Current and future prospects for the application of systematic theoretical methods to the study of problems in physical oceanography

• Systematic theoretical methods in studies of equatorial ocean dynamics.
• Linear wave-current interactions in stratified flows.
• Exact solutions – Kelvin waves, azimuthal non-uniform currents.
• Three-dimensional nonlinear currents.
• Hamiltonian formulation for the governing equations and for structure-preserving/enhancing approximations.

This essay is a commentary on the pivotal role of systematic theoretical methods in physical oceanography. At some level, there will always be a conflict between theory and experiment/data collection: Which is pre-eminent? Which should come first? This issue appears to be particularly marked in physical oceanography, to the extreme detriment of the development of the subject. It is our contention that the classical theory of fluids, coupled with methods from the theory of differential equations, can play a significant role in carrying the subject, and our understanding, forward. We outline the philosophy behind a systematic theoretical approach, highlighting some aspects of equatorial ocean dynamics where these methods have already been successful, paving the way for much more in the future and leading, we expect, to the better understanding of this and many other types of ocean flow. We believe that the ideas described here promise to reveal a rich and beautiful dynamical structure.