Journal Article

Scale Analysis on Unstructured Grids: Kinetic Energy and Dissipation Power Spectra on Triangular Meshes

Bellinghausen, K., Oliver, M., Kutsenko, A., Juricke, S., Danilov, S.

2023

Overview

Fourier spectra are powerful tools to analyze 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, that is, 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. Plain Language Summary To better understand the physical processes that drive and define the circulation in our oceans, it is necessary to analyze the temporal and spatial scales on which these processes act. The classical method to investigate the spatial scale behavior is Fourier analysis which splits any given data into waves of different amplitudes and wavelengths. Mathematically this requires data on an equidistantly spaced grid. However, many ocean models apply triangular or other irregular grids for their computations of oceanic flows. In this study, we describe the advantages and disadvantages of applying Fourier analysis for models that use triangular meshes, with prior interpolation of data to regularly spaced rectangular meshes. We also introduce two other methods that can analyze the distribution of kinetic energy and kinetic energy dissipation across scales without interpolation. The results show that one needs to be very careful when choosing a specific scale analysis and, potentially, an interpolation method for triangular grids, especially when it comes to analyzing the process of kinetic energy dissipation. Key Points Three different scale analysis methods for unstructured triangular grids are presented and discussed Fourier spectra after interpolation of fields should be applied with caution especially for dissipation power spectra Scale analysis via indicator functions does not rely on interpolation and can be applied to non‐smooth, unstructured data

• Publisher: John Wiley & Sons, Inc,American Geophysical Union (AGU)
• Subject: Analysis / Backscatter / Channel flow / Climate models / Computation / dissipation power spectra / Energy / Energy spectra / Fourier analysis / Interpolation / Interpolation methods / Kinetic energy / kinetic energy spectra / Methods / momentum closure / Ocean models / Oceanic analysis / Oceans / Power spectra / scale analysis / Sea ice / Spectra / spectral analysis / unstructured grids