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\begin{document}

\title{A Reynolds and coarse-graining hybrid eddy transport diagnostic
framework and its application in the Southern Ocean}



\author[1]{Jingwei Xie}%
\author[1]{Hailong Liu}%
\author[1]{Pengfei Lin}%
\affil[1]{Institute of Atmospheric Physics, Chinese Academy of Sciences}%


\vspace{-1em}



  
  \date{June 13, 2024}


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\begin{abstract}
Mesoscale ocean eddies dramatically impact oceanic material transport,
momentum and energy budgets, and large-scale ocean circulation;
therefore, reasonably diagnosing their effects is crucial for providing
insights into eddy parameterization scheme development. In this work, a
Reynolds and coarse-graining hybrid eddy transport diagnostic framework
is proposed and applied in the Southern Ocean. Both the isotropic
transport coefficient and anisotropic transport tensor are diagnosed and
decomposed into contributions from transient and stationary eddies. The
tensor can be split into its symmetric and antisymmetric parts, and the
symmetric tensor is further diagonalized to analyze the eigenvalues and
eigenvectors. We verify that the anisotropic assumption better fits the
ocean mesoscale eddy transport process than the isotropic assumption, at
least in the Southern Ocean. We place particular emphasis on the
transport tensor's stationary component affected by large-scale
topographies, nonconservative processes, and large-scale flow structures
and find that its influence is highly anisotropic horizontally and
varies vertically. We probe all tensor-related elements that emerge in
our hybrid framework, especially the eigenvalues and eigenvectors of the
symmetric tensor. We reveal all three configurations of the major and
minor eigenvalues that appear in the Southern Ocean, where the one
representing vortex filamentation is the most common scenario. In
addition, we discover a high randomness of the eigenvectors, which
implies the possibility of a semideterministic and semistochastic
anisotropic parameterization scheme.%
\end{abstract}%



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