This book derives and classifies the most common dynamic equations used in physical oceanography, from the planetary geostrophic equations that describe the wind and thermohaline driven circulations to the equations of small-scale motions that describe three-dimensional turbulence and double diffusive phenomena. It does so in a systematic manner and within a common framework. It first establishes the basic dynamic equations that describe all oceanic motions and then derives reduced equations, emphasizing the assumptions made and physical processes eliminated.

The basic equations of oceanic motions consist of:

• the thermodynamic specification of sea water;

• the balance equations for mass, momentum, and energy;

• the molecular flux laws; and

• the gravitational field equation.

These equations are well established and experimentally proven. However, they are so general and so all-encompassing that they become useless for specific practical applications. One needs to consider approximations to these equations and derive equations that isolate specific types or scales of motion. The basic equations of oceanic motion form the solid starting point for such derivations.

In order to derive and present the various approximations in a systematic manner we use the following concepts and organizing principles:

• distinction between properties of fluids and flows;

• distinction between prognostic and diagnostic variables;

• adjustment by wave propagation;

• modes of motion;

• Reynolds decomposition and averaging;

• asymptotic expansion;

• geometric, thermodynamic, and dynamic approximations; and

• different but equivalent representations,

which are discussed in the remainder of this introduction.