66
DETERMINISTIC DESCRIPTIONS OF OFFSHORE WAVES
3.
The water depth d is uniform.
4.
The water is nonviscous and irrotational.
5.
The water is incompressible and nonstratified (homogeneous).
6.
The Coriolis forces due to the earth’s rotation are negligible.
7.
Surface tension is negligible.
8.
The sea floor is smooth and imperméable.
9. The sea level atmospheric pressure pa is uniform. Here, the hydrostatic
pressure is —pgz, and the dynamic water pressure is denoted by p.
Assumption 1 actually implies 2, although this is not immediately obvious.
Assumption 5 excludes acoustic and internai wave phenomena. It is known
that Assumption 6 is valid if the very long waves associated with tides and
seiches in large seas are excluded. It is also known that surface tension effects
are negligible, Assumption 7, for ail but very short wave lengths. The other
assumptions, needed to make the governing équations tractable for closed form
solutions, are reasonable approximations for a large number of applications.
Figure 3 6 Schematic représentation of a simple harmonie wave. The vertical scale
of the surface profile is exaggerated for clarity.
W hen the nine assumptions are invoked, the differential équations and boundary restraints for the water particle velocity and pressure reduce to the following
for ms:
du
dz
dw
77- =0
dx
(3.11a)
du
dw
(3.11b)
dx
= o
dz
du
1 dp
(3.11c)
dt = p dx
dw
dp
(3.11d)
~dt = ~dz~9