1 - INTRODUCTION AND PRELIMINARIES

Summary

The topics to be discussed

It seems useful to begin by outlining the range of subjects covered in this book, to give a broad picture of the way in which the several parts of the field have developed, and at the same time some explanation of the theme which has been used to connect them. The phenomena studied all depend on gravity acting on small density differences in a non-rotating fluid. Often the undisturbed fluid has a density distribution which varies in the vertical but is constant in horizontal planes; this will be called a stratified system whether the density changes smoothly or discontinuously. Special attention will be given to the problems of buoyant convection (arising from an unstable density distribution) and to various mechanisms of mixing when the stratification is stable.

Chapters 2 and 3 summarize relevant results on internal waves, and these were also historically the first phenomena to be studied. The original applications of the methods of perfect fluid theory to motion under gravity were to the problems of small amplitude surface waves and tides (subjects which will not be discussed here). These were soon extended to the case of two layers of uniform density with a density discontinuity between them. Some of the basic results had already been obtained by 1850 (notably by Stokes 1847), and they were applied to phenomena such as the drag experienced by a ship when it creates a wave on an interface close to the surface (Ekman 1904), and to internal seiches in lakes.