TABLE OF CONTENTS In this chapter we will review the basic results from water wave theory which are necessary to develop the wave-induced forces to be discussed in the next chapter. For a more thorough treatment of the theory, the reader is referred to the many excellent texts on the subject, e.g., Mei [1989]; Sumer and Fredscae [1997].
When energy is imparted to a body of water, by the action of wind and other atmospheric effects, or by the motion of bodies such as ships, surface waves are created. The form of these waves is determined by the physical properties of the water, the principle of conservation of mass (or "continuity"), and by Newton's laws of motion (conservation of momentum). When the latter are applied to a "fluid element", we obtain the "Navier-Stokes equations" which, together with the continuity equation, govern the velocity and pressure fields in the water. These nonlinear partial differential equations are difficult to solve in general. However, if we assume that the effects of viscosity are negligibly small compared with gravitational effects, the equations can be simplified considerably. Unfortunately this does not justify neglecting viscous effects; but it turns out that the results obtained for inviscid fluids are sufficiently accurate to produce useful results in many (if not most) cases of practical interest.
If we assume that the flow is irrotational in addition to being inviscid [a], it follows that the velocity field in the water can be expressed as the gradient of...
