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\begin{document}

\title{A physical-statistical recipe for representation of small scale oceanic
turbulent mixing in climate models}



\author[1,1]{Ali Mashayek}%
\author[2,2]{Brendan Barry}%
\author[3,3]{Matthew Alford}%
\author[4,4]{Laura Cimoli}%
\author[5,5]{Colm-cille Caulfield}%
\affil[1]{Imperial College London}%
\affil[2]{National Oceanography Centre, Southampton}%
\affil[3]{University of California San Diego, Scripps Institution of OCeanography}%
\affil[4]{University of California San Diego, Scripps Institution of Oceanography}%
\affil[5]{University of Cambridge}%


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  \date{May 26, 2024}


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\begin{abstract}
It is well established that small scale cross-density (diapycnal)
turbulent mixing induced by breaking of overturns in the interior of the
ocean plays a significant role in sustaining the deep ocean circulation
and in regulation of tracer budgets such as those of heat, carbon and
nutrients. There has been significant progress in the fluid mechanical
understanding of the physics of breaking internal waves. Connection of
the microphysics of such turbulence to the larger scale dynamics,
however, is significantly underdeveloped. We offer a hybrid
theoretical-statistical approach, informed by observations, to make such
a link. By doing so, we define a bulk flux coefficient,
\$\textbackslash{}Gamma\_B\$, which represents the partitioning of
energy available to an `ocean box' (such as a grid cell of a coarse
resolution climate model), from winds, tides, and other sources, into
mixing and dissipation. \$\textbackslash{}Gamma\_B\$ depends on both the
statistical distribution of turbulent patches and the flux coefficient
associated with individual patches, \$\textbackslash{}Gamma\_i\$. We
rely on recent parameterizations of
\textasciitilde{}\$\textbackslash{}Gamma\_i\$\textasciitilde{} and the
seeming universal characteristics of statistics of turbulent patches, to
infer \$\textbackslash{}Gamma\_B\$, which is the essential quantity for
representation of turbulent diffusivity in climate models. By applying
our approach to climatology and global tidal estimates, we show that on
a basin scale, energetic mixing zones exhibit moderately efficient
mixing that induces significant vertical density fluxes, while quiet
zones (with small background turbulence levels), although highly
efficient in mixing, exhibit minimal vertical fluxes. The transition
between the less energetic to more energetic zones marks regions of
intense upwelling and downwelling of deep waters. We suggest that such
upwelling and downwelling may be stronger than previously estimated,
which in turn has direct implications for the closure of the deep branch
of the ocean meridional overturning circulation as well as for the
associated tracer budgets.%
\end{abstract}%



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