it is necessary for the hull to seek a static point in the ocean, such as fixing the
Mighty Whale energy converter on the ocean surface with six huge chains. Here, it
is assumed that the hull is rigid.
It is assumed that the water in the chamber resonates with the incident wave.
Therefore, the natural frequency x 0 of water in the cavity is the same as the angular
frequency x of the wave, as shown in the following equation.
x 0 ¼ x
ð14:1Þ
where
x Angular frequencies of ocean waves.
When the compressibility of air is neglected, the equation of motion of water in
the chamber can be expressed by the following, whose inertia force and recovery
force are in equilibrium:
qs a l
d
2 x
dt 2 ¼ Àqs a gx
ð14:2Þ
where
l Longitudinal length of water chamber mass block;
q Density of water;
s a Static surface area of water chamber;
x Vertical displacement of water chamber.
From the above equation, there are
d
2 x
dt 2 ¼ g=l
ð Þx
ð14:3Þ
x 0 ¼
ffiffiffiffiffiffi ffi
g=l
p
ð14:4Þ
x ¼ x 0 ¼ 2p=T
ð14:5Þ
where
T Period of incident wave.
l ¼
gT
2
4p 2
ð14:6Þ
For example, if the incident wave period T = 6 s, the longitudinal length of the
mass block in the water chamber is l ¼ 8:95 M. When the period of incident wave
T ¼ 6 s and the water level h ¼ 8 m, the wavelength of incident wave is
k % 45:2 M. It can be concluded that l=k % 8:95=45:2 % 1=5. In this example, the
14.3 Mathematical Model of Oscillating Water Column
357