Basic Physical Elements

Equations of Motion

The ocean circulation is governed by Newton's laws of motion plus those of the thermodynamics of a heat and salt stratified fluid. That these physics govern the system is a concise statement that a great deal is known about it. Our problem is to exploit this knowledge to the fullest extent possible in the context of anything we can observe about the ocean. Elaborate theoretical studies of the ocean circulation exist; here we assume that the reader has a knowledge of this theory at a basic level, with a working knowledge of Ekman layers, geostrophy, the simplest theories of western boundary currents, and the existence of internal waves and similar phenomena. Extended treatments are provided by Fofonoff (1962), Phillips (1963), Veronis (1981), Gill (1982), Pedlosky (1987a), and others.

The full equations of motion describing the ocean are the Navier-Stokes equations for a thin shell of temperature and salinity-stratified fluid on a bumpy near-spheroidal body undergoing rapid rotation. Appropriate boundary conditions are those of no flow of fluid into the bottom and sides, statements about the stress exerted on these boundaries, and those appropriate to exchange of momentum, heat, and moisture with the atmosphere at the surface. It is not really possible to separate the study of the ocean and atmosphere; a rigorous treatment must describe the movement of both fluids together, but both meteorology and oceanography remain at a stage of understanding where a great deal is to still to be learned by discussing them separately.