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

Abstract

Abstract 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.

Keywords

• spectral analysis
• scale analysis
• momentum closure
• kinetic energy spectra
• dissipation power spectra
• unstructured grids