vertical distance between the crest and the trough is the height of the wave
H, which is twice the amplitude, a. The wavelength, L, is the horizontal
distance between the crests. The phase velocity, or celerity, of the wave,
c, is:
cL/T. (14.1)The steepness of the wave is H/L. If the height of the wave is extremely
small compared with the wavelength and the depth of water, the governing
equations are linear and the waveform is usually referred to as a linear or
Airy wave. Some other waves that a coastal engineer may find as a better
approximation of waves on shorelines are shown in Fig. 14.2. These are
non-linear waves which occur for large wave heights. In non-linear theory
it is usual to classify waves in terms of the wavelength relative to the water
depth. In deep water or for short waves, a finite-height wave known as a
Stokes wave is applicable (Fig. 14.2(a)). In shallow water or for long
waves, the cnoidal wave theory is applied as an approximation. Both
Stokes and cnoidal waves (Fig. 14.2(b)) are asymmetrical with respect to
the still-water level and have sharp crests and elongated troughs. A soli-
tary wave characterized by a single hump above still water, moving in
shallow water, is shown in Fig. 14.2(c). Linear wave theory is widely used in
engineering applications because of its simplicity, but, for cases where
better evaluation of wave properties is required, complex non-linear wave
theories have to be applied. However, if the waves are not large in relation
to the depth, or steep enough to break, linear theory is sufficiently accurate.
WAVE MOTION 577
Fig. 14.2 Some non-linear waves