean
mixing.%
\end{abstract}%



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