Disentangling the Oceanic General Circulation

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. To address this problem, we are working toward mapping out a Lorenz Energy Cycle concurrently in (i) scale, (ii) space, and (iii) time. We have developed a coarse-graining framework on the sphere that is more versatile and powerful than the classical `mean-eddy' decomposition. Coarse-graining has a rigorous mathematical foundation and is closely related to well-established physics techniques, including macroscopic electromagnetism, renormalization group, and large eddy simulation. Moreover, unlike the classical decomposition, coarse-graining is consistent with the parameterization requirements of coarse-resolution climate simulations. I will focus on three applications using satellite and model data: the first measurement of the global oceanic energy spectrum, the energy cascade, and the killing of eddies by wind.