Environmental Engineering Reference
In-Depth Information
+
H
(a)
(b)
Figure 7.25
(a) The profile of an ocean wave of wavelength
λ
and wave height
H
. (b) A sketch of the Salter
cam, a device for extracting power from a wave.
of waves could provide a source of electrical energy analogous to that of the wind. The technology
for doing so, however, presents both economic and engineering challenges.
Ocean waves are formed on the ocean's surface by action of the wind. By friction and pressure
forces exerted at the air-water interface, wind energy is transferred to the energy of gravity waves
moving across the ocean surface. The wave energy moves with the wave, but the ocean water has
no net motion in the direction of the wave propagation. By suitable mechanical devices, the energy
in a wave may be converted to mechanical power.
Ocean waves involve periodic motion of the water at or close to the ocean surface that is
sustained by gravity [see Figure 7.25(a)]. The cyclic frequency
f
of an ocean wave is related to its
wavelength
λ
by
g
2
f
=
(7.18)
πλ
where
g
is the acceleration of gravity. The velocity
c
at which the wave pattern moves across the
surface of the water, called the phase velocity, is the product of the wavelength times the frequency:
g
λ
g
c
=
f
λ
=
=
(7.19)
2
π
2
π
f
Long-wavelength waves move faster than those of shorter wavelength, leading to dispersion, or
spreading of the energy in an ocean wave system.
The energy of an ocean wave consists of two parts: the kinetic energy of the moving water
particles in the wave and the gravitational potential energy of the fluid displaced from its equilibrium
position of a flat horizontal surface. It is this motion and displacement imparted to the ocean surface
by the wind that constitutes the source of power that can be abstracted by a wave power system.
The motion of the water in an ocean wave is confined mostly to a layer of depth
below
the surface. If
H
is the wave height, measured from crest to trough as in Figure 7.25, then the
velocity of a water particle in the wave is about
Hf
and the kinetic energy of the water in this layer,
per unit of surface area of the wave, is the product of the water mass density
λ/
2
π
ρ
times the depth
λ/
2
π
times the kinetic energy per unit mass,
(
Hf
)
2
/
2, for a total of
ρλ
H
2
f
2
/
4
π
=
ρ
gH
2
/
8
π
2
.
Thus the average kinetic energy per unit surface area of a wave system is of the order of
gH
2
and
is independent of the wavelength or frequency. The potential energy of the wave, per unit surface
area, is approximately the product of the displaced mass per unit area
ρ
ρ
H
, its vertical displacement
gH
2
. An exact calculation of the kinetic and
potential energies per unit of wave surface area reveals that they are equal and their sum can be
H
, and the gravitational acceleration
g
, for a total of
ρ
