1 Introduction

It is perhaps not an overstatement to say that wave motion is the most basic feature of all physical phenomena. Waves are the means by which information is transmitted between two points in space and time, without movement of the medium across the two points. The energy and phase of some disturbance travels during a wave motion, but motion of the matter is generally small. Waves are generated due to the existence of some kind of "restoring force" that tends to bring the system back to its undisturbed state, and of some kind of "inertia" that causes the system to overshoot after the system has returned to the undisturbed state. One type of wave motion is generated when the restoring forces are due to the compressibility or elasticity of the material medium, which can be a solid, liquid, or gas. Theresulting wave motion, in which the particles move to and fro in the direction of wave propagation, is called a compression wave, elastic wave, or pressure wave. The small-amplitude variety of these is called a "sound wave." Another common wave motion, and the one we are most familiar with from everyday experience, is the one that occurs at the free surface of a liquid, with gravity playing the role of the restoring force. These are called surface gravity waves. Gravity waves, however, can also exist at the interface between two fluids of different density, in which case they are called internal gravity waves. The particle...