Wave
Spectrum
The wave spectrum is the term that
describes mathematically the distribution of wave energy with frequency and
direction. The wave spectrum consists of a
range of frequencies.
Remember that ocean waves are
composed
of a
multitude of sine
waves, each having a different frequency. For purposes
of explanation, these frequencies are
arranged in ascending order from left to right, ranging from the low-valued
frequencies on the left to the high-valued
frequencies on the right, as illustrated in figure 6-3.
A
particular
range of frequencies, for
instance, from 0.05 to 0.10 does not, however, represent only six different
frequencies of sine waves, but an infinite
number of sine waves whose frequencies range between 0.05 and 0.10. Each sine wave contains a certain amount of energy,
and the energy of all the sine waves added together is equal to the total energy
present in the ocean waves. The total
energy present in the ocean waves is not distributed equally throughout the
range of frequencies; instead, in every spectrum,
the energy is concentrated around a particular frequency (fmax), that
corresponds
to a certain wind speed. For instance, for
a wind speed of 10 knots (kt) fcnax is 0.248; for 20 kt, 0.124; for 30 kt,
0.0825; for 40 kt, 0.0619. For more
Figure 6-3.-A typical frequency range of a
wave spectrum.
information refer to the publication Practical
Methods for Observing and Forecasting Ocean Waves (H.O. Publication
603), which gives the complete range of fu
values and the corresponding periods for wind speeds, starting from 10 kt, at
2-kt intervals, Notice that the frequency
decreases as the wind speed increases, This suggests that the higher wind speeds
produce higher ocean waves. The table
mentioned above can be graphed for each wind speed, An example of such a graph
can also be found in H.O. publication 603.
It is difficult to work with actual energy
values of these sine waves; for this reason the square of the wave amplitude has
been
substituted for energy. This value is
proportional to wave energy.
The square of the wave amplitude plotted
against frequency for a single value of wind speed constitutes the spectrum of
waves. Thus, a graph of the spectrum is
needed for each wind speed, and the energy associated with each sine wave can be
determined from these graphs. Each wind
speed produces a particular spectrum; and the higher the wind speed, the larger
the spectrum.
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