Wavelet-based wavenumber spectral estimate of eddy kinetic energy: Idealized quasi-geostrophic flow

Abstract

A wavelet-based method is introduced in an oceanographic context to estimate wavenumber spectrum and spectral flux of kinetic energy and enstrophy. We apply this to a numerical simulation of idealized, doubly-periodic quasi-geostrophic flows, i.e.~the flow is constrained by the Coriolis force and vertical stratification. The double periodicity allows for a straightforward Fourier analysis as the baseline method. Our wavelet spectra and spectral flux agree well with the canonical Fourier approach but with the additional strengths of negating the necessity for the data to be periodic and being able to extract local anisotropies in the flow.

Spatio‐Temporal Coarse‐Graining Decomposition of the Global Ocean Geostrophic Kinetic Energy

“…The approach is very general, allows for probing the dynamics simultaneously in scale and in space, and is not restricted by assumptions of homogeneity or isotropy commonly required for traditional methods such as Fourier or structure‐function analysis. We note that coarse‐graining includes wavelet analysis (Uchida et al., 2023) as a special case with the proper choice of convolution kernel, which disentangles the flow from a band of scales instead of partitioning it into large‐scales and small‐scales (Sadek & Aluie, 2018). Coarse‐graining offers a way to probe and quantify the energy budget at different length‐scales globally while maintaining local information about the heterogeneous oceanic regions.…”

“…Wavelet analysis, which has been recently used by Uchida et al. (2023) to analyze quasigeostrophic turbulence, can be regarded as a special case of coarse‐graining by choosing the convolution kernel to be a wavelet (Sadek & Aluie, 2018). The approach has been recently generalized to account for the spherical geometry of flow on Earth (Aluie, 2019), and applied to study the nonlinear cascade in the North Atlantic from an eddying simulation (Aluie et al., 2018).…”

Wavelet‐Based Wavenumber Spectral Estimate of Eddy Kinetic Energy: Idealized Quasi‐Geostrophic Flow

“…The pyqg model is available through Github (Abernathey et al, 2022). Jupyter notebooks used to run the pyqg simulation and conduct analyses are available via Github (Uchida, 2023). study is a contribution to the "Assessing the Role of forced and internal Variability for the Ocean and climate Response in a changing climate" (ARVOR) project supported by the French "Les Enveloppes Fluides et l'Environnement" (LEFE) program.…”