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\begin{document}

\title{Numerical mixing suppresses submesoscale baroclinic instabilities over
sloping bathymetry}



\author[1]{Dylan Schlichting}%
\author[2]{Robert D. Hetland}%
\author[1]{C Spencer Jones}%
\affil[1]{Texas A\&M University}%
\affil[2]{Pacific Northwest National Laboratory}%


\vspace{-1em}



  
  \date{May 21, 2024}


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\begin{abstract}
In this work, the impacts of spurious numerical salinity mixing
(\$\textbackslash{}mathcal\{M\}\_\{num\}\$) on the larger-scale flow and
tracer fields are characterized using idealized simulations. The
idealized model is motivated by realistic simulations of the
Texas-Louisiana shelf and features oscillatory near-inertial wind
forcing. \$\textbackslash{}mathcal\{M\}\_\{num\}\$ can exceed the
physical mixing from the turbulence closure
(\$\textbackslash{}mathcal\{M\}\_\{phy\}\$) in frontal zones and within
the mixed layer. This suggests simulated mixing processes in frontal
zones may be driven largely by
\$\textbackslash{}mathcal\{M\}\_\{num\}\$. Near-inertial alongshore wind
stress amplitude is varied to identify a base case that maximizes the
ratio of \$\textbackslash{}mathcal\{M\}\_\{num\}\$ to
\$\textbackslash{}mathcal\{M\}\_\{phy\}\$. We then we test the
sensitivity of the base case with three tracer advection schemes
(MPDATA, U3HC4, and HSIMT) and conduct ensemble runs with perturbed
bathymetry. Instability growth is evaluated with several analysis
methods: volume-integrated eddy kinetic energy (\$EKE\$) and available
potential energy (\$APE\$), surface and bottom isohaline variability,
and alongshore-averaged salinity sections. While all schemes have
similar total mixing, HSIMT simulations have over double the
volume-integrated \$\textbackslash{}mathcal\{M\}\_\{num\}\$ and
20\textbackslash{}\% less \$\textbackslash{}mathcal\{M\}\_\{phy\}\$
relative to other schemes, which suppresses the release of \$APE\$ and
reduces the \$EKE\$ by roughly 25\textbackslash{}\%. HSIMT instabilities
are confined shoreward relative to the other schemes. This results in
reduced isohaline variability and steeper isopycnals, evidence that
enhanced numerical mixing suppresses instability growth.%
\end{abstract}%



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