Page 117 - Fundamentals of Ocean Renewable Energy Generating Electricity From The Sea

108 Fundamentals of Ocean Renewable Energy

FIG. 5.1 Schematic of a monochromatic sinusoidal wave and important wave parameters.

There are various properties of ocean waves that are common to almost all
waves that occur in the natural environment. Consider a ‘linear’ wave in the
space domain that can be represented by a sinusoidal profile (Fig. 5.1). The
maximum displacement of the wave from still water level (z = 0) is the wave
amplitude, a. The vertical distance between the crest and trough (i.e. 2a)is
defined as the wave height, H, and the distance between two successive crests (or
troughs) is the wave length, L. Although not shown in Fig. 5.1, a corresponding
sketch in the time domain would show that the time between two successive
wave crests (or troughs) is the wave period, T. The reciprocal of the wave period
(1/T) is the wave frequency, with units of s −1 or Hz.
As all trigonometric functions repeat over the interval 2π, the mathematical
description of waves is much simplified if we introduce the concepts of
wavenumber (k = 2π/L) and angular frequency (σ = 2π/T). To give the
wavenumber physical meaning, k is the number of complete wave cycles that
exist in 1 m of linear space. A commonly reported property of waves is the
significant wave height (H s ). This is defined as the mean height of the highest
one-third of the waves in a record. This approximately corresponds to the wave
height that can be estimated visually by a trained observer.

5.1.1 Linear Wave Theory
Waves in the ocean are nonlinear, and do not exactly follow linear wave theory;
nevertheless, linear wave theory is very helpful in understanding and assessing
more complicated waves such as nonlinear, irregular, and random waves, which
will be discussed further later in this chapter. Linear wave theory can also be
applied to many engineering and science problems with reasonable accuracy.
A detailed derivation of linear wave theory can be found in many standard