Specifications
23
5.2 Measuring waves with Datawell buoys
5.2.1 Wave height
Waves at sea are the result of orbital motions of the water particles, characterized by their
frequency f, amplitude A and direction. The water forces at the hull of the buoy cause a mass
equal to the displaced water volume to follow the orbital motion. Since the mass of the buoy m
equals the mass of the displaced water volume, the buoy will follow the orbital motion as well.
Measuring the vertical motion of the buoy yields the wave height.
The high frequency response of the wave buoy is limited by the dimensions of the buoy.
For wavelengths smaller than the buoy’s circumference, the wave motion is not followed
anymore by the buoy. On the other side, the horizontal low frequency response is determined by
the combination of the buoy and the mooring. The mooring forces hinder the following of the
waves. The extra mooring force on the buoy in an orbit of amplitude A is
CAF
moor
= (5.2.1)
where C is the spring constant of the rubber cord in the horizontal direction. Introducing the
mass spring resonance frequency
m
C
f
π
2
1
0
= (5.2.2)
(m including the added mass of the buoy) and the wave forces being
AfmF
wave
2
)2(
π
= (5.2.3)
we find the ratio of the forces to be
2
0
2
)2(
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
==
f
f
Afm
CA
F
F
wave
moor
π
(5.2.4)
For wave frequencies higher than f
0
, the buoy rides the waves perfectly, whereas for wave
frequencies lower than f
0
the horizontal motion is hindered by the mooring forces. In case the
buoy does not follow the horizontal motion of the wave, the orbital energy will be spread over
different frequencies [Rad93].
5.2.2 Wave direction
Slope following directional wave buoys (like the Wavec) measure the wave direction from the
correlation between the buoy’s tilt angles (pitch and roll) and heave motion. This type of buoy
requires a disk shape that follows the slope of the wave at any water velocity. By proper design
the mooring force acts on the pivotal point of the buoy. In this way the mooring forces do not
affect the tilt of the buoy.
Measuring the direction of the waves by means of an orbital following buoy (like the
DWR-G and DWR-MkIII) requires the buoy to follow precisely the two dimensional horizontal
part of the orbital motions. Mooring forces cause the dynamic response tangent to the mooring
line to differ from the dynamic response normal to the mooring line. As a result, the direction of
motion of the buoy will deviate from the direction of motion of the water particles. To meet the
directional specifications a large resilience of the mooring line is required.
For further information on measuring waves Datawell suggests [Tuck01].