AOPP Seminar - Coarse-graining to gain insight into the multi-scale dynamics of the oceans

Fluid flows in nature and engineering span a vast range of scales, making them difficult to understand and model. An important example is the global ocean circulation, which has spatial scales ranging from dissipation on sub-mm scales to 40,000 km, the circumference of the Earth, and temporal scales from seconds to decades and longer. Our understanding of the ocean’s spatial scales and their energetic coupling has been derived mostly from Fourier analysis in small "representative" regions, typically a few hundred kilometers in size, that cannot capture the vast dynamic range on planetary scales. I will highlight the diagnostic power of coarse-graining, an analysis technique that allows us to scale-decompose complex flows while maintaining spatial information. While there are many established methods for coarsening data (e.g. block averaging), our approach preserves the underlying symmetries at different scales because our coarse-graining commutes with derivatives, allowing us to derive the dynamics of different scales self-consistently. I present recent results, including the first global kinetic energy (KE) wavenumber spectrum, as well as the first measurements of the global KE cascade across this entire range of scales. Further, by analyzing global spatial maps of KE transfer across scales, we find that the global atmospheric circulation cells (Hadley, Ferrel, Polar) induce direct energy exchanges between the gyre-scales (>1000 km) and mesoscales (~50-500 km), a previously unobserved coupling.