This book about the equations of oceanic motions grewout of the course “Advanced Geophysical Fluid Dynamics” that I have been teaching for many years to graduate students at the University of Hawaii. In their pursuit of rigorous understanding, students consistently asked for a solid basis and systematic derivation of the dynamic equations used to describe and analyze oceanographic phenomena. I, on the other hand, often felt bogged down by mere “technical” aspects when trying to get fundamental theoretical concepts across. This book is the answer to both. It establishes the basic equations of oceanic motions in a rigorous way, derives the most common approximations in a systematic manner and uniform framework and notation, and lists the basic concepts and formulae of equilibrium thermodynamics, vector and tensor analysis, curvilinear coordinate systems, and the kinematics of fluid lows and waves. All this is presented in a spirit somewhere between a textbook and a reference book. This book is thus not a substitute but a complement to the many excellent textbooks on geophysical fluid dynamics, thermodynamics, and vector and tensor calculus. It provides the basic theoretical background for graduate classes and research in physical oceanography in a comprehensive form.

The book is about equations and theorems, not about solutions. Free wave solutions on a sphere are only included since the emission of waves is a mechanism by which fluids adjust to disturbances, and the assumption of instantaneous adjustment and the elimination of certain wave types forms the basis of many approximations.