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\begin{document}

\title{Scale analysis on unstructured grids: Kinetic energy and dissipation
power spectra on triangular meshes}



\author[1]{Stephan Juricke}%
\author[2]{Marcel Oliver}%
\author[3]{Sergey Danilov}%
\author[2]{Anton Kutsenko}%
\author[3]{Kai Bellinghausen}%
\affil[1]{Jacobs University Bremen}%
\affil[2]{KU Eichstätt-Ingolstadt}%
\affil[3]{Alfred Wegener Institute for Polar and Marine Research}%


\vspace{-1em}



  
  \date{May 15, 2024}


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\begin{abstract}
Fourier spectra are powerful tools to analyse the scale behavior of
turbulent flows. While such spectra are mathematically based on regular
periodic data, some state-of-the-art ocean and climate models use
unstructured triangular meshes. Observational data is often also
available only in an unstructured fashion. In this study, scale analysis
specifically for the output of models with triangular meshes is
discussed and the representable wavenumbers for Fourier analysis are
derived. Aside from using different interpolation methods and
oversampling prior to the computation of Fourier spectra, we also
consider an alternative scale analysis based on the Walsh--Rademacher
basis, i.e. indicator functions. It does not require interpolation and
can be extended to general unstructured meshes. A third approach based
on smoothing filters which focus on grid scales is also discussed. We
compare these methods in the context of kinetic energy and dissipation
power of a turbulent channel flow simulated with the sea ice-ocean model
FESOM2. One simulation uses a classical viscous closure, another a new
backscatter closure. The latter is dissipative on small scales, but
anti-dissipative on large scales leading to more realistic flow
representation. All three methods clearly highlight the differences
between the simulations as concerns the distribution of dissipation
power and kinetic energy over scales. However, the analysis based on
Fourier transformation is highly sensitive to the interpolation method
in case of dissipation power, potentially leading to inaccurate
representations of dissipation at different scales. This highlights the
necessity to be cautious when choosing a scale analysis method on
unstructured grids.%
\end{abstract}%



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