Abstract

Large-scale currents and eddies pervade the ocean and play a prime role in the general circulation and climate. The coupling between scales ranging from $O(10^4)_{$km down to $O(1)}$mm presents a major difficulty in understanding, modeling, and predicting oceanic circulation and mixing, where our constraints on the energy budget suffer from large uncertainties. Identifying the energy sources and sinks at various scales and geographic locations can reduce such uncertainty and yield insight into new parameterizations of nonlinear physical processes. To this end, we develop the coarse-graining framework to analyze the multi-scale dynamics on the sphere. This is made possible by generalizing the definition of convolution to ensure that our filtering operators and spatial derivatives on the sphere commute, thereby allowing us to derive the PDEs governing any sets of scales. The approach is very general, allows for probing the dynamics simultaneously in scale and in space, and is not restricted by usual assumptions of homogeneity or isotropy. We will demonstrate the application of this framework to satellite altimetry data and to strongly eddying high-resolution simulations using General Circulation Models, focusing on the energy cascade, eddy-killing by wind, and measuring the global oceanic energy spectrum.