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

• Published in: Journal of advances in modeling earth systems 2023-03, Vol.15 (3), p.1619-n/a
• Main Authors: Uchida, Takaya, Jamet, Quentin, Poje, Andrew C., Wienders, Nico, Dewar, William K., Deremble, Bruno
• Format: Article
• Language: English
• Subjects: Coriolis force; Eddy kinetic energy; Energy; Enstrophy; Fourier analysis; Fourier transforms; Geostrophic flow; Kinetic energy; Numerical simulations; Periodicity; quasi geostrophy; Random variables; Sciences of the Universe; Spacetime; spectral analysis; Stratification; Wavelet transforms; wavelets
• ISSN: 1942-2466; 1942-2466
• DOI: 10.1029/2022MS003399

A wavelet‐based method is re‐introduced in an oceanographic and spectral 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, that is, 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 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. Caution is warranted, however, when computing higher‐order quantities, such as spectral flux. Plain Language Summary Chaotic flows such as the ocean currents, atmospheric winds, and turbulence in general are fundamentally impossible to analytically predict, namely, to formulate a mathematical general solution. Nevertheless, the interest in describing such chaotic flows can be found in examples as old as Leonardo da Vinci's sketch of turbulence. While we cannot obtain an analytical description of turbulence, we can extract statistical information from turbulent flows and a common descriptor has been the wavenumber spectrum. The spectrum reveals at each spatial scale, the level of variability the flow carries. Here, we re‐introduce an alternative method in estimating the spectrum based on wavelet functions. Key Points A wavelet‐based spectral method to estimate eddy variability is described Wavenumber spectra of eddies are estimated for a doubly periodic quasi‐geostrophic flow The wavelet and Fourier approach agree well in their estimates of spectra and spectral flux