Global energy spectrum of the general oceanic circulation

Advent of satellite altimetry brought into focus the pervasiveness of mesoscale eddies [Formula: see text] km in size, which are the ocean's analogue of weather systems and are often regarded as the spectral peak of kinetic energy (KE). Yet, understanding of the ocean's spatial scales has been derived mostly from Fourier analysis in small "representative" regions that cannot capture the vast dynamic range at planetary scales. Here, we use a coarse-graining method to analyze scales much larger than what had been possible before. Spectra spanning over three decades of length-scales reveal the Antarctic Circumpolar Current as the spectral peak of the global extra-tropical circulation, at ≈ 10⁴ km, and a previously unobserved power-law scaling over scales larger than 10³ km. A smaller spectral peak exists at ≈ 300 km associated with mesoscales, which, due to their wider spread in wavenumber space, account for more than 50% of resolved surface KE globally. Seasonal cycles of length-scales exhibit a characteristic lag-time of ≈ 40 days per octave of length-scales such that in both hemispheres, KE at 10² km peaks in spring while KE at 10³ km peaks in late summer. These results provide a new window for understanding the multiscale oceanic circulation within Earth's climate system, including the largest planetary scales.