Introduction

The simplest possible water wave theory is that of linear waves, which emerge as solution to a simplified version of the general equations of motion. In this chapter, we first discuss the assumptions leading to the simplified equations, then derive the solution for linear waves. We then analyze the physical characteristics of that solution such as velocity and pressure fields, and special cases of the theory such as waves in very deep and very shallow water. We also analyze wave averaged quantities such as mean wave energy density, and the mean flux of mass (or volume), momentum and energy caused by a linear wave motion. We also consider the superposition of linear waves, both some simple canonical examples and the most general form described by wave spectra. We then go on to consider the propagation of linear waves in regions of varying depth and thereby derive the basic equations for many of the modern wave models. ^[1]

Throughout we seek to clarify the physical properties and the limitations of the approximate solutions found.