Page 101 - Introduction to Naval Architecture

88 THE ENVIRONMENT

through 6, the centre of the circle will move E0 and the wave
generating point, P, has co-ordinates:

Figure. 5.2 Sub-trochoids

Referring to Figure 5.2, the following mathematical relationships can
be shown to exist:

(1) The velocity of the wave system, C =

(2) The still water surface will be at z reflecting the fact that the

crests are sharper than the troughs.
(3) Particles in the wave move in circular orbits.
(4) Surfaces of equal pressure below the wave surface are trochoidal.
These subsurface amplitudes reduce with depth so that, at z
below the surface, the amplitude is:

(5) This exponential decay is very rapid and there is little movement
at depths of more than about half the wavelength.
Wave pressure correction
The water pressure at the surface of the wave is zero and at a reasonable
depth, planes of equal pressure will be horizontal. Hence the pressure
variation with depth within the wave cannot be uniform along the