Physical oceanography is an exciting, fruitful and important field of study, particularly relevant to the current discourse on, and the effects of, climate change. However, the tried and tested techniques of (and wealth of knowledge available from) classical fluid mechanics seem to have been sidelined, in favor of an emphasis on modeling and numerical methods. In this article, we make the case for returning to fundamental ideas, explaining the essentials of this approach in the context of the Euler (or Navier-Stokes) equation written in a rotating, spherical coordinate system. We support our contention that this is the way forward by presenting (descriptively only) a number of examples that show what can be done, and suggesting that much more is possible. Indeed, we argue that this is the route to be taken before recourse to other, more ad hoc, methods. We will use this approach to provide new insight (and new results) related to the Pacific Equatorial Undercurrent, the Antarctic Circumpolar Current (including the role of exact solutions), and large gyres.

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