Page 108 - Introduction to Naval Architecture
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THE ENVIRONMENT 95
Shapes of wave spectra
Even in deep water, a wave system will only become fully developed if
the duration and fetch are long enough. The wave components
produced first are those of shorter length, higher frequency. With time
the longer length components appear so that the shape of the
spectrum develops as in Figure 5.7. A similar progression would be
found for increasing wind speed. As the wind abates and the waves die
down, the spectrum reduces, the longer waves disappearing first
because they travel faster, leaving the storm area.
Figure 5.7 Developing spectra
The problem remains as to the shape a fully developed spectrum can
be expected to take for a given wind speed. Early formulae attempted
to define the spectrum purely in terms of wind speed and Pierson and
Moskowitz's formula is:
2
l
where g-and Fare in ms and ms units respectively, Vbeing the wind
speed.
The spectrum now most widely adopted is the Bretschneider spectrum.
This takes the form:
where A and B are constants.
When both the significant wave height £1 and the characteristic
period T } are known:
